|speed||distance travelled per unit time|
|scalar||quantity described by magnitude but not direction (time, area, volume)|
|displacement||distance and direction of an object's change in position from the starting point|
|acceleration||(physics) a rate of change of velocity|
|velocity||a measure of both the speed and direction of a moving object. V=∆x/∆t|
|Ohm's Law||RESISTANCE=VOLTAGE/CURRENT. V = I•R|
|Density||mass per unit of volume.ρ=m/V(unit : kg /m3 )|
|Friction||the resistance encountered when one body is moved in contact with another. FF = μ•FN|
|Torque||"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.|
|Beats||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
|Friction||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
|Density||mass/volume p= m/V|
|Torque||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|
|Work|| (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||T=mv^2/L|
|Projectile Motion|| Horizontal: x-xο= vο•t + 0|
Vertical: y-yο = vο•t + ½•a•t²
|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|
| 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|
|Magnification||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 JNm (Q₁Q₂/r), E = energy, Q = numeric ion charges, r = distance between centers|
|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 ...)**|
|Work done on a gas or by a gas||W = P•ΔV|
|Magnetic Field around a wire||B=μoI/2πr|
|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|
|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
|Thermodynamics||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|
|Refraction||( 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
|Torque|| τ = F•L•sin θ|
Where θ is the angle between F and L; unit: Nm
|Projectiles||•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.|
|Density|| 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||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.
|Force||•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.
|Equilibrium|| •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.
|•Lever||◦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|| •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.
|Work||•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.