505 terms

MCAT Physics Review

Combination of terms from other sets
ac current
(alternating current) the movement of electric charge periodically reverses direction
alpha decay
an alpha particle is lost (type of radioactive decay)
alpha particle
a helium nucleus (2 protons, 2 neutrons)
angular magnification
magnification expressed as the ratio of the angle α′ subtended at the eye by the image to the angle α subtended at the eye by the object
point on two waves with the same wavelength traveling in opposite direction where the movement is maximized; highest amplitude
atmospheric pressure
101,000 Pa
occur when two waves with slightly different frequencies are superimposed
beta decay
expulsion of an electron (type of radioactive decay)
bulk modulus
modulus for compression and expansion
buoyant force
(Fb) an upward force acting on a submerged object, and is equal to the weight of the fluid displaced by the submerged object
the ability to sore charge per unit voltage; a high capacitance means it can store a lot of charge at low voltage
chromatic dispersion
the dispersion of light; the phenomenon in which the phase velocity of a wave depends on its frequency
completely inelastic collisions
occur when objects stick together; lose some energy to internal energy
concave mirror
a mirror with a curved reflective surface that is bulging inward
conservative force
energy change is the same regardless of the path taken by the system; total work done is zero if the system moves from A to B and back to A
constructive interference
occurs when the sum of the displacements of waves results in a greater displacement
converging lens
a lens that acts like a convex mirror; larger at the middle
convex mirror
a mirror with a curved reflective surface that is bulging outward
critical angle
the angle of incidence above which total internal reflection occurs; angle at which light is reflected
dc current
(direct current) the unidirectional flow of electric charge
(p) the 'heaviness' of a fluid; mass/volume
density of water
1000 kg/m^3 aka 1 gm/cm^3
destructive interference
occurs when the sum of the displacements of waves results in a smaller displacement
dielectric constant, K
refers to the substance between the plates of a capacitor; the ratio of the capacitance of a capacitor in which a particular insulating material is the dielectric, to its capacitance in which a vacuum is the dielectric
when a wave disperses as it goes through a small hole
diverging lens
a lens that acts like a concave mirror; thin in the middle
elastic collisions
mechanical energy is conserved which means no energy is dissipated to internal energy
electric dipole
created by two opposite charges with equal magnitude
electron capture
capture of an electron along with the merging of that electron with a proton to create a neutron; a proton is destroyed and a neutron is created (type of radioactive decay)
(electromotive force) that which tends to cause current to flow; the voltage of electricity in a circuit
equipotential surfaces
points in an electric field that have the same voltage
first harmonic
(aka fundamental wavelength) - the longest wavelength in a harmonic series
the splitting of an single nucleus to form two lighter nuclei
a liquid or a gas
fluid pressure
pressure at some point within a fluid; results from the impulse of molecular collisions
focal length
a measure of how strongly the system converges (focuses) or diverges (defocuses) light
focal point
point at which initially collimated rays of light meet after passing through a convex lens, or reflecting from a concave mirror
the number of wavelengths that pass a fixed point in one second; measured in hertz (Hz), or cycles per second (1/s)
the combing of two nuclei to form a single heavier nucleus
gamma ray emission
when a gamma ray is given off; often accompanies other types of radioactive decay and does not change the identity of an element
harmonic series
the list of wavelengths from largest to smallest of the possible standing waves for a given situation; numbered from longest to shortest wavelength
transfer of energy by natural flow from warmer body to cooler body
hydraulic lift
a simple machine that works via Pascal's principle
ideal fluid
hypothetical fluid used to make calculations simple
(J) change in momentum
index of refraction
(n) compares the speed (c) of light in a vacuum to the speed (v) of light in a particular medium
a redistribution of electrical charge in an object, caused by the influence of nearby charges
inelastic collisions
lose some energy to internal energy
intensity (waves)
(I) the power of a wave
intensity level
(b) an intuitive scale of intensities based on the unit of decibels (dB)
Kirchoff's first rule
at any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node
Kirchoff's second rule
the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop
lateral magnification (m)
Magnification of a lens or of an optical system, expressed as the ratio of the size of the image h′ to the size of the object h
mass defect
when proton + neutrons + electrons combine, the atom they form has less mass than the sum of the masses of the protons + neutrons + electron on their own; the difference is lost as energy
mechanical energy
kinetic and potential energy of macroscopic systems
mechanical wave
waves that obey the laws of classical physics; require a medium through which to travel; ex: water droplets, slinky, sound, ocean waves
modulus of elasticity
(p) a measure of a moving object's tendency to continue along its present path
point on two waves with the same wavelength traveling in opposite directions where there is no movement; also where the two waves collide
nonconservative force
change in mechanical energy when work is done; ex: kinetic frictional forces and the pushing and pulling forces applied by animals
Ohm's law
V= iR
Pascal's Principle
pressure applied anywhere to an enclosed incompressible fluid will be distributed undiminished throughout that fluid; think of a hydraulic lift
(T) the reciprocal of frequency; the number of seconds required for one wavelength to pass a fixed point
relates to the wavelength, frequency, and place and time of origin; "a wave is either in or out of phase"
plane-polarized light
light that has only an electric field oriented in one direction
like an electron with a positive charge (type of anti-matter)
positron emission
expulsion of a positron (type of radioactive decay)
rate of energy transfer; J/s or watt (W)
power (lenses)
the degree to which a lens, mirror, or other optical system converges or diverges light
random translational motion
motion of a fluid that contributes to fluid pressure (as in a fluid at rest)
the quantitative measure of an object of a particular shape and size to resist the flow of charge; measured in ohms
resonant frequency
(aka natural frequency) frequency at which a standing wave will resonate; if an outside driving force is applied to a structure at the resonant frequency, the structure will experience maximum vibration velocities and maximum displacement amplitudes
rms value
found by taking the square of all the terms, then taking the average, and then taking the square root
second harmonic
the second longest wavelength in a harmonic created by adding another node
shear modulus
modulus for shear stress
simple harmonic motion
motion that creates a sinusoidal function in time
specific gravity
the density of that substance compared to the density of water
standing wave
(aka stationary wave) a wave that remains in a constant position; can occur because the medium is moiving in the opposite direction or two waves are moving in opposing directions
the fractional change in an object's shape; ratio of change in dimension compared to original dimension, so no units
force applied to an object divided by the area over which the force is applied
twisting force that will be clockwise or counterclockwise (at least on MCAT)
total internal reflection
an optical phenomenon that happens when a ray of light strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface
uniform translational motion
motion of a fluid as a whole; doesn't contribute to fluid pressure
Universal Law of Conservation of Charge
the universe has no net charge
(V) given in volts; it is the potential for work by an electric field in moving any charge from one point to another
the transfer of momentum and energy from one point to another
wave amplitude
(A) a wave's maximum displacement from zero; always positive!
