A rotor experiences a net torque counterclockwise about a fixed axis and has angular acceleration counterclockwise. If the net torque is unchanged but the rotational inertia decreases by 20%, what happens to ?
- decreases by 20% because inertia decreased.
- increases by 25% because . (correct answer)
- is unchanged because torque is unchanged.
- depends on angular velocity, so it cannot be determined.
Explanation: This question assesses understanding of Newton's second law for rotation, which states that net torque equals rotational inertia times angular acceleration, τ_net = I α. Qualitatively, rotational inertia opposes changes in angular velocity, so decreasing it allows greater acceleration for the same torque. The inverse proportionality means a reduction in I increases α by the reciprocal factor. With I decreasing to 80% (0.8 times) and τ unchanged, α increases by 1/0.8 = 1.25 times, or 25%. A common distractor is choice A, claiming α decreases by 20% because inertia decreased, but this mistakes the inverse relationship for a direct one. A key strategy is to express changes as fractions or percentages and use α ∝ 1/I to find the percentage change in α.