Question

As the rope of a tethered ball winds around a pole, what happens to the angular velocity of the ball?

a) Increases
b) Decreases
c) Remains constant
d) Reverses direction

Answer 1

As the rope of a tethered ball winds around a pole, the angular velocity of the ball increases due to the conservation of angular momentum.

Step-by-step explanation:

When the rope of a tethered ball winds around a pole, the angular velocity of the ball increases. This is due to the conservation of angular momentum, which is the product of the moment of inertia and the angular velocity. As the rope winds around the pole, the distance between the ball and the axis of rotation decreases, which means the moment of inertia of the ball decreases. To conserve angular momentum, the angular velocity must increase (since the product of moment of inertia and angular velocity must remain constant in the absence of external torques). This explanation is analogous to a figure skater pulling in their arms to spin faster.