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Q. 54

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 332

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Short Answer

Calculate the moment of inertia of the rectangular plate in FIGURE P12.54 for rotation
about a perpendicular axis through the center.

The moment of Inertia is

See the step by step solution

Step by Step Solution

Step 1: Given Information

A rectangular plate with length and width = L

Axis of rotation passing through center and perpendicular to plane

Step2: Explanation

Lets assume a strip of small width say dx has mass of dm as in figure below

dm = σ x L x dx ............................(1)

where σ is mass per unit area and L is length and dx is width of trip

Substitute in equation(1) we get

So the moment of inertia of this strip about its central axis perpendicular length,

Substitute the value of dm from equation (2), we get

Using the parallel axis theorem, find the moment of inertia of this strip about the given axis of rotation

Integrate this to get the inertia of the plate

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