measured from any point in the wave to the point where the wave begins to repeat itself
transfer of energy using force; measured in joules
Young's modulus
modulus for tensile stress (E)
longitudinal wave
transverse wave
a physical quantity with magnitude but no direction
a physical quantity with magnitude and direction
component vectors
two perpendicular vectors whose vector sum is equal to the original vector
Pythagorean Theorem
two common triangles
uniformly accelerated motion
motion with constant acceleration; both direction and magnitude of the acceleration must remain the same
three forces
1. gravitational
2. electromagnetic
3. contact
Newton's first law
law of inertia
Newton's second law
F = ma
Newton's third law
for every action there exists an equal and opposite reaction
number of full rotations per second (1/s)
centripetal force
force due to circular movement
no translational or angular acceleration; moving and rotating at a constant velocity
static equilibrium
equilibrium with a velocity of zero
dynamic equilibrium
equilibrium with constant, nonzero velocity
mechanical energy
the kinetic and potential energy of macroscopic systems
two types of energy transfer
1. work
2. heat
radioactive decay
atoms that spontaneously break apart
gamma ray
a high frequency photon that often accompanies the other decay types
the proton and neutron
gauge pressure
a measure of pressure compared to local atmospheric pressure; local air pressure is arbitrarily given a value of zero
four conditions of an ideal fluid
1. no viscosity
2. incompressible
3. no turbulence
4. irrotational flow
surface tension
phenomenon due to intermolecular forces; can cause a needle to "float" on water
three types of waves
1. mechanical
2. electromagnetic
3. matter
two aspects of the medium through which a wave travels that affects the velocity
1. elasticity (resistance to change in shape)
2. inertia (resistance to change in motion)
resonance (waves)
condition where the natural frequency and the driving frequency are equal
direction of electric fields
positive to negative
direction of gravitational fields
towards mass creating the field
used in a circuit to temporarily store energy in the form of separated charge (voltage)
direction of magnetic fields
north to south
electromagnetic wave
traveling oscillation of an electric and a magnetic field; ex: light
wavelengths of visible light

700 nM
Linear Motion, V, Vo, a, t
Linear Motion, Δx, Vo, a, t
Δx=V₀t+1/2 a a*t²
Linear Motion, V, Vo, a, x
Linear Motion, Δx, avg. V, t
∑F=ma, in newtons 1 N=1 kgg*m/s²
W=m*g, where g= 9.8 m/s²
F=Gm₁m₂/r², where G is the gravitational constant
Gravitational Constant
6.67E-11 N*m²/kg²
τ=rFsinθ, where θ=angle between r and F
Kinetic friction
f=μN, where N=normal force and μ=friction coefficient
Centripetal Force
W=Fdcosθ, measured in Joules, 1 J=1 N*m
P=W/t, measured in Watts, 1 watt=1 J/s
Kinetic Energy
KE=mv²/2, measured in Joules
Potential Energy
U=mgh, measured in joules
Specific Heat
Q=mcΔT; only where there is no phase change
Heat of Transformation
Q=mL, where L is the heat required to change phase of 1 kg of substance
P=F/A, in Pascals, 1 Pa=1 N/m²
Thermodynamic Work
First Law of Thermodynamics
ΔU=Q-W, where ΔU is change in internal energy.
Absolute Pressure of a Fluid
P=P₀+ρgh, where P₀ is pressure at the surface, h is depth of the point measured.
Pascal's Principle
Continuity Equation
Bernoulli's Equation
P₁+ρv₁²/2+ρgy₁=P₂+ρv₂²/2+ρgy₂, where P=absolute pressure, ρ=density, and y=height relative to reference height
Fundamental Unit of Charge
e=1.60E-19 C
Coulomb's Law
F=K q₁*q₂/r², magnitude of force between two charges
Electric Potential Energy
Electric Field
F=q₀E, where Force is acted upon charged particle in E, electric field
Electric Potential
V=W/q₀, W is work needed to move test charge
Magnetic Force
F=qvBsinθ, on moving charge q at angle θ relative to magnetic field B
right-hand rule
hand on plane with forefingers pointing B and thumb pointing qv, F will come out of palm
Magnetic Centripetal Force
F=qvB=mv²/r, for when qv is perpendicular to B
i=Δq/Δt, in Ampere, 1 A=1C/s
Force for Current-carrying Wire
F=iLBsinθ, for wire length L carrying i at angle θ to B
Ohm's Law
V=iR, where R is resistance
Power dissipation by Resistor
Resistors in Series
Resistors in Parallel
1/R=1/R₁+1/R₂+1/R₃+... V=V₁=V₂=...
C=Q/V, in Farads, 1 F=1C/V
Capacitors in Parallel
Capacitors in Series
Angular Frequency
ω=√(k/m)=√(g/L); k/m for spring, g/L for pendulum
Simple Harmonic Motion: acceleration
Simple Harmonic Motion: Linear Restoring Force
Speed of Wave
v=fλ, where λ=wavelength
Wave variable relationships
v=fλ=ω/k=λ/T; k=2π/λ, ω=2πf=2π/T
Sound Intensity
P=IA, where P=power, I=intensity, A=surface area
Sound Level
β=10log(I/I₀) where I₀=1E-12 W/m²
Beat Frequency
Doppler Effect
f=f₀(v±Vd)/(v±Vs), Vd is speed of detector, Vs is speed of source. + top - bottom for moving towards, - top + bottom for moving away
Speed of Light
c=fλ, c=3.00E8
m=-i/o, i is distance of image from mirror, o distance object from mirror
Snell's Law
n=c/v, n₁sinθ₁=n₂sinθ₂, where n is index of refraction
Exponential Decay
n=n₀e^(-λt), λ is decay constant
Decay Constant
λ=ln2/T, where T is half life
Photon Energy
E=hf, where h=6.626E-34 (Planck's constant)
distance travelled per unit time
quantity described by magnitude but not direction (time, area, volume)
distance and direction of an object's change in position from the starting point
(physics) a rate of change of velocity
a measure of both the speed and direction of a moving object. V=∆x/∆t
Ohm's Law
mass per unit of volume.ρ=m/V(unit : kg /m3 )
the resistance encountered when one body is moved in contact with another. FF = μ•FN
"rotational equivalent of force"; a force applied so as to cause an angular acceleration. τ = F•L•sin θ
Newton's Second Law
The acceleration produced by a net force on a body is directly proportional to the magntude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the body. Fnet = ΣFExt = m•a
rotational equilibrium
sum of all torques acting on an object is zero. No net angular acceleration.
Angular frequency
ω. equal to √(k/m) or , 2(pi)(f)
Anti node
The point of maximum displacement in a standing wave.
Periodic frequency resulting from the superposition of two waves that have slightly different frequencies. f(beat) = |f₁-f₂|
Constructive interference
Addition of two waves when the crest of one overlaps the crest of another, so that their individual effects add together. The result is a wave of increased amplitude.
Destructive interference
interference in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave. Must 180 degrees out of phase
Doppler effect
change in the apparent frequency of a wave as observer and source move toward or away from each other. Toward
Simple Pendulum
a hypothetical pendulum suspended by a weightless frictionless thread of constant length. f = 1/ T and T=2π(sqrt L/g)
Sinusoidal motion
Back and forth oscillatory motion corresponding to sound. x = A•cos(ω•t) = A•cos(2•π•f •t)
ω = angular frequency
f = frequency
2nd Law of Thermodynamics
The principle whereby every energy transfer or transformation increases the entropy of the universe. Ordered forms of energy are at least partly converted to heat, and in spontaneous reactions, the free energy of the system also decreases. ΔU = QAdded + WDone On - Qlost - WDone By
Force caused by a magnetic field
on a moving charge
F = q•v•B•sin θ
Potential Energy stored in a Capacitor
P = ½•C•V² An electronic device that can maintain an electrical charge for a period of time and is used to smooth out the flow of electrical current. Capacitors are often found in computer power supplies.
Magnetic Flux
Φ = B•A•cos θ
Heating a Solid, Liquid or Gas
Q = m•c•ΔT (no phase changes!)
Q = the heat added c = specific heat.
ΔT = temperature change, K
FF = μ•FN, the force that opposes the motion of one surface as it moves across another surface
Linear Momentum
An object's mass times its velocity. Measures the amount of motion in a straight line. momentum = p = m•v = mass • velocity
momentum is conserved in collisions
Center of Mass - point masses on a line
xcm = Σ(mx) / Mtotal
Angular Speed vs. Linear Speed
Linear speed = v = r•ω = r • angular speed
Pressure under Water
P = ρ•g•h
h = depth of water
ρ = density of water
Universal Gravitation
F=g(m1m2/r^2) G = 6.67 E-11 N m² / kg²
Mechanical Energy
PEGrav = P = m•g•h
KELinear = K = ½•m•v²
Impulse = Change in Momentum
F•Δt = Δ(m•v)
Snell's Law
n1•sin θ1 = n2•sin θ2
Index of Refraction
n = c / v
c = speed of light = 3 E+8 m/s
Ideal Gas Law
P•V = n•R•T
n = # of moles of gas
R = gas law constant
= 8.31 J / K mole., law that states the math relationship of pressure (P), volume (V), temperature (T), the gas constant (R), and the number of moles of a gas (n); PV=nRT.
