Final answer:
Halving the radius of a cylinder would likely double its angular velocity because angular velocity is inversely proportional to radius. The angular acceleration would also increase due to the reduced moment of inertia from the smaller radius.
Step-by-step explanation:
If you had a cylinder that was half the size you tested, the angular velocity would likely increase. This is because the angular velocity of a spinning object is inversely proportional to its radius when the linear velocity at the edge is constant. If the radius is halved, the angular velocity must double for the linear velocity to remain unchanged. As for angular acceleration, if the torque remains the same, the smaller cylinder would have a larger angular acceleration because the moment of inertia is smaller. The moment of inertia is directly proportional to the mass and the square of the radius. Halving the radius would reduce the moment of inertia significantly, allowing for a greater angular acceleration given the same torque.
For example, considering two spinning tops with different radii but the same linear velocity at their edges, the top with the smaller radius has a higher angular velocity because the radius of curvature is inversely proportional to the angular velocity (option a). In the scenario where someone is pushing a merry-go-round, providing twice as much torque, one would expect the angular velocity to increase because of the direct relationship between torque and angular acceleration, leading to a change in angular velocity over time.