Concept explainers
To Calculate: The ratio of angular speeds for a spinning skater with outstretched arms and with arms held tightly against her body.
Answer to Problem 82GP
Explanation of Solution
Assumption:
Let the human has a mass of 60 kg. The total percentage of masses of arms and hands is 12.5 % of the total mass of the human. The total percentage of the mass of the rest of the body is about 87.5% of the total mass of the body.
The mass of the skater is 52 kg. Each arm of the skater has a mass of 4 kg. The height of the skater is 150 cm with a radius of 15 cm and the length of the arm is 50 cm.
Given :
Formula used:
The moment of inertia of the cylinder is:
The moment of inertia of the rod is:
The moment of inertia of skater when the arms held tightly:
The moment of inertia of the skater with stretched arms:
From the conservation of angular momentum:
Calculation:
Putting the values in equation (1):
Conclusion:
The ratio of angular speeds for a spinning skater with outstretched arms and with arms held tightly against her body is 0.54.
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