Periodic Waves
v = f •λ
f = 1 / T T = period of wave
Constant-Acceleration Circular Motion
ω = ωο + α•t θ
θ−θο= ωο•t + ½•α•t² ω
ω2 = ωο
2 + 2•α•(θ−θο) t
θ−θο = ½•(ωο + ω)•t α
θ−θο = ω•t - ½•α•t² ωο
Constant-Acceleration Linear Motion
v = vο + a•t x
(x-xο) = vο•t + ½•a•t² v
v ² = vο² + 2•a• (x - xο) t
(x-xο) = ½•( vο + v) •t a
(x-xο) = v•t - ½•a•t² vο
mass/volume p= m/V
a force that causes rotation. τ = F•L•sin θ Where θ is the angle between F and L; unit: Nm
Newton's Second Law
Force equals mass times acceleration. Fnet = ΣFExt = m•a
(physics) a manifestation of energy F•D•cos θ
Where D is the distance moved and
θ is the angle between F and the
direction of motion,
unit : J
Buoyant Force - Buoyancy
FB = ρ•V•g = mDisplaced fluid•g = weightDisplaced fluid
ρ = density of the fluid
V = volume of fluid displaced
Ohm's Law
V = I•R
V = voltage applied
I = current
R = resistance
Resistance of a Wire
R = ρ•L / Ax
ρ = resistivity of wire material
L = length of the wire
Ax = cross-sectional area of the wire
Hooke's Law
F = k•x
Potential Energy of a spring
W = ½•k•x² = Work done on spring
Electric Power
P = I²•R = V ² / R = I•V
Speed of a Wave on a String
Projectile Motion
Horizontal: x-xο= vο•t + 0
Vertical: y-yο = vο•t + ½•a•t²
Centripetal Force
Kirchhoff's rules
Loop Rule: ΣAround any loop ΔVi = 0
Node Rule: Σat any node Ii = 0
Resistor's in series
Each resistor has the same current; differenct voltage drop. Total resistance = R1+R2+R3+. . .
Resistor's in parallel
1/Rₓ = 1/R₁ + 1/R₂ + 1/R₃ + etc. **When resistors are in parallel, the voltage drop is equal across the entire combination, i.e. Vₓ = V₁ = V₂ = V₃ = ...
Newton's Second Law and
Rotational Inertia
τ = torque = I•α
I = moment of inertia = m•r² (for a point mass
Resistance of a Wire
R = ρ•L / Ax
ρ = resistivity of wire material
L = length of the wire
Ax = cross-sectional area of the wire
Heat of a Phase Change
Q = m•L
L = Latent Heat of phase change
Hooke's Law
the distance of stretch or squeeze of an elastic material is directly proportional to the applied force F = k•x
Potential Energy of a spring
W = ½•k•x² = Work done on spring
Continuity of Fluid Flow
Ain•vin = Aout•vout A= Area
v = velocity
Thermal Expansion
The increase in volume of a substance due to an increase in temperature. Linear: ΔL = Lo•α•ΔT
Volume: ΔV = Vo•β•ΔT
Bernoulli's Equation
P + ρ•g•h + ½•ρ•v ² = constant
QVolume Flow Rate = A1•v1 = A2•v2 = constant
Rotational Kinetic Energy
KErotational = ½•I•ω2 = ½•I• (v / r)2
KErolling w/o slipping = ½•m•v2 + ½•I•ω2
Simple Harmonic Motion
vibration about an equilibrium position in which a restoring force is proportional to the displacement from equilibrium. T=2π(sqrt(m)/(k)) where k = spring constant
f = 1 / T = 1 / period
Banked Circular Tracks
v2 = r•g•tan θ
First Law of Thermodynamics
ΔU = QNet + WNet
Change in Internal Energy of a system =
+Net Heat added to the system
+Net Work done on the system
Flow of Heat through a Solid
ΔQ / Δt = k•A•ΔT / L
k = thermal conductivity
A = area of solid
L = thickness of solid
Potential Energy stored in a Capacitor
P = ½•C•V² RC Circuit formula (Charging)
Vc = Vcell•(1 − e− t / RC )
R•C = τ = time constant
Vcell - Vcapacitor − I•R = 0
Sinusoidal motion
x = A•cos(ω•t) = A•cos(2•π•f •t)
ω = angular frequency
f = frequency
Doppler Effect
When a source emitting a sound and a detector receiving the sound move relative to each other, the virtual frequency vf' detected is less than (distance increases) or greater (distance decreases) than the actual emitted frequency. f' = f(V±V(d))/(V±Vs)
2nd Law of Thermodynamics
The change in internal energy of a system is
ΔU = QAdded + WDone On - Qlost - WDone By
Thin Lens Equation
f=(p*q)/(p+q), 1/f=1/p+1/q, f=focal length p=object distance q=image distance
M = −Di / Do = −i / o = Hi / Ho, Dimensionless value denoted by m given by the equation: m = -i/o, where i is image height and o is object height. A negative m denotes an inverted image, whereas a positive m denotes an upright image.
Coulomb's Law
E=2.3110⁻¹⁹ J
Capacitors in parallel
Cₓ = C₁ + C₂ + C₃ + etc. **When capacitors are in parallel, the voltage drop is equal across the entire combination, i.e. Vₓ = V₁ = V₂ = V₃ = ...
Capacitors in series
1/Cₓ = 1/C₁ + 1/C₂ + 1/C₃ + etc. **Voltages sum when capacitors are in series (Vₓ = V₁ + V₂ + V₃ ...)₂ + V₃ ...)***
Work done on a gas or by a gas
W = P•ΔV
Magnetic Field around a wire
Magnetic Flux
Φ = B•A•cos θ
Force caused by a magnetic field
on a moving charge
F = q•v•B•sin θ
Entropy change at constant T
ΔS = Q / T
(Phase changes only: melting, boiling, freezing, etc)
Capacitance of a Capacitor
C = κ•εo•A / d
κ = dielectric constant
A = area of plates
d = distance between plates
εo = 8.85 E(-12) F/m
Induced Voltage
Voltage created by the combination of movement and a magnetic field. Emf=N(ΔΦ/Δt)
Lenz's Law
induced current flows to create a B-field
opposing the change in magnetic flux
Inductors during an increase in current
VL = Vcell•e− t / (L / R)
I = (Vcell/R)•[ 1 - e− t / (L / R) ]
L / R = τ = time constant
Decibel Scale
logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power or intensity) relative to a specified or implied reference level. B (Decibel level of sound) = 10 log ( I / Io )
I = intensity of sound
Io = intensity of softest audible sound
Poiseuille's Law
ΔP = 8•η•L•Q/(π•r4)
η = coefficient of viscosity
L = length of pipe
r = radius of pipe
Q = flow rate of fluid
Stress and Strain
Y or S or B = stress / strain
stress = F/A
Three kinds of strain: unit-less ratios
I. Linear: strain = ΔL / L
II. Shear: strain = Δx / L
III. Volume: strain = ΔV / V
Postulates of Special Relativity
1. Absolute, uniform motion cannot be
2. No energy or mass transfer can occur
at speeds faster than the speed of light
Lorentz Transformation Factor
β=sqrt 1-v^2/c^2
Quadratic Formula
Relativistic Time Dilation
Δt = Δto / β
Relativistic Length Contraction
Δx = β•Δxo
Relativistic Mass Increase
m = mo / β
Energy of a Photon or a Particle
E = h•f = m•c2
h = Planck's constant = 6.63 E(-34) J sec
f = frequency of the photon
Radioactive Decay Rate Law
A = Ao•e− k t = (1/2n)•A0 (after n half-lives)
Where k = (ln 2) / half-life
Blackbody Radiation and
the Photoelectric Effect
E= n•h•f where h = Planck's constant
de Broglie Matter Waves
For light: Ep = h•f = h•c / λ = p•c
Therefore, momentum: p = h / λ
Similarly for particles, p = m•v = h / λ,
so the matter wave's wavelength must be
λ = h / m v
Energy Released by Nuclear
Fission or Fusion Reaction
E = Δmo•c2
Translational motion
Motion of a particle fom point A to point B. x = x 0 + v 0 t + 1/2at2 and Vƒ = Vo + at
Momentum, Impulse
I = F Δt = ΔM and M=mv
Work, Power
W = F d cosθ and P = ΔW/Δt
Energy (conservation)
ET = Ek + Ep and E = mc2
Spring Force, Work
F = -kx and W = kx2 /2
Continuity (fluids)
A v = const. and ρAv = const.
