== UNIT 5: TORQUE AND ROTATIONAL DYNAMICS ==
Torque: τ = r*F*sin(θ) = F_perp*r
r is distance from pivot to force application point
Lever arm: perpendicular distance from pivot to force line
τ = I*α (rotational analog of F = ma)
Moment of inertia: I = Σ(m_i*r_i^2)
Parallel axis theorem: I = I_cm + M*d^2
Rotational KE: KE_rot = 0.5*I*ω^2
Angular momentum: L = I*ω
Angular momentum conserved if no external torque
Rotational work: W = τ*Δθ
Rotational power: P = τ*ω
Rolling without slipping: v = r*ω, a = r*α
Static friction enables rolling
Angular acceleration same for all points
Angular velocity same for all points
Angular momentum: L = m*v*r*sin(θ) for point mass
Rotational inertia depends on mass distribution