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MCAT Physics Equations, Important

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Linear Motion, V, Vo, a, t
V=V₀+at
Linear Motion, Δx, Vo, a, t
Δx=V₀t+1/2 a a*t²
Linear Motion, V, Vo, a, x
V²=V₀²+2aΔx
Linear Motion, Δx, avg. V, t
Δx=avgVt=t*(V₀+V)/2
Force
∑F=ma, in newtons 1 N=1 kgg*m/s²
Weight
W=m*g, where g= 9.8 m/s²
Gravity
F=Gm₁m₂/r², where G is the gravitational constant
Gravitational Constant
6.67E-11 N*m²/kg²
Torque
τ=rFsinθ, where θ=angle between r and F
Kinetic friction
f=μN, where N=normal force and μ=friction coefficient
Centripetal Force
F=ma=mv²/r
Work
W=Fdcosθ, measured in Joules, 1 J=1 N*m
Power
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
Momentum
p=mv
Impulse
J=F*t=Δp
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
Pressure
P=F/A, in Pascals, 1 Pa=1 N/m²
Thermodynamic Work
W=PΔV
First Law of Thermodynamics
ΔU=Q-W, where ΔU is change in internal energy.
Density
ρ=m/v
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
ΔP=F₁/A₁=F₂/A₂
V=A₁d₁=A₂d₂
W=F₁d₁=F₂d₂
Continuity Equation
v₁A₁=v₂A₂
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
U=kqQ/r
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
Current
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
P=iV=i²R=V²/R
Resistors in Series
R=R₁+R₂+R₃+...
Resistors in Parallel
1/R=1/R₁+1/R₂+1/R₃+... V=V₁=V₂=...
Capacitance
C=Q/V, in Farads, 1 F=1C/V
Capacitors in Parallel
C=C₁+C₂+C₃+...
Capacitors in Series
1/C=1/C₁+1/C₂+...
Angular Frequency
ω=√(k/m)=√(g/L); k/m for spring, g/L for pendulum
Simple Harmonic Motion: acceleration
a=-ω²x
Simple Harmonic Motion: Linear Restoring Force
F=-kx
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
f=|f₁-f₂|
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
Magnification
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)