Current and Resistance
I = Q/t and R = ρl/A
Kirchoff's Laws
Σi = 0 at a junction and
ΣΔV = 0 in a loop
Q = mc Δ T (MCAT !) and Q = mL
Torque forces
L1 = F1× r1 (CCW + ve) and L2 = F2 × r2 (CW -ve)
beta (β) particle
-1e0 (an electron);
Torque force at Equilibrium
ΣFx = 0 and ΣFy = 0
( sin θ1 )/(sin θ2 ) = v1 /v2 = n2 /n1 = λ1 /λ2 n = c/v
Bernouilli's Equation
Ρ + ρgh + 1/2 ρv2 = constant
Linear Expansion
L = L0 (1 + αΔ T )
Laplace's Law
dF = dq v(B sin α) = I dl(B sin α)
Doppler Effect: when d is decreasing use + vo and - vs
fo = fs (V ± vo )/( V ± vs )
Vector addition
•You can only directly add vectors if they are in the same direction.
•To add vectors in different directions, you must add their x, y and z components. The resulting components make up the added vector.
•The vector sum of all components of a vector equal to the vector itself.
•Operation involving a vector and a vector may or may not result in a vector (kinetic energy from the square of vector velocity results in scalar energy).
•Operation involving a vector and a scalar always results in a vector.
•Operation involving a scalar and a scalar always results in a scalar.
Speed, velocity (average and instantaneous)
•Speed: scalar, no direction, rate of change in distance.
•Velocity: vector, has direction, rate of change in displacement.
•Instantaneous speed is the speed at an instant (infinitesimal time interval).
•Instantaneous velocity is the velocity at an instant (infinitesimal time interval).
•Instantaneous speed equals instantaneous velocity in magnitude.
•Instantaneous velocity has a direction, instantaneous speed does not.
•The direction of instantaneous velocity is tangent to the path at that point Ave speed = distance / time = v = d/t
•Average acceleration:
◦Uniformly accelerated motion along a straight line
◦If acceleration is constant and there is no change in direction, all the following applies:
◦The value of speed/velocity, distance/displacement are interchangeable in this case, just keep a mental note of the direction. Ave acceleration = change in velocity / time
Friction Force
FF = μ•FN
If the object is not moving, you are dealing with static
friction and it can have any value from zero up to μs FN
If the object is sliding, then you are dealing with kinetic
friction and it will be constant and equal to μK FN
Freely falling bodies
•Free falling objects accelerate toward the ground at a constant velocity.
•On Earth, the rate of acceleration is g, which is 9.8 m/s2.
•Whenever something is in the air, it's in a free fall, even when it is being tossed upwards, downwards or at an angle.
•For things being tossed upwards, take all upward motion such as initial velocity as negative. Leave all
•The acceleration due to gravity is constant because the force (weight) and mass of the object is constant.
•However, if you take air resistance into consideration, the acceleration is no longer constant.
•The acceleration will decrease because the force (weight - friction) is decreasing due to increasing friction at high speeds.
•At terminal velocity, weight = friction, so the net force is 0. Thus, the acceleration is 0. So, the speed stays constant at terminal velocity
τ = F•L•sin θ
Where θ is the angle between F and L; unit: Nm
•Projectiles are free falling bodies.
•The vertical component of the projectile velocity is always accelerating toward the Earth at a rate of g.
•The vertical acceleration of g toward the Earth holds true at all times, even when the projectile is traveling up (it's decelerating on its way up, which is the same thing as accelerating down).
•There is no acceleration in the horizontal component. The horizontal component of velocity is constant.
•What is the time the projectile is in the air?
Ans: use the vertical component only- calculate the time it takes for the projectile to hit the ground.
•How far did the projectile travel?
Ans: first get the time in the air by the vertical component. Then use the horizontal component's speed x time of flight. (Don't even think about over-analyzing and try to calculate the parabolic path).
•When you toss something straight up and it comes down to where it started, the displacement, s, for the entire trip is
0. Initial velocity and acceleration are opposite in sign.
mass / volume
(unit : kg /m3 )
ρ = m/v
Orbiting in space
•Satellites orbiting the Earth are in free fall.
•Their centripetal acceleration equals the acceleration from the Earth's gravity.
•Even though they are accelerating toward the Earth, they never crash into the Earth's surface because the Earth is round (the surface curves away from the satellite at the same rate as the satellite falls).
Center of mass
The center of mass is the average distance, weighted by mass
•In a Cartesian coordinate, the center of mass is the point obtained by doing a weighted average for all the positions by their respective masses.
•The center of mass of the Earth and a chicken in space is going to be almost at the center of the Earth, because the chicken is tiny, and its coordinate is weighted so.
•The center of mass between two chickens in space is going to be right in the middle of the two chickens, because they're positions are weighted equally.
•You do not have to obtain the absolute coordinates when calculating the center of mass. You can set the point of reference anywhere and use relative coordinates.
•The center of mass for a sphere is at the center of the sphere.
•The center of mass of a donut is at the center of the donut (the hole). point masses on a line xcm = Σ(mx) / Mtotal
Newton's first law, inertia
The law of inertia basically states the following: without an external force acting on an object, nothing will change about that object in terms of speed and direction.
In the absence of an external force:
•Something at rest will remain at rest
•Something in motion will remain in motion with the same speed and direction.
•Objects are "inert" to changes in speed and direction.
Newton's second law (F = ma)
A net force acting on an object will cause that object to accelerate in the direction of the net force.
•The unit for force is the Newton.
•Both force and acceleration are vectors because they have a direction.
Newton's third law, forces equal and opposite
Every action has an equal and opposite reaction
Concept of a field
•For the purposes of the MCAT, fields are lines.
•When lines are close together, that's shows a strong field.
•When lines are far apart, that shows a weak field.
•Lines / fields have direction too, and that means they are vectors.
•Things travel parallel, perpendicular, or spiral to the field line.
Law of gravitation (F = Gm1m2/r^2)
•Gravity decreases with the square of the distance.
•If the distance increases two fold, gravity decreases by a factor of four.
•The "distance" is the distance from the center of mass between the two objects.
•Gravity is the weakest of the four universal forces.
•This weakness is reflected in the universal gravitational constant, G, which is orders of magnitude smaller than the Coulomb's constant.
Uniform circular motion
Memorize the equations:
a = v^2/r f= mv^2/r cir = 2TT*r •note that theta is always in radians. To convert degrees to radians, use this formula:
•The simple harmonic laws of frequency and period applies here also.
◦For displacements and distances that approach zero, the instantaneous velocity equals
the speed.
◦For a quarter around the circle (pi/4 radians or 45 degrees), the displacement is
the hypotenuse of a right-angled triangle with the radius as the other two sides. Using Pythagoras, the displacement is square root of 2r^2. The distance is the arc of 1/4 circumference.
velocity and displacement
•The velocity is always less or equal to the speed.
•The displacement is always less or equal to the distance.
•Displacement and velocity are vectors. Distance and speed are not.
•Moving around a circle at constant speed is also simple harmonic motion.
•frequency = how many times the object goes around the circle in one second.
•period = time it takes to move around the entire circle.
Centripetal Force (F=-mv2/r)
Centripetal force is due to centripetal acceleration. Centripetal acceleration is due to changes in velocity when going around a circle. The change in velocity is due to a constant change in direction. ◦Sometimes a negative sign is used for centripetal force to indicate that the direction of the force is toward the center of circle. •The direction of both the acceleration and the force is toward the center of the circle.
•The tension force in the string (attached to the object going in circles) is the same as the centripetal force.
•When the centripetal force is taken away (Such as when the string snaps), the object will fly off in a path tangent to the circle at the point of snap.
Weight is the force that acts on a mass
•Weight is a force. It has a magnitude and a direction. It is a vector.
