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Q6CQ

Expert-verifiedFound in: Page 353

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Why is the moment of inertia of a hoop that has a mass M and a radius R greater than the moment of inertia of a disk that has the same mass and radius? Why is the moment of inertia of a spherical shell that has a mass M and a radius R greater than that of a solid sphere that has the same mass and radius?**

The hoop has more mass concentrated at the outer radius than the disk. The spherical shell has more mass concentrated at the outer radius than the solid sphere.

**Moment of inertia is obtained by the addition of the product of mass and the distance squared for all the masses comprising the body.**

In the case of a hoop, they have all the masses situated on the outer boundary. Therefore, the presence of mass at the maximum possible distance makes the hoop have more moment of inertia than the disk which has mass distributed equally in its body.

Refer to the moment of inertia definition as stated above.

In the case of the spherical shell, they have all the masses situated on the outer boundary. Therefore, the presence of mass at the maximum possible distance makes the spherical shell have more moment of inertia than the solid sphere which has mass distributed equally in its body.

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