Question Detail
Question
If the angular speed ω of a particle in circular motion is not constant (non-uniform circular motion), how is the torque related to its moment of inertia I and angular acceleration α?
Correct Answer
Option D is the correct answer.
Detailed Explanation
Torque is the rate of change of angular momentum: τ = dL/dt. For a particle in circular motion, L = m r² ω = I ω. Taking the time derivative, and assuming the radius r (and thus I) is constant, gives τ = d(Iω)/dt = I (dω/dt) = I α. This is the rotational analogue of F = m a.
Hint
Relate torque to the time derivative of angular momentum, and then express angular momentum in terms of moment of inertia and angular velocity.