•Because it is a force, F=ma holds true.
•Your weight on the surface of the Earth: F=mg, where g is the acceleration due to Earth, which is just under 10.
•You weigh more on an elevator accelerating up because F=mg + ma, where a is the acceleration of the elevator.
•An elevator accelerating up is the same thing as an elevator decelerating on its way down, in terms of the acceleration in F=mg + ma.
•You weigh less on an elevator accelerating down because F=mg - ma, where a is the acceleration of the elevator.
•An elevator accelerating down is the same thing as an elevator decelerating on its way up, in terms of the acceleration in F=mg - ma.
•You weight less when you are further away from the Earth because the force of gravity decreases with distance.
•However, you are not truly "weightless" when orbiting the Earth in space. You are simply falling toward the Earth at the same rate as your space craft.
•You gain weight as you fall from space to the surface of the earth.
•For a given mass, its weight on Earth is different from its weight on the Moon.
•When something is laying still on a horizontal surface, the normal force is equal and opposite to the weight.
•When something is laying still on an inclined plane, the normal force and friction force adds up in a vector fashion to equal the weight.
Friction, static and kinetic
Friction is a force that is always in the direction to impede motion •Like any other force, friction is a vector. However, its direction is easy because it's always opposite to motion.
•Static friction pertains to objects sitting still. An object can sit still on an inclined plane because of static friction.
•Kinetic friction pertains to objects in motion. A key sliding across the table eventually comes to a stop because of kinetic friction.
•Static friction is always larger than kinetic friction.
•The coefficient static friction is always larger than the coefficient of kinetic friction.
•The coefficient of friction is intrinsic to the material properties of the surface and the object, and is determined empirically.
•The normal force at a horizontal surface is equal to the weight
•The normal force at an inclined plane is equal to the weight times the cosine of the incline angle (see inclined planes).
•We can walk and cars can run because of friction.
•Lubricants reduce friction because they change surface properties and reduce the coefficient of friction.
•Every time there is friction, heat is produced as a by-product.
Motion on an inclined plane
•Gravity is divided into two components on an inclined plane.
◦One component is normal (perpendicular) to the plane surface: FN = mg·cosθ
◦The other component is parallel to the plane surface: F|| = mg·sinθ
•To prevent the object from crashing through the surface of the inclined plane, the surface provides a normal force that is equal and opposite to the normal component of gravity.
•Friction acts parallel to the plane surface and opposite to the direction of motion.
•In a non-moving object on an inclined plane: normal component of gravity = normal force; parallel component of gravity = static friction.
•Unless the object levitates or crashes through the inclined plane, the normal force always equals the normal component of gravity.
•In an object going down the inclined plane at constant velocity: parallel component of gravity = kinetic friction (yes, they're equal, don't make the mistake of thinking it's larger. Constant velocity = no acceleration = no net force).
•In an object that begins to slip on the inclined plane: parallel component of gravity > static friction.
•In an object that accelerates down the inclined plane: parallel component of gravity > kinetic friction.
•When you push an object up an inclined plane, you need to overcome both the parallel component of gravity and friction.
•When you push or pull an object up an inclined plane, make sure you divide that force into its components. Only the component parallel to the plane contributes to the motion.
Analysis of pulley systems
Pulleys reduce the force you need to lift an object. The catch - it increases the required pulling distance. •Complex pulleys will have additional ropes that contribute to the pulling of the load (most likely not tested on the MCAT).
•The distance of pulling increases by the same factor that the effort decreases.If the weight of the box is 100 N, you have to pull with a force of 100 N. For every 1 meter you pull, the box goes up 1 meter. When there is one moving pulley, the force needed to pull is halved because strings on both side of the pulley contribute equally. You supply 50 N (which is transmitted to the right-hand rope) while the left-hand rope contributes the other 50 N. Because effort here is halved, the distance required to pull the box is doubled.
•There are 4 universal four-ces... get it?
•Universal forces are also called fundamental forces.
•The four forces are:
◦The strong force: also called the nuclear force. It is the strongest of all four forces, but it only acts at subatomic distances. It binds nucleons together.
◦Electromagnetic force: about one order of magnitude weaker than the strong force, but it can act at observable distances. Binds atoms together. Allows magnets to stick to your refrigerators. It is responsible for the fact that you are not falling through your chair right now (MCAT people love to throw you quirky examples like this one).
◦Weak force: roughly 10 orders of magnitude weaker than the strong force. Responsible for radioactive decay.
◦Gravity: roughly 50 orders of magnitude weaker than the strong force. Responsible for weight (not mass!). Also, responsible for planet orbits.
•When something is in equilibrium, the vector sum of all forces acting on it = 0.
•Another way to put it: when something is in equilibrium, it is either at rest or moving at constant velocity.
•Yet another way to put it: when something is in equilibrium, there is no overall acceleration.
Concept of force, units
•Force makes things accelerate, change velocity or change direction.
•In the MCAT, a force is indicated by an arrow.
•The direction of the arrow is the direction of the force.
•The magnitude of the force is often labeled beside the arrow.
•F=ma, so the unit for the force is kg·m/s2
Translational equilibrium (Sum of Fi = 0)
•When things are at translational equilibrium, the vector sum of all forces = 0.
•Things at translational equilibrium either don't move, or is moving at a constant velocity.
•If an object is accelerating, it's not in equilibrium.
•Deceleration is acceleration in the opposite direction.
•At translational equilibrium:
◦An apple sitting still.
◦A car moving at constant velocity.
◦A skydiver at falling at terminal velocity.
•NOT at translational equilibrium:
◦An apple falling toward the Earth with an acceleration of g.
◦A car either accelerating or decelerating.
◦A skydiver before he or she reaches terminal velocity.
Rotational equilibrium (Sum of Torque = 0)
•When things are at rotational equilibrium, there the sum of all torques = 0.
•Conventionally, positive torques act counterclockwise, negative torques act clockwise.
•When things are at rotational equilibrium, they either don't rotate or they rotate at a constant rate (angular velocity, frequency).
•You cannot have rotational equilibrium if there is angular acceleration.
•Deceleration is acceleration in the opposite direction.
•At rotational equilibrium:
◦Equal weights on a balance.
◦Propeller spinning at a fixed frequency.
◦Asteroid rotating at a constant pace as it drifts in space.
•NOT at rotational equilibrium:
◦Unequal weights in a balance such that the balance is begins to tilt.
◦Propeller spinning faster and faster.
◦Propeller slowing down.
Analysis of forces acting on an object
•Draw force diagram (force vectors).
•Split the forces into x, y and z components (normal and parallel components for inclined planes).
•Add up all the force components.
•The resulting x, y and z components make up the net force acting on the object.
•Use Pythagoras theorem to get the magnitude of the net force from its components.
•Use trigonometry to get the angles.
Newton's first law, inertia
•The significance of Newton's first law on equilibrium is: things in equilibrium will remain in equilibrium unless acted on by an external force.
•The significance of Newton's first law on momentum is: things resist change in momentum because of inertia (try stopping a truck. It's not easy because it resists changes to its huge momentum).
Torques, lever arms
◦Torque is the angular equivalent of a force - it makes things rotate, have angular acceleration, change angular velocity and direction.
◦The convention is that positive torque makes things rotate anticlockwise and negative torque makes things rotate clockwise.
◦The lever arm consists of a lever (rigid rod) and a fulcrum (where the center of rotation occurs).
◦The torque is the same at all positions of the lever arm (both on the same side and on the other side of the fulcrum). ◦If you apply a force at a long distance from the fulcrum, you exert a greater force on a position closer to the fulcrum.
◦The catch: you need to move the lever arm through a longer distance.
•There are two kind of weightlessness - real and apparent.
◦Real weightlessness: when there is no net gravitational force acting on you. Either you are so far out in space that there's no objects around you for light-years away, or you are between two objects with equal gravitational forces that cancel each other out.
◦Apparent weightlessness: this is what we "weightlessness" really means when we see astronauts orbiting in space. The astronauts are falling toward the earth due to gravitational forces (weight), but they are falling at the same rate as their shuttle, so it appears that they are "weightless" inside the shuttle.
