Imagine two circular plates; one is solid and the other has a hole cut out of th
ID: 1471872 • Letter: I
Question
Imagine two circular plates; one is solid and the other has a hole cut out of the center. Both plates have the same radius, same thickness, and same mass. The same force F is applied tangential to the edge of each plate in such a way that the plates rotate about an axis passing through the center and perpendicular to the surface of the plates.
Which one of the following statements is true regarding the angular acceleration?
1. Both plates will rotate with the same angular acceleration.
2. The solid plate will have the greater angular acceleration.
3. The plate with the hole will have the greater angular acceleration.
Which of the following statements helps to explain the question asked above? (Select all that apply.)
1. Because both plates have the same mass, they will have the same moment of inertia.
2. Angular acceleration is inversely proportional to the moment of inertia.
3. Angular acceleration is directly proportional to the moment of inertia.
4. The plate with the hole has its mass distributed further out from the axis of rotation, which will increase its moment of inertia.
5. Both plates will be subjected to the same torque.
Explanation / Answer
We have Torque, T = I * angular acceleration.
From the above equation we see that the angular acceleration depends on the moment of inertia and the torque.
Let us first consider torque. The same force is applied at the same distance from the axis of rotation. Torque = rF and therefore both plates will be subjected to a torque of equal magnitude.
Now let us consider the moment of inertia of each plate. Both plates have the same mass, radius, and thickness.
In the case of the plate with a hole, more of the mass will be distributed further away from the center and closer to the edge.
Therefore it will have a greater moment of inertia. From = / I we see that the angular acceleration is inversely proportional to the moment of inertia.
Therefore the plate with the hole will rotate with a smaller angular acceleration.
So, Answer is 2 and reasoning is 2,4,5.