During a spin, if the moment of inertia decreases and angular momentum is conserved, what happens to the angular velocity?

• A. Angular velocity increases
• B. Angular velocity decreases
• C. Angular momentum increases
• D. Angular velocity remains the same due to energy conservation

Answer: (A)

Conservation of angular momentum means the product Iω stays constant when there’s no external torque. If the moment of inertia I decreases, the angular velocity ω must increase to keep Iω the same. For example, if I is cut in half, ω must double. This is why a skater pulling in their arms spins faster. It’s also worth noting that rotational kinetic energy K = (1/2)Iω^2 changes even as L stays constant: with L fixed, K = L^2/(2I), so as I decreases, K increases. So the angular velocity increases to conserve angular momentum, while the energy changes due to the redistribution of inertia.