A solid sphere of mass m and radius b is spinning freely on its axis with
The ratio
Answer to Problem 27SP
Solution:
Explanation of Solution
Given data:
A solid sphere of mass
The angular velocity of the sphere changes to
The linear expansion coefficient for the material of the sphere is
Formula used:
Write the expression for angular momentum:
Here,
Write the expression for conservation of angular momentum:
Here,
Write the expression for moment of inertia of solid sphere:
Here,
Write the expression for linear expansion of solids:
Here,
Write the expression for binomial expansion of the term
Explanation:
Recall the expression for the initial moment of inertia of solid sphere:
Substitute
Recall the expression for the initial angular momentum of solid sphere:
Here,
Substitute
When the sphere is heated by an amount
Recall the expression for the final radius of solid sphere:
Here,
Substitute
Recall the expression for the final moment of inertia of solid sphere:
Substitute
Recall the expression for the final angular momentum of solid sphere when it is heated by an amount
Here,
Substitute
Apply the conservation of angular momentum on the solid sphere:
Substitute
Solve the expression
The expression for binomial expansion of the term
Substitute
Conclusion:
The ratio
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Chapter 15 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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