Once a diver leaves the board, their angular momentum is fixed. Change the body shape and watch spin speed change to keep L constant.
Model: 60 kg diver, 1.75 m tall. I is calculated live from where each body segment sits relative to the centre of mass.
Run a dive and the three panels trace the classic sketch examiners ask for. Angular momentum stays a straight horizontal line. Moment of inertia drops when the diver tucks, and angular velocity rises by the same factor.
In free spin the panels show the last 3 seconds.
Factors affecting moment of inertia:
Newton's first law applied to angular motion. A rotating body will continue to turn about its axis of rotation with constant angular momentum unless acted upon by an external rotational force (torque). This is conservation of angular momentum: during flight, angular momentum remains constant.
Rotation is generated at take-off by an eccentric force: a force applied outside the centre of mass. The board or ground pushes back through a line that misses the centre of mass, creating a torque.
The diver on this page rotates about the transverse axis in the sagittal plane. An ice skater's spin is about the longitudinal axis in the transverse plane. Name the axis in exam answers.
Once airborne, the performer cannot add or remove angular momentum. What they can control is the distribution of mass around the axis, which changes I. Because L is fixed, ω must change in the opposite direction.
| Performer | Axis | Action | I | ω | Why it helps |
|---|---|---|---|---|---|
| Diver | Transverse | Tucks after take-off | ↓ | ↑ | Completes more somersaults in the time available |
| Diver | Transverse | Opens out before entry | ↑ | ↓ | Slows rotation for a controlled, vertical entry with less splash |
| Ice skater | Longitudinal | Pulls arms in during a spin | ↓ | ↑ | Faster spin for a higher-tariff element |
| Ice skater | Longitudinal | Extends arms and free leg | ↑ | ↓ | Slows and exits the spin under control |
| Gymnast | Transverse | Tucks on a dismount | ↓ | ↑ | Extra rotation, then opens out to stick the landing |
| Sprinter | Transverse (hip) | Heel to buttock in leg recovery | ↓ | ↑ | Leg swings through faster, raising stride frequency. Not a flight example, but shows the I and ω relationship |
Define moment of inertia and angular momentum. State the unit of angular momentum.
Identify two factors that affect the moment of inertia of a rotating body.
An ice skater spins about her longitudinal axis with a moment of inertia of 3.0 kg m² and an angular velocity of 5 rad/s. She brings her arms in, reducing her moment of inertia to 1.2 kg m². Calculate her new angular velocity. Show your working.
Using Newton's first law applied to angular motion, explain how a diver is able to complete a multiple somersault and still achieve a controlled entry.
Sketch and label a graph to show the changes in angular momentum, moment of inertia and angular velocity for a gymnast performing a tucked back somersault, from take-off to landing.
Using an example from figure skating, explain how a performer can change the speed of a spin without changing their angular momentum.