Answer: Find the moment of inertia of a hoop (a

Chapter 9, Problem 54E

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QUESTION:

 Problem 54E

Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass M and radius R about an axis perpendicular to the hoop’s plane at an edge.

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QUESTION:

 Problem 54E

Find the moment of inertia of a hoop (a thin-walled, hollow ring) with mass M and radius R about an axis perpendicular to the hoop’s plane at an edge.

ANSWER:

Step 1 of 2

The moment of inertia of the hoop about the axis passing through it’s center which is parallel to the plane of the hoop is,

       .

By perpendicular axis theorem,

        .

Where are the respective moment of inertias along the three perpendicular axes.

But by symmetry, .

So,

.

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