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Chapter 1: Q42E (page 332)

A diver comes off a board with arms straight up and legs straight down, giving her a moment of inertia about her rotation axis of 18kgm2. She then tucks into a small ball, decreasing this moment of inertia to 3.6kgm2. While tucked, she makes two complete revolutions in 1.0 s. If she hadn’t tucked at all, how many revolutions would she have made in the 1.5 s from board to water?

Short Answer

Expert verified

Hence, she made revolution in 1.5 s from board to water is 0.60rev.

Step by step solution

01

Conservation of angular momentum.

If a system experience no external torques from the environment, the total angular momentum of the system is conserved.

ΔL→t→=0

Apply the law of conservation of angular momentum to a system whose moment of inertia changes gives:

Iiωi=Ifωf=constant

02

She made revolution from board to water.

Apply conservation of angular momentum to the diver.

The number of revolutions she makes in a certain time is proportional to her angular velocity.

The ratio of her untucked to tucked angular velocity is:

3.618=0.2

If she had tucked, then she made revolution in the last 1.0sas:

23.618=0.4rev

In the last 1.0s, so the revolution made in the total 1.5sis:

0.41.51=0.60rev

Hence, she made revolution in 1.5sis 0.60reV.

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