•Momentum = mv, where m is mass, v is velocity and the symbol for momentum is p. •Impulse = Ft, where F is force and t is the time interval that the force acts.
•Impulse = change in momentum:
•Conservation of linear momentum
◦Total momentum before = total momentum after.
◦Momentum is a vector, so be sure to assign one direction as positive and another as negative when adding individual momenta in calculating the total momentum.
◦The momentum of a bomb at rest = the vector sum of the momenta of all the shrapnel from the explosion.
◦Total momentum of 2 objects before a collision = total momentum of 2 objects after a collision
•Elastic collisions
◦Perfectly elastic collisions: conservation of both momentum and kinetic energy.
◦Conservation of kinetic energy: total kinetic energy before = total kinetic energy after.
◦Kinetic energy is scalar, so there are no positive / negative signs to worry about.
◦If you drop a ball and the ball bounces back to its original height - that's a perfectly elastic collision.
◦If you throw a ball at a wall and your ball bounces back with exactly the same speed as it was before it hit the wall - that's a perfectly elastic collision.
•Inelastic collisions
◦Conservation of momentum only.
◦Kinetic energy is lost during an inelastic collision.
◦Collisions in everyday life are inelastic to varying extents.
◦When things stick together after a collision, it is said to be a totally inelastic collision.
•W = Fdcosθ
•F is force, d is the distance over which the force is applied, and θ is the angle between the force and distance. •Derived units, sign conventions
◦Work is energy, and the unit is the Joule.
◦Joule = N·m = kg·m/s2·m = kg·m2/s2
◦If the force and the distance applied is in the same direction, work is positive.
◦For example, pushing a crate across a rough terrain involves you doing positive work (you are pushing forward and the crate is moving forward).
◦If the force and the distance applied is in opposite directions, work is negative.
◦Friction always does negative work because frictional forces always act against the direction of motion.
◦If the force is acting in one direction, but the object moves in a perpendicular direction, then no work is done.
◦The classic example is that no work is done by your arms when you carry a bucket of water for a mile. Because you are lifting the bucket vertically while its motion is horizontal.
◦If you like math, then everything you need to know is already contained in the mathematical formula. Cosine of 90 is zero; cosine of anything below 90 is positive and between 90-180 is negative ...so forth
•Amount of work done in gravitational field is path-independent
◦Unlike friction, gravity always acts downwards. Thus, it does not matter what detour you take because sideward motion perpendicular to the gravitational force involves no work.
◦Pushing an object at constant speed up a frictionless inclined plane involves the same amount of work as directly lifting the same object to the same height at constant speed.
◦Sliding down a frictionless inclined plane involves the same gravitational work as doing a free fall at the same height.
Vector quantity describing a change in velocity over the elapsed time for which that change occurs. a = Δv/Δt
Vector quantity describing the straight-line distance between an initial and a final position of some particle or object.
Quantity that has only a magnitude but no direction, ie speed.
Scalar quantity describing the distance traveled over the time required to travel that distance.
Quantity with both magnitude and direction: velocity, acceleration, force, momentum, etc.
Vector quantity describing an object's displacement over the elapsed time. v = Δx/Δt
Centripetal Acceleration
Acceleration of an object traveling in a circle with a constant speed, equal in magnitude to the velocity squared divided by the radius of the circle traversed (v²/r). Direction of the acceleration always points towards the center of the circle.
Vector quantity describing the push or pull on an object. SI unit for force is the Newton, N.
Friction Force
Antagonistic force that points parallel and opposite in direction to the (attempted) movement of an object expressed as the product of friction coefficient and the force normal, static, kinetic (Ff = µN) or angular (tanθ = µ).
Ubiquitous attractive force existing between any two objects, whose magnitude is directly proportional to the product of the two masses observed and inversely proportional to the square of their distance from each other. (F = G([m₁*m₂]/r²]) where G is the gravitational constant.
Scalar quantity used as a measure of an object's inertia.
Newton's First Law
A body at rest or constant velocity will remain so unless acted upon by an outside net force.
Newton's Second Law
Force = mass*acceleration. A net force acting on a body will have a net acceleration in the direction of the net force, proportional to the body's mass.
Newton's Third Law
If a body exerts a force (F) on another body, there will be an equal and opposite reaction (-F).
Normal Force
Perpendicular component of the force caused when two surfaces push against each other, denoted by Fn.
Rotational Equilibrium
State where the sum of the torques acting on a body is zero, giving it no net angular acceleration.
Magnitude of a force acting on a body times the perpendicular distance between the acting force and the axis of rotation, denoted by τ with the SI unit Nm (Newton meter). τ = radius*Force
Translational Equilibrium
State where the sum of the forces acting on an object is zero, giving it no net acceleration.
Force that measures the gravitational pull on an object, given as the product of the object's mass times its gravitational acceleration (mg, where g(Earth) = 9.8m/s²).
Center of Gravity
Point on some object or body at which the entire force of gravity is considered to act on the object.
Center of Mass
The point on some object/body at which all of its mass is considered to be concentrated.
Completely Elastic Collision
Type of collision in which both momentum and kinetic energy are conserved. The sum of initial and final kinetic energies in a collision are equal. (initial) m₁v₁ + m₂v₂ = (final) m₁v₁ + m₂v₂
Completely Inelastic Collision
Type of collision in which the two bodies stick together after colliding, resulting in a single final mass and velocity. Momentum is conserved, Kinetic Energy is not. m₁v₁ + m₂v₂ = (m₁+m₂)vf
Conservation of Mechanical Energy
When only conservative forces act on an object and work is done, energy is conserved and described by the equation: ΔE = ΔKE + ΔPE = 0
Conservation of Momentum
Momentum of a system remains constant when there are no net external forces acting on it.
Conservative Force
A force, such as gravity, that performs work over a distance that is independent of the path taken.
Often denoted by 'j,' it is the change in momentum, given by Δp
Kinetic Energy
Energy of an object in motion, calculated by the equation KE = 1/2mv² given in the SI unit Joules (J)
Often denoted as p, it is a vector quantity, as the product of an object's mass and velocity. p = mv
Nonconservative Force
A force, like friction, that performs work over a distance that is dependent on the path taken between the initial and final positions.
Potential Energy
Energy of an object due to its height of ground level. PE = mgh
Rate at which work is doen, given by the equation. P = W/Δt
Quantity measured when a constant force acts on a body to move it a distance d. Calculated as W = Fdcosθ, cosθ indicates the component force parallel to motion direction.
Work-Energy Theorem
Theorem stating that net work performed on an object is related to the change in kinetic energy of that body. W = ΔKE
Unit of heat (C), 10³ calories (c), 4184 Joules.
Form of heat transfer where heat energy is directly transferred between molecules through molecular collisions or direct contact.
Heat transfer applying to fluids (liquids and gases) where heated material transfers energy by bulk flow and physical motion.
First Law of Thermodynamics
Change in internal energy of a system (ΔU) is equal to the heat (Q) transferred into the system minus the energy lost by the system when it performs work (W). ΔU = Q - W
Heat of Fusion
Heat of transformation corresponding to a phase change from either solid to liquid or liquid to solid.
Heat of Transformation
Amount of heat required to change the phase of a substance, calculated by (substance mass)*(substance's heat of transformation) q = mL.
Heat of Vaporization
Heat of transformation corresponding to a phase change from liquid to gas or gas to liquid.
Most commonly used temperature scale (SI units), ranges up from absolute zero. Tk = Tc +273
Force per unit area : F/A
Heat transfer by electromagnetic waves, which can travel through a vacuum.
Second Law of Thermodynamics
When a thermodynamic process moves a system from one state of equilibrium to another, the entropy (S) of that system combined with that of its surroundings will either increase or remain unchanged; irreversible processes will increase entropy, reversible processes will leave entropy unchanged.
Measure of heat content that a body possesses, measured in Kelvin, Celsius or Fahrenheit.
Thermal Expansion
Expansion of a solid as a result of increasing temperatures. ΔL = αLΔT. L = Length, α = coefficient of linear expansion, T = temperature.
