# Following the procedure used in Example 10.7, prove that the moment of inertia about the y ′ axis of the rigid rod in Figure 10.15 is 1 3 M L 2 .

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781337553278
Chapter 10, Problem 23P
Textbook Problem
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## Following the procedure used in Example 10.7, prove that the moment of inertia about the y′ axis of the rigid rod in Figure 10.15 is 1 3 M L 2 .

To determine

The moment of inertia about the y' axis of the rigid rod.

### Explanation of Solution

Moment of inertia is defined as the product of the mass of the body to the distance from the rotational axis.

The figure that shows the rigid rod is shown below:

Figure (I)

Consider a small mass dm at a distance of x from the vertical y' axis. Assume the linear mass density of the rod is λ.

Formula to calculate the moment of inertia of the rod from the vertical y' axis is,

Iy'=0Lx2dm        (I)

Here, Iy' is the moment of inertia of the rod from the vertical y' axis, x is the distance of the small mass from the vertical axis and dm is the arbitrary small mass of the rod.

Formula to calculate the arbitrary small mass of the rod is,

dm=λdx

Here, dx is the length of the small mass.

Formula to calculate the linear mass density of the rod is,

λ=ML

Here, M is the mass of the rigid rod and L is the length of the rod

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