AP PHYSICS C EQUATIONS

1. Time-Independent Kinematics Equation

V² = V₀² + 2ax

2. Net Force (Newton’s Second Law)

ΣF = ma

3. Force in terms of momentum (Newton’s 2nd law as a derivative)

F = dp/dt

4. Force in terms of Potential Energy

F = - dU/dx

5. Impulse

J = ∫ F dt

Definition of momentum

p = mV

Impulse - Momentum theorem

J =Δp

Force of Friction

F_F < uF_n

Work done by a constant Force (dot product)

W = F * d

Work done by a variable force

W = ∫ F ds

Kinetic energy (linear)

E_k = ½ mv²

Work - Energy Theorem

W_net = ΔE_k

Power (as a rate of change)

P = dW/dt

Power - alternate expression (dot product)

P = F * v

Centripetal acceleration

a_c = v²/r = w²r

Torque (defined as a cross product)

τ = r × F

Newton’s second law for rotation (torque and angular acceleration)

Στ = Ia

moment of inertia in a collection of particles (no integral)

I = Σ (mᵢ rᵢ²)

Parallel Axis Theorem

I _parallel = I_COM + mh²

Rotational inertia of a rod about an axis through its center

I _Rod = ml²/12

Angular Momentum of a moving particle (cross product)

l = r x p

Angular momentum of a rigid rotation body

L = Iw

Position of center of mass for a collection of particles (sigma notation)

r_com = Σm_ir_i /M

Conversion between linear and angular velocity (No slip)

w x r = V → V = rw

Rotational Kinetic Energy

E_k = ½ Iw²

Force of a Spring (Hooke’s Law)

F = -kx

Potential energy of a spring

U_spring = ½ kx²

Period of a Spring Mass System

T = 2π√(m/k)

Angular frequency of a general pendulum

w = √(MgD)/I

Period of a simple pendulum

T = 2π√(L/g)

Relationships between period, frequency, and angular frequency

1/T = f = w/2π

Newton’s Law of Gravitation

F_G = G (m₁m₂)/r²

Gravitational potential Energy

U_G = -G (m₁m₂)/r

Total Mechanical Energy of an object in circular orbit

U_total = -G (m₁m₂)/2r

Kepler’s 3rd law

T²/r³ = 4π²/GM_s (r is average of r_min and r_max)

Escape Velocity

v_escape = √(2GM_e / R_e) = √2R_eg