Chapter 16.4, Problem 26E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use Exercise 25 to find the moment of inertia of a circular disk of radius *a* with constant density *ρ* about a diameter. (Compare with Example 15.4.4.)

To determine

**To find**: The moment of inertia of a circular disk.

Explanation

**Given data:**

A circular disk of radius *a* and constant density

**Formula used:**

Write the expression for moment of inertia about *y*-axis

Here,

The curve of circular disk is symmetrical curve. Hence, the moment of inertia is symmetric about any two diameters are same. Consider the center of circular disk is located at origin. Therefore, the moment of inertia about diameter is as same moment of inertia about *y*-axis.

Consider a circular disk *C*,

Differentiate equation (2) with respect to *t*.

Differentiate equation (3) with respect to *t*.

Substitute

Expand the equation

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