AP Physics C Equations

Kinematics for final velocity

v=v₀+at

Kinematics for final position

x=x₀+v₀t+½at²

Kinematics for final velocity squared

v²=v₀²+2a(x-x₀)

Net force

∑F=Fnet=ma

Power-force differential

F=dP/dt

Impulse

J=∫Fdt=∆p

Momentum

p=mv

Friction

Ffric≤µN

Work integral

W=∫F·dr

Kinetic Energy

K=½mv²

Power-work differential

P=dW/dt

Power dot product

P=F·v

Gravitational Potential Energy

∆Ug=mgh

Centripetal acceleration

ac=v²/r=ω²r

Torque

τ=r×F

Net torque

Στ=τnet=Iα

Rotational Inertia

I=∫r²dm=∑mr²

Center of mass

rcm=∑mr/∑m

Translational velocity

v=rω

Angular momentum

L=r×p=Iω

Rotational kinetic energy

K=½Iω²

Rotational kinematics for final velocity

ω=ω₀+αt

Rotational kinematics for final position

θ=θ₀+ω₀t+½αt²

Hooke's law

Fs=-kx

Elastic Potential Energy

Us=½kx²

General period

T=2π/ω=1/ƒ

Period of spring

Ts=2π√(m/k)

Period of pendulum

Tp=2π√(l/g)

Gravitation force

Fg=-(Gm₁m₂/r²)∧r

General gravitational potential energy

Ug=-Gm₁m₂/r

Coulomb's Law

F=(1/(4πε₀))(q₁q₂/r)

Electric Field

E=F/q

Charge-line integral

∮E·dA=Q/ε₀

Differential for electric field

E=-dV/dr

Electric potential

V=(1/(4πε₀))∑i(qi/ri)

Electric potential energy

UE=qV=(1/(4πε₀)(q₁q₂/r)

Capacitance-charge

C=Q/V

Capacitance-dielectric

C=κε₀A/d

Parallel capacitance

Cp=∑iCi

Capacitance in series

1/Cs=∑i1/Ci

Differential current

I=dQ/dt

Capacitance potential energy

Uc=½QV=½CV²

Resistance

R=ρl/A

Electric Field-resistivity

E=ρJ

Current

I=NevA

Electric Potential-simplified

V=IR

Resistance in series

Rs=∑iRi

Resistance in parallel

1/Rp=∑i1/Ri

Power-EM

P=IV

Magnetic force

Fm=qv×B

Ampere's Law

∮B·dl=µ₀I

Biot-Savart Law

dB=(µ₀/(4π))(Idl×r/r³)

Force magnetic field

F=∫I dl × B

Magnetic field series

Bs=µ₀nI