AP Physics 1 Formulas + Units

kinematic equation #1 (vf=)

kinematic equation #1 (vf=)

vf=vi+at

kinematic equation #2 (vf²=)

vf²=vi²+2aΔx

kinematic equation #3 (Δx=)

Δx=vit+1/2at²

kinematic equation #4 (Δx=)

Δx=1/2(vi+vf)t

displacement (d)

d=vt

velocity (v)

v=Δx/t

acceleration (a)

a=v/t

Net Force (ΣF, newton’s second law)

ΣF=ma

static friction (f_s)

f≤μF_n

kinetic friction (f_k)

f=μF_n

Universal law of gravitation (Fg=)

Fg=G(m1m2/r²)

surface gravity of a planet (not earth)

g=GM/R²

θ(rad)

arclength/rad

convert to Δθ

Δx/r

convert to ω

v/r

convert to α

a/r

angular velocity (ω)

ω=2π/T

tangential velocity (v_T)

2πr/T

centripetal acceleration (a_c)

a_c=v²/r

tangential acceleration

a_t=rα

total acceleration

a_tot=√ac²+at²

circular net force

ΣF=mv²/r

gravitational force between two objects

F=GMm/r²

orbital velocity

v=√GM/r

spring force equation (F_s)

F_s=-kx

kinetic energy

KE=1/2mv²

gravitational potential energy

U_g=mgh

Net Work (W_net)

W_net=ΔK=1/2mvf²-1/2mvi²

spring potential energy (U_sp)

U_sp=1/2kx²

power

P=W/t

work (W)

W=F∥Δx

avg speed

avg d/avg t

average velocity

Δx/Δt

instantaneous velocity

Δx/Δt (where t gets infinitely small)

weight (Fg)

Fg=mg

instantaneous angular speed

ω=Δθ/Δt (where t gets infinitely small)

average angular speed

ω=Δθ/Δt

Kepler’s Law

T²=(4π²/GM)r³ » T²∝r³

find net force using momentum

ΣF=Δp/Δt

impulse/change in momentum (impulse-momentum theorum)

Δp=ΣFΔt

law of conservation of momentum

m_Av_Ai+m_Bv_Bi=m_Av_Af+m_Bv_Bf

recoil collision (begin together, move apart)

m_Av_Af=-m_Bv_Bf

perfectly inelastic collision (begin apart, stick together)

m_Av_Ai+m_Bv_Bi=(m_A+m_B)v_f

elastic collision (objects collide but dont lose KE)

v_Ai+v_Af=v_Bi+v_Bf

center of mass distance

x_com=m₁x₁+m₂x₂/m₁+m₂

velocity of center of mass

v_com=m₁v₁+m₂v₂/m₁+m₂

acceleration of a harmonic oscilator (spring)

a=-(k/m)x

angular frequency (rate of change of angular displacement)

ω=2πf

period of an oscillating spring

T=2π√m/k

period of an oscillating pendulum

T=2π√L/g

max displacement of an oscillating spring (x_max)

x_max=±A

max velocity of an oscillating spring (v_max)

v_max=±A√k/m

max acceleration of an oscillating spring (a_max)

a_max=±A(k/m)

acceleration of a harmonic oscillator (pendulum)

a=(g/L)x

torque formula

τ=F⊥r

moment of inertia

I=Σmr²

Newton’s second law of rotation

τ=Iα

angluar momentum (L)

L=Iω

rotational kinetic energy

K_R=1/2(Iω²)

angular impluse-momentum

Στ⋅t=ΔL=Iω_f-Iω_i

conservation of energy while rolling

U_g=K_T+K_R

Unit of Force

Newton (N=kg⋅m/s²)

Unit of Frequency

Hertz (Hz)

Unit of Distance

Meter (m)

Unit of Time

Second (s)

Unit of Velocity

m/s

Unit of Acceleration

m/s²

Unit for Coefficient of Friction (μ)

No Units

Unit for Angular Displacement

Rad

Units for Angular Velocity

rad/s

Units for Angular Acceleration

rad/s²

velocity of an object in uniform circular motion (v)

v=2πr/T

total acceleration of a rotating object (non-UCM)

a_tot=√a_c²+a_t²

maximum velocity at which you can go around a circle

v≤√rgμ

velocity of an object on a simple circular pendulum

v=√rgtanθ

Unit of Energy

Joules (J=(kg⋅m²)/s²)

Unit of Power

Watt (W=(kg⋅m²)/s³)

Unit of Momentum

kg⋅m/s

Unit for a spring constant (k)

N/m

frequency formula

f=1/T

angular velocity of an object oscillating on a pendulum

ω=√g/L

Unit for Torque

N⋅m

Newton’s second law (torque)

τ = mr²α

Unit for Angular Momentum (L)

kg⋅m²/s

velocity of an object that starts at rest and ends at zero level (conservation of energy)

v=√2gh

acceleration in an atwood’s machine

a=(m₁-m₂)⋅g/m₁+m₂