Conservation of angular momentum
Pull your arms in, and the swivel chair spins faster and faster.
Angular momentum is conserved when no external torque acts on a system. When a person on a swivel chair pulls in their arms, the dumbbells move closer to the axis, the moment of inertia decreases and the angular velocity increases; stretching the arms out slows the rotation. Pulling the arms in actually increases the rotational kinetic energy; the extra energy comes from the work the person does on the dumbbells.
Angular velocity vs. time
Angular velocity rises while the arms are pulled in and falls back while they are stretched out; in both stages the angular momentum L = Iω stays constant.
Think about it
After the arms are pulled in, does the rotational kinetic energy increase, decrease or stay the same?
It increases. With L fixed, E = L²/(2I), so a smaller I means a larger E. This energy comes from the work the person does in pulling the dumbbells toward the axis.
Model assumptionsAxle friction neglected · Body moment of inertia (without dumbbells) 1.5 kg·m² · Arms-out radius 0.8 m
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.