AP Physics C: Mechanics Unit 6 Cheatsheet: Energy and Momentum of Rotating Systems

Formula: K_rot = ½Iω²

• Scalar quantity; depends on rotational inertia and angular velocity
• Object can have K_rot while center of mass is at rest (points within system move)
• Equivalent to translational KE when expressed via rotational inertia

Total kinetic energy of rigid system:

K_tot = K_trans + K_rot = ½mv_cm² + ½Iω²

Sum of translational KE (center of mass motion) and rotational KE (rotation about center of mass).

Gravitational potential energy:

U_g = −GMm/r

(Zero at infinite distance)

Circular orbits: Total energy, U, L, and K are constant.

Elliptical orbits: Total energy and L are constant; U and K vary.

Energy relations (circular):

K = −½U

E_total = ½U = −GMm/(2r)

Escape velocity:

v_esc = √(2GM/r)

• Velocity at which total mechanical energy = 0
• Satellite reaches infinite distance with zero speed