AP Physics 1 Formulas

Acceleration

a=(vf-vi)/t

acceleration = change in velocity / time

Instantaneous Velocity

vx=vi+at

velocity at position x = initial velocity + acceleration * time

Displacement

Δd=vit+1/2at^2

distance from beginning = initial velocity * time + 1/2 acceleration * time squared

Velocity (Displacement)

vx^2=vi^2+2aΔd

velocity at position x squared = initial velocity squared + 2 * acceleration * displacement

Newton's 2nd law

a=F/m

acceleration = force / mass

Friction

f=μN

friction = coefficient of friction * newtons

Acceleration (Centripetal)

ac=v^2/r

centripetal acceleration = velocity squared / radius

Momentum

p=mv

momentum = mass * velocity

Impulse (Change in Momentum)

Δp=mΔv

Δp=Ft

change in momentum = mass * change in velocity

change in momentum = force * time

Kinetic Energy (Linear)

K=1/2mv^2

kinetic energy = 1/2 mass * velocity squared

Work-Energy Theorem

W=ΔE

work = change in energy

Work

W= Fdcosθ

work = force * distance * cosine angle

Work

w=ΣFd

work = net force * distance

Power

P=ΔE/t

power = change in energy / time

Mechanical Power

P=W/t

power = work / time

Rotational Displacement

θ=θi+ωit+1/2αt^2

angle of rotational displacement = initial angle + initial angular velocity * time + 1/2 acceleration * time squared

Instantaneous Rotational Velocity

ω=ωi+αt

angular velocity = initial angular velocity + acceleration * time

Displacement for Harmonic Motion

x=Acos(2πft)

position x = amplitude * cosine (2π * frequency * time)

Angular Acceleration

α=Στ/I

angular acceleration = net torque / rotational inertia

Net Torque

Στ=Iα

net torque = length * angular acceleration

Torque & Force

τ=rFsinθ

torque = radius * force * sine angle

Angular Momentum

L=Iω

angular momentum = length * angular velocity

Change in Angular Momentum

ΔL=τt

change in angular momentum = torque * time

Kinetic Energy (Rotational)

K=1/2Iω^2

kinetic energy = 1/2 length * angular velocity squared

Hooke's Law

Fs=kx

spring force = spring constant * position x

Elastic Potential Energy (Spring)

Us=1/2kx^2

spring potential energy = 1/2 spring constant * position x squared

Density

ρ=m/V

density = mass / volume

Potential Energy (Gravitational)

ΔUg=mgΔy

change in gravitational potential energy = mass * gravity * change in height (position y)

Period (Angular Velocity)

T=2π/ω

period = 2π / angular velocity

Period (Frequency)

T=1/f

period = 1 / frequency

Period (Spring)

Ts=2π√m/k

spring period = 2π * √ (mass / spring constant)

Period (Pendulum)

Tp=2π√l/g

pendulum period = 2π * √ (length / gravity)