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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 9 / Problem 9.56

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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Solved: (a) For the thin rectangular plate shown in part

Chapter 9, Problem 9.56

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QUESTION:

(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 in the figure. (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)

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QUESTION:

(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 in the figure. (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)

ANSWER:

Step 1 of 6

(a)

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 color be the origin

Mass of the rectangular plate = M

Breadth of the plate = a

The axis of rotation lies at the distance $\frac{a}{2}$ from its origin and center of mass passes through the axis of rotation.

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