Suppose we take a disk of radius $R$ and remove the material from $r=\frac{1}{2} R$ outward. Note that this decreases both the disk's mass and its radius. Will the value of $\alpha$ for the new object be larger, smaller, or the same as that for the original object?

Question

Quizplus · Accepted Answer

The value of $\alpha$, which represents the moment of inertia factor for a disk, is determined by the distribution of mass relative to the axis of rotation. For a solid disk, $\alpha$ is $\frac{1}{2}$, regardless of changes in mass or radius, as long as the mass remains uniformly distributed. Removing material from the outer part of the disk does not change this distribution pattern relative to the axis, hence $\alpha$ remains the same.

Suppose We Take a Disk of Radius RRR And Remove the Material From

Suppose We Take a Disk of Radius $R$ And Remove the Material From