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# (a) For the thin rectangular plate shown in part (d) of ISBN: 9780321675460 31

## Solution for problem 56E Chapter 9

University Physics | 13th Edition

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Problem 56E

Problem?(a) For the thin rectangular plate shown in part (d) of Table 9.2, find the moment of inertia about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the axis shown. (b) Find the moment of inertia of the plate for an axis that lies in the plane of the plate, passes through the center of the plate, and is perpendicular to the axis in part (a).

Step-by-Step Solution:

Solution 56E Problem (a) Step 1: To find the moment of inertia about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the axis. Consider axis shown in blue colour be the origin Mass of the rectangular plate = M Breadth of the plate = a a The axis of rotation lies at the distance 2 from its origin and center of mass passes through the axis of rotation. Step 2: We can apply parallel axis theorem to solve this problem I = ICM+ MR 2 a Here R = 2 I = Ma 2 3 Step 3: Therefore the moment of inertia about the axis through which the center of mass passes I = Ma - Ma 1 2 CM 3 4 Simplifying the above equation 1 2 ICM= 12Ma Problem (b) Step 1: To Find the moment of inertia of the plate for an axis that lies in the plane of the plate, passes through the center of the plate, and is perpendicular to the axis. The problem is same as that of the previous problem. There is a small change here. Breadth a is changed as length b. Mass of the plate = M Length of the plate = b b The axis of rotation lies at the distance 2from its origin and center of mass passes through the axis of rotation. Step 2: Applying parallel axis theorem I = ICM+ MR 2 b Here R = 2 1 2 I = M3

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##### ISBN: 9780321675460

The answer to “Problem?(a) For the thin rectangular plate shown in part (d) of Table 9.2, find the moment of inertia about an axis that lies in the plane of the plate, passes through the center of the plate, and is parallel to the axis shown. (b) Find the moment of inertia of the plate for an axis that lies in the plane of the plate, passes through the center of the plate, and is perpendicular to the axis in part (a).” is broken down into a number of easy to follow steps, and 79 words. The full step-by-step solution to problem: 56E from chapter: 9 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This full solution covers the following key subjects: plate, axis, Find, inertia, Lies. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. This textbook survival guide was created for the textbook: University Physics, edition: 13. Since the solution to 56E from 9 chapter was answered, more than 562 students have viewed the full step-by-step answer.

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