Study of heat transfer and its effects.
Volume Expansion
Expansion in volume of a liquid as a result of increasing temperatures, calculated by ΔV = ßVΔT. V = volume, ß = coefficient of volume expansion, T = temperature.
Absolute Pressure
Pressure below the surface of a liquid that depends on gravity and surface pressure, calculated by P = P₀ + ρgz. P = Absolute pressure. z is depth. P₀ is the surface pressure. ρ = is the density.
Type of attractive force that molecules of a liquid feel toward molecules of another substance, such as in the adhesion of water droplets to a glass surface.
Archimedes' Principle
Body that is fully or partially immersed in a liquid will be buoyed up by a force that is equal to the weight of the liquid displaced by the body. F(buoyant) = ρ(liq)*g*V(liq) = ρ(obj)ggy that is fully or partially immersed in a liquid will be buoyed up by a force that is equal to the weight of the liquid displaced by the body. F(buoyant) = ρ(liq)*g*V(liq) = ρ(obj)*g*V(obj). V(obj) = is the volume of the object submerged.
Bernoulli's Equation
Equation describing the conservation of energy in fluid flow, given by P₁ + (1/2)ρV₁² + ρgy₁ + P₂ + (1/2)ρv₂² + ρgy₂.
Bulk Modulus
A term that describes a fluid's resistance to compression under a pressure, denoted by B and measured by the ratio of stress (pressure change) to strain: ΔP/(ΔV/V)
Type of attractive force felt by liquid molecules toward each other. Cohesion is responsible for surface tension.
Continuity Equation
Equation following the law that the mass flow rate of fluid must remain constant from one cross-section of a tube to another, given by A₁V₁ = A₂V₂
Scalar quantity defined as the mass per unit volume, often denoted by ρ.
Gauge Pressure
Pressure above the atmospheric pressure, given only by ρgz; the difference between P(absolute) and P₀
Laminar Flow
Simplest type of liquid flow through a tube where thin layers of liquid slide over one another, occurring as long as the flow rate remains below a critical velocity Vc
Pascal's Principle
Principle stating that when a pressure is applied to one point of an enclosed fluid, that pressure is transmitted in equal magnitude to all points within that fluid and to the walls of its container. This principle forms the basis of the hydraulic lift.
Shear Modulus
Term describing a solid's resistance to shear stress, denoted by S and measured by the ratio of shear stress (F/A) to strain (x/h). Results when a force is applied parallel to the surface area.
Specific Gravity
Dimensionless quantity given by the density of a substance divided by the density of water, where ρ(water) = 1g/ml, or 1g/cm³. ρ(x)/ρ(water)
Lines that trace the path of water particles as they flow in a tube without ever crossing each other.
Turbulent Flow
Type of liquid flow that occurs when the flow rate in a tube exceeds Vc. Motion of the fluid that is not adjacent to the container walls is highly irregular, forming vortices and a high flow resistance.
Measure of internal friction in a fluid, often denoted by µ
Young's Modulus
Term used in characterizing the elasticity of a solid, denoted by Y and measured by the ratio of the stress (F/A) to strain (ΔL/L). Results when force is applied perpendicular to the surface area.
SI unit of electric charge, denoted as C
Coulomb's Law
Law describing the electrostatic force that exists between two charges, q₁ and q₂, given as F(coul) = (kq₁q₂)/r²
Dipole Moment
Vector quantity resulting from an electric dipole, equal to the product of the charge magnitude q and the distance separating the two charges d, often denoted by p.
Electric Dipole
Result of having two charges of opposite sign and equal magnitude separated by a short distance d.
Electric Field
Electrostatic force that a source charge qs would exert on a positive test charge q₀ within its proximity divided by that test charge; E = F(coul)/q₀
Electric Field Lines
Imaginary lines that show the direction in which a positive test charge is accelerated by the coulombic force due to the electric field of a source charge.
Electric Potential
Amount of electric potential energy per unit charge; the work required to bring a positive test charge q₀ from infinity to within an electric field of another positive source charge Q, divided by that test charge, calculated by the equation V = (kQ)/r
Electric Potential Energy
Amount of work required to bring a test charge q₀ from infinity to a point within the electric field of some source charge Q, given by the equation EPE = q₀V
Study of electric charges at rest or in motion and the forces between them.
Equipotential Lines
Concentric circles emanating from a source charge that cross its electric field lines perpendicularly. No work is required for a test charge to travel along the circumference of one of these since the potential at every point along that line is the same.
Fundamental Unit of Charge
Smallest measured electric charge, belonging to an electron. -1.6 X 10⁻¹⁹C
Potential Difference
Also called Voltage (ΔV). Difference in electric potential between two points in an electric field
Flow of charge as it moves across a potential difference (voltage), denoted as I and measured by the amount of charge passing through a conductor over a unit of time: Δq/Δt
Diamagnetic Material
Material whose atoms have no net magnetic field. The material is therefore repelled from the pole of a magnet.
Ferromagnetic Material
Material whose atoms have net magnetic field and, below a critical temperature, are strongly attracted to a magnet pole.
Loop-Wire Magnetic Field
Magnetic field produced at the center of a circular loop of current-carrying wire, with a radius of r, calculated by: B = µ₀i/2r
Magnetic Field
Field Vectors created by moving charges and permanent magnets that in turn exert a magnetic force on moving charges and current-carrying wires.
Magnetic Force
Force exerted on a charged particle moving through a magnetic field, calculated using the equation, F(B) = qvBsinθ, where the angle denotes that only charges moving perpendicular to the magnetic field experience a force.
Magnetic Force on Current-Carrying Wire
Equation used to measure the force exerted on a current-carrying wire, due to a magnetic field, given by F = I L Bsinθ. I = current, L = length of the wire, B = magnitude of the magnetic field, θ = angle at which the wire intersects B-Field vectors.
Paramagnetic Material
Material whose atoms have a net magnetic field; under conditions that allow the alignment of the individual magnetic fields, the material exhibits an attraction toward the pole of a magnet.
Permeability of Free Space, µ₀
Term denoted by µ₀ and equal to 4∏ X 10⁻⁷. Tesla meter/ampere; used in the equation measuring the magnetic field produced by a current-carrying wire, B = µ₀I/2∏r.
Right Hand Rule
Common method used to determine the direction of the magnetic force vector. Thumb points in the direction of charge's velocity, fingers point in direction of magnetic (B) field, palm points in the direction of the acting force.
Straight-Wire Magnetic Field
Magnetic field produced at a perpendicular distance r, from a straight current-carrying wire, calculated by: B = µ₀i/2∏r
Alternating Current
Current that flows through a conductor in two directions that are periodically altered.
Measure of a capacitor's ability to store charge, calculated by the ratio of the magnitude of charge on one plate to the voltage across the two plates, expressed in SI units, farads.
Electric device used in circuits that is composed of two conducting plates separated by a short distance and works to store electric charge.
Material in which electrons can move with relative ease.
Insulating material placed between the two plates of a capacitor. If the circuit is plugged into a current source, more charge will be stored in the capacitor. If the circuit is not plugged into a current source, the voltage of the capacitor will decrease.
Dielectric Constant
Dimensionless number that indicates the factor by which capacitance is increased when a dielectric is placed in between the plates of a capacitor, given by C' = KC, where C' is the new capacitance.
Direct Current
Current that flows through a conductor in one direction only.
Electric Circuit
A conducting pathway that contains one or more voltage sources that drive an electric current along that pathway and through connected passive circuit elements, such as resistors.
Electromotive Force
Energy gained by an electron when it is accelerated through a potential difference of 1 volt, given by qV where q is 1.6 x 10⁻¹⁹ C and V is 1 volt.
Electron Volt
Voltage created by a potential difference between the two terminals of a cell when no current is flowing.
Material in which electrons cannot move freely.
Kirchhoff's Laws
A.) In accordance with the conservation of electric charge, the sum of currents directed into a node or junction point in a circuit equals the sum of the currents directed away from that point. B) Sum of the voltage sources in a circuit loop is equal to the sum of voltage drops along that loop.
