Suppose you make a new kind of compact disk that is the same thickness as a current disk but twice the diameter. By what factor will the rotational inertia increase? Idisk= 1/2MR^2 8 2 16

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terryyang1933 terryyang1933

23-12-2022
Physics

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Suppose you make a new kind of compact disk that is the same thickness as a current disk but twice the diameter. By what factor will the rotational inertia increase? Idisk= 1/2MR^2 8 2 16

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contexto1019 contexto1019 · Answer 1 · 2022-12-27T02:06:23-05:00

If you make a new kind of compact disk that is twice the diameter of a current disk but has the same thickness, the rotational inertia of the new disk will increase by a factor of 8.

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. It is given by the formula:

I = 1/2 * m * r^2

where I is the rotational inertia, m is the mass of the object, and r is the distance from the axis of rotation to the mass of the object.

If you double the diameter of a compact disk but keep the thickness the same, you are effectively doubling the distance from the axis of rotation to the mass of the disk (since the disk is the same thickness). This means that the rotational inertia of the disk will increase by a factor of 8 (2^2), since it is proportional to r^2.

Learn more about Rotational Inertia here:

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