In this problem you will be given the mass and description of various objects an

Question

In this problem you will be given the mass and description of various objects and will determine their moments of inertia I. All results are of the form X * M R2. You will find the numerical value of X.

What is the moment of inertia for a ring with mass 4 M and an axis of rotation through the center of the ring (perpendicular to the plane of the ring) with radius 2 R.
M R2

What is the moment of inertia for a disk with mass 3 M and an axis of rotation through the center of the disk with radius 1 R.
M R2

What is the moment of inertia for a hollow sphere with mass 3 M and an axis of rotation through the center of the sphere with radius 1 R.
M R2

What is the moment of inertia for a solid sphere with mass 2 M and an axis of rotation through the center of the sphere with radius 1 R.
M R

Explanation / Answer

I = m r^2

I = (4 M )(2 R^2) = 16 M R^2

Ans: 16

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I = m r^2 /2 = (3 M )(R^2)/2 = 1.5 M R^2 /2

Ans: 1.5

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I = 2 m r^2 / 3 = 2 (3 M) (R^2)/3 = 2 M R^2

Ans: 2

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I = 2 m r^2 / 5 = 2 ( 2 M )(1 R^2) / 5 = 0.8 M R ^2

Ans: 0.8

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