Ohm's Law
Law stating that the voltage drop across a resistor is proportional to the current flowing through it, given by V = IR
Permittivity of Free Space
ε₀. Used in the calculation of capacitance, given by the equation C = ε₀A/d. A = area of one plate. d = distance between the plates.
Power Dissipated by Resistor
Rate at which the energy of flowing charges through a resistor is dissipated given by the equation P = IV
Natural tendency of a conductor to block current flow to a certain extent resulting in loss of energy or potential. Resistance is equal to the ratio of the voltage applied to the resulting current.
Intrinsic property of a conductor denoted by ρ used to measure its resistance in the equation R = ρ L/A. L = length of the conductor, A = cross-sectional area.
RMS Current
Quantity used to calculate the average dissipated in an AC circuit, given by I(max)/(√2). Must be used because the average current, when calculated conventionally, equals zero as a result of the periodic nature of that current.
RMS Voltage
V(max)/(√2); average voltage in an AC circuit, where voltage alternates in a sinusoidal pattern.
Point of maximum displacement from the equilibrium position.
Angular Frequency
ω. equal to √(k/m)
Point of maximum displacement in a standing wave.
Periodic frequency resulting from the superposition of two waves that have slightly different frequencies. f(beat) = |f₁-f₂|
Constructive Interference
When two overlapping waves are in phase and their amplitudes add together.
Destructive Interference
When two overlapping waves are out of phase, they subtract and cancel each other out if they have the same amplitude and are 180˚ out of phase
Doppler Effect
When a source emitting a sound and a detector receiving the sound move relative to each other, the virtual frequency vf' detected is less than (distance increases) or greater (distance decreases) than the actual emitted frequency. f' = f(V±V(d))/(V±Vs)
Number of cycles per second measured in SI units of Hz, where 1 Hz = 1 cycle/second
Fundamental Frequency
Lowest frequency a standing wave can support, given by f = nv/2L for strings fixed at both ends, f = nv/4L for pipes open at one end, n = 1 when pipes are closed at one end; first harmonic.
Harmonic Series
All the possible frequencies a standing wave can support.
Hook's Law
Equation describing the restoring force of a mass-spring system, given by F = -kx, where x is the displacement from the equilibrium position.
Power transmitted per unit area, given by P = IA. I = Intensity, A = Area, P = Power.
Longitudinal Wave
Type of wave, such as sound, whose oscillation is along the direction of its motion.
Point of zero displacement in a wave.
Number of seconds it takes to complete one cycle, denoted by T; the inverse value of frequency.
Phase Difference
Angle by which the sine curve of one wave leads or lags the sine curve of another wave.
If a standing wave undergoes a forced oscillation due to an external periodic force that has a frequency equal to the natural frequency of the oscillating system, the amplitude will reach a maximum.
Simple Harmonic Motion
Motion of an object oscillating back and forth about some equilibrium point when it is subject to an elastic linear restoring force.
Sound Level
A quantity measured in decibels (dB) and denoted by ß. Given by ß = 10logI/I₀. I₀ = reference intensity of 10⁻¹²W/m².
Spring Constant
A measure of a spring's stiffness, denoted by k.
Transverse Wave
Type of wave, such as light, whose oscillation is perpendicular to its direction of motion.
Quantity Equal to the distance between any two equivalent consecutive points along a wave, such as two consecutive crest peaks, expressed as λ.
Wave Speed
Speed of a wave, related to the frequency and wavelength. v = fλ
Converging Lens
Lens with a thick center that converges light rays at a point where the image is formed.
Converging Mirror
Concave mirror with a positive focal length.
Spreading-out effect of light when it passes through a small slit opening.
Phenomenon observed when white light is incident on the face of a prism and emerges on the opposite side with all its wavelengths split apart. Occurs because λ is related to the index of refraction by the expression n = c/fλ. Therefore a small λ has a large n and, in turn, a small angle of refraction (θ₂)
Diverging Lens
Lens with a thin center that diverges light after refraction and always forms a virtual image.
Diverging Mirror
Convex mirror with a negative focal length. Diverging mirrors always produce virtual images.
Electromagnetic Spectrum
Full range of frequencies and wavelengths for electromagnetic waves broken down into the following region, in order of descending/decreasing λ: radio, infrared, visible light, ultraviolet, X-ray, Gamma Ray.
Electromagnetic Waves
When a magnetic field is changing, it causes a change in an electric field and vice versa, resulting in the propagation of a transverse wave containing a magnetic and an electric field that are perpendicular to each other.
Focal Length
Distance between the focal point and the mirror or lens. For spherical mirrors, focal length is equal to one-half the radius of curvature.
Index of Refraction
Ratio of the speed of light in a vacuum to the speed of light through a medium, given by: n = c/v; factor by which the c is reduced as light travels from a vacuum into another medium.
When superimposed light waves are in phase, their amplitudes add (constructive interference) and the appearance is brighter. When superimposed light waves are out of phase, their amplitudes subtract (destructive interference) and the appearance is darker.
Law of Reflection
Law stating that when light waves strike a medium, the angle of incidence θi is equal to the angle of reflection θr
Dimensionless value denoted by m given by the equation: m = -i/o, where i is image height and o is object height. A negative m denotes an inverted image, whereas a positive m denotes an upright image.
Plane Mirror
Mirror in which incident light rays remain parallel after reflection, always producing a virtual image that appears to be the same distance behind the mirror as the object is in front of the mirror.
Plane-Polarized Light
Light that has been passed through a polarizing filter, allowing only the transmission of waves containing electric field vectors parallel to the lines of the filter.
Real Image
An image produced at a point where the light rays actually converge or pass through. For mirrors, this would be on the side of the object, for lenses, it would be on the opposite side of the object.
Snell's Law
Equation describing the angle of refraction for a light ray passing from one medium to another, given by n₁sinθ₁ = n₂sinθ₂, where n is the index of refraction.
Speed of Light
Speed of electromagnetic waves traveling through a vacuum, given by the equation c = λf = constant equal to 3.00 x 10⁸m/s
Spherical Mirror
Curved mirror that is essentially a small, cut-out portion of a sphere mirror, having a center of curvature C and a radius of curvature r.
Total Internal Reflection
Condition in which the θ₁ of light traveling from a medium with a high n to a medium with a low n is greater than the critical angle θc resulting in all of the light being reflected with none being refracted.
Virtual Image
An image produced at a point where light does not actually pass or converge. For mirrors, this would be the opposite side of the object; for lenses, it would be on the same side as the object.
Phenomenon observed when an atom is excited by UV light and the electrons return to the ground state in two or more steps, emitting photons of lower frequency (often in the visible light spectrum) at each step.
Photoelectric Effect
Phenomenon observed when light of a certain frequency is incident on a sheet of metal and causes it to emit an electron.
Work Function
Minimum amount of photon energy required to emit an electron from a certain metal. This quantity, denoted by W, is used to calculate the residual kinetic energy of an electron emitted by a metal, given by KE = hf - W. hf is the energy of a photon,
Alpha Decay
Nuclear reaction in which an α-particle (⁴₂He) is emitted.
Beta Decay
Nuclear reaction in which a ß-particle (e⁻) is emitted.
Binding Energy
Energy that holds the protons and neutrons together in the nucleus, defined by the equation E = mc². m = mass defect, c = speed of light in a vacuum.
Electron Capture
Radioactive process in which a nucleus captures an inner-shell electron that combines with a proton to form a neutron. As a result, the atomic number decreases by 1, but the atomic mass remains the same.
Exponential Decay
A decrease in the amount of substance N, given by: N = N₀ x e^(-λt)
Nuclear reaction in which a large nucleus splits up into smaller nuclei.
Nuclear reaction in which two or more small nuclei combine to form a larger nucleus.
Gamma Decay
Atomic emission of high energy photons, aka γ-particles.
Amount of time it takes for one-half of a radioactive sample to decay, given by the equation T1/2 = ln2/λ. λ = decay constant.
Mass Defect
Difference between an atom's atomic mass and the sum of its protons and neutrons.
An anti-electron, denoted ß+ or e+, emitted in a nuclear reaction.