Suppose we take a disk of radius $R$ and remove the material from $r=0$ to $r=\frac{1}{2} R$, making a hole at the center of the disk. Note that this decreases the mass of the disk. 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

Removing material from the center of the disk increases the moment of inertia since mass is distributed further from the axis of rotation. The moment of inertia is directly related to $\alpha$, the angular acceleration, for a given torque. Therefore, with a higher moment of inertia, the same torque will produce a smaller angular acceleration, implying that the original object had a higher $\alpha$ due to its lower moment of inertia.

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