A diver leaves the board with a moment of inertia of 12 kg m² and an angular velocity of 1.8 rad/s.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A diver leaves the board with a moment of inertia of and an angular velocity of . In the air she tucks, and her moment of inertia drops to .
- What is her angular velocity in the tuck?
- By what factor does her kinetic energy of rotation change?
Need a reminder? The key ideaShow
Angular momentum: for a body on a fixed axis, and (size ) for a particle. With no external torque, is conserved: . The kinetic energy need not be.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Conserve angular momentum.
Step 1. (a) , so .
Step 2. (b) With fixed, : it grows by , from to .
Answer: (a) . (b) Four times as much.
Check. , and . Ratio .
Watch out. Gravity acts at her centre of mass, so it gives no torque about it: her spin is unchanged by her fall.
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