AP Physics 1 Theorems/Laws/Definition equations

Linear Fab 5 w/o displacement

v=v_o+at

Linear Fab 5 w/o final velocity

x = x_o + v_ot + ½ at²

Linear Fab 5 w/o time

v² = v_o² + 2a(x - x₀)

Linear Fab 5 w/o initial velocity

x = x_o + vt - ½ at²

Linear Fab 5 w/o acceleration

x = ½(v_o + v)t + x_o

Angular Fab 5 w/o displacement

ω = ω_o + αt

Angular Fab 5 w/o Angular Velocity

θ = θ_o + ω_ot + ½αt²

Angular Fab 5 w/o time

ω² = ω_o² + 2α(θ - θ_o)

Angular Fab 5 w/o Initial Angular Velocity

θ = θ_o + ωt - ½αt²

Angular Fab 5 w/o Angular Acceleration

θ = ½(ω_o + ω)t + θ_o

Newton’s Second Law Equation

ΣF = ma

Force of Friction

F_f = μF_N

Gravitational Force

F = G m₁m₂/r²

Net Centripetal Force Equation

F_c = mv²/r

Centripetal Acceleration

a_c = v²/r

Work

W = Fdcosθ

Power

P = W/t

Translational Kinetic Energy

K = ½mv²

Rotational Kinetic Energy

K = ½Iω²

Gravitational Potential Energy

U = mgh

Elastic Potential Energy

U = ½kx²

Total Mechanical Energy

TME = ΔK + ΔU

Work-Energy Theorem

W_net = ΔKE

Conservation of Energy

K_o + U_o = K_f + U_f

Conservation of Total Mechanical Energy

K₁ + U₁ = K₂ + U₂

Impulse Momentum Theorem

p = m(v - v_o) = F(t - t_o) = J

Elastic Conservation of Momentum

m₁v_1o + m₂v_2o = m₁v_1f + m₂v_2f

Perfectly Inelastic Conservation of Momentum

m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

translational Displacement to rotational displacement

s = rθ

translational velocity to angular velocity

v = rω

translational acceleration to angular acceleration

a = rα

Moment of Inertia for a point mass

I = L/ω

Individual torque

τ = rFsinθ

Rotational Newton’s Second Law

ΣF = Iα

Conservation of Angular Momentum

L_o = L_f or I_oω_o = I_fω_f

Hooke’s Law

F = -kx

Period of a Spring

T_s = 2π (m/k)^1/2

Period of pendulum

T_p = 2π (L/g)^1/2

General Wave Function (A is amplitude)

y = A sin(kx + ωt), y = A cos(kx + ωt), y = A sin(kx - ωt), y = A cos(kx - ωt)

Max Velocity

v_max = Aω

Max Acceleration

a_max = Aω²

Pressure

P = F/A

Pascale’s Principle

P₁ = P₂

Bernoulli’s Equation

P + ½ρv² + ρgh = constant

Continuity Equation

A₁v₁ = A₂v₂

Buoyant Force

F_b = ρVg

Volume Flow Rate w/ Area

Q = Av

Volume Flow rate w/ Voume

Q = V/t