A regulation table tennis ball has a fixed of 2.7g and also is 40mm in diameter. What is its minute of inertia about an axis the passes v its center?
Concepts and reasonThe concepts required to deal with this trouble are minute of inertia the the hollow sphere and also conversion of units.First resolve for the radius that the sphere from diameter and convert mass to kilogram. Then, instead of the values in the expression of minute of inertia that hollow ball to calculation the minute of inertia of the tennis ball around an axis the passes through its center.
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FundamentalsThe radius the a ball is fifty percent of the diameter. That is,Here, r is the radius and also d is the diameter.The moment of inertia of hole sphere about an axis that passes with its center is,Here, I is the moment of inertia, m is the mass, and r is the radius.The relations provided to coverts units space as follows:
The relation of diameter and also radius is.
Explanation:The radius is half of the diameter the the tennis ball.
The expression of minute of inertia that the tennis ball is,Substitute
The moment of inertia the the tennis ball about an axis the passes through its center is
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Explanation:The tennis ball is do of a plastic cover through hollow inside. The hollow ball is the closest symmetry the the tennis ball.