Rotational Motion
What this domain tests
Rotational Motion tests torque, moment of inertia, angular momentum, rolling motion and conservation laws.
Core rules
- Torque τ = Iα; angular momentum L = Iω; τ = dL/dt.
- Moment of inertia: point mass mr²; ring MR²; disc ½MR²; solid sphere (2/5)MR²; hollow sphere (2/3)MR²; rod about centre ML²/12.
- Parallel-axis theorem I = I_cm + Md².
- Rotational KE = ½Iω²; a rolling body has K = ½Mv² + ½Iω².
- Rolling without slipping: v = ωR; acceleration down an incline a = g sinθ/(1 + I/MR²).
- If external torque is zero, L is conserved.
Worked example
A disc of mass 2 kg and radius 0.5 m has I = ½MR² = ½ × 2 × 0.25 = 0.25 kg m². A torque of 0.5 N m produces α = τ/I = 0.5/0.25 = 2 rad s⁻². Starting from rest, its angular speed after 3 s is ω = αt = 6 rad s⁻¹.
Traps
- Using linear formulas for rotational quantities without converting.
- Forgetting the rotational part of kinetic energy for a rolling body.
- Assuming all bodies roll down an incline equally fast; the one with smaller I/MR² wins.
- Treating angular momentum as a scalar.