ap phys 1 equations

definition of acceleration

a=Δv/t

instantaneous velocity

vx=vo+at

displacement function

Δd=vot+1/2at^2

velocity no time

vx^2=vo^2+2aΔd

2nd law

a=F/m

friction

f=μN

centripetal acceleration

ac=v^2/r

momentum

p=mv

impulse

change in momentum

Δp=Ft

Δp=mΔv

linear kinetic energy

K=1/2mv^2

work-energy theorem

ΔE=W

work equation

W= Fdcosθ

power, general

P=ΔE/t

mechanical power

P=W/t

rotational displacement function

θ=θo+ωot+1/2αt^2

instantaneous rotational velocity

ω=ωo+αt

displacement for harmonic motion

x=Acos(2πft)

angular acceleration

α=Στ/I

net torque

Στ=Iα

torque & force

τ=rFsinθ

angular momentum

L=Iω

change in angular momentum

ΔL=τt

rotational kinetic energy

K=1/2Iω^2

Hooke's Law

Fs=kx

spring potential energy

elastic potential energy

Us=1/2kx^2

density

ρ=m/V

gravitational potential energy

ΔUg=mgΔy

period with angular velocity

T=2π/ω

period with frequency

T=1/f

period of a spring

Ts=2π√m/k

period of a pendulum

Tp=2π√l/g

universal gravitation

Fg=Gm1m2/r^2

weight

g=Fg/m

gravitational acceleration for any planet

g=GM/r^2

electrical force

force between charges

Fe=kq1q2/r^2

current in terms of charge

I=Δq/Δt

resistivity

R=ρl/A

Ohm's Law

I=V/R

electrical power

P=IV

resistance in series

Rs=R1+R2+…Rn

resistance in parallel

1/Rp=1/R1+1/R2+…1/Rn

wavespeed

λ=v/f

time to fall

t=√2h/g

x-component of velocity

vx=vocosθ

y-component of velocity

voy=vosinθ

net force for elevator

ΣF=Fs+-mg

weight parallel

W//=Wsinθ

weight perpendicular

W-I=Wcosθ

area under F vs. x graph

work

area under F vs. t graph

impulse

critical velocity at top of circle

v=√gr

maximum velocity on a road curve

v=√rμg

satellite velocity

v=√GM/r