Energy and Momentum of Rotating Systems practice quiz

Key ideaAngular momentum is Iω for a rotating object, or mvr⊥ for a particle about a point.

Common mistakeForgetting that a particle moving in a straight line can still have angular momentum about a point it doesn’t pass through.

Key ideaAngular impulse, torque times time (τΔt), equals the change in angular momentum.

Common mistakeUsing force times time (linear impulse) in place of torque times time.

Key ideaWith no net external torque, Iω stays constant: pulling mass inward lowers I, so ω increases.

Common mistakeAssuming the rotational kinetic energy stays constant too. It increases when I decreases, because the person or object does work.

Key ideaA rotating object stores kinetic energy ½Iω², in addition to any translational ½mv².

Common mistakeLeaving out the rotational term for a rolling object, which both rotates and translates.

Key ideaIn rolling without slipping, v = rω, and the kinetic energy is split between translation and rotation. Objects with more of their mass near the rim roll down a ramp more slowly.

Common mistakeThinking a heavier or larger object reaches the bottom first. The race depends only on the shape (the fraction I/mr²).

Key ideaA quantity is conserved for a system only when its condition holds: momentum when there is no net external force, mechanical energy when no nonconservative forces do work, and angular momentum when there is no net external torque.

Common mistakeApplying a conservation law to a system without checking its condition, for example conserving mechanical energy when friction acts.