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Q. 82

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 334

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Short Answer

A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg, 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 66 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder. What is her new angular velocity, in rev/s?

Her new angular velocity = 3.3 rev/sec

See the step by step solution

Step by Step Solution

Step1: Given information

Mass of the skater 45 kg Angular velocity of the skater= 1 rev/sec

Now details about the model

Mass of model =40 kg Average diameter of model =20cm =0.2 m so average radius of=0.1m Length of the model =1.6 m The specifications for the rod : Mass of the rod =2.5 kg each Length of arm =0.66 m

Step2: Explanation

First consider when arms are stretched,

The torso acts like a solid cylindrical shape, and the arms stretched acts like a rod

Total moment of inertia = Moment of inertia of the solid cylinder + Moment of inertia of cylindrical rod

angular momentum = Iω,

substitute the values we get

Now consider when her arms are above head:

Total mass is on center and total mass is 45 kg.

So the moment of inertia is

Susbstitute the values

Calculate the momentum

From the momentum conservation, equate equation(1) and equation(2)

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