Question

Visualize an ice skater rotating faster and faster in a clockwise direction. What are the signs of rotational velocity and rotational acceleration? As the skater starts slowing down, what are the signs of rotational velocity and acceleration? A solid wooden ball and a smaller solid metal ball have equal mass (the metal ball is smaller because it is much denser than wood). Both can rotate on an axis going through their centers. You exert a force on each that produces the same torque about the axis of rotation. Which sphere's rotational motion will change the least? Explain.

Answer 1

* As skater is moving clockwise direction hence rotational velocity points in downward direction and it's sign is negative (-ve).

As rotational velocity is increasing clockwise hence the sense of rotational acceleration is also negative (-ve).

When skater starts slowing it's rotation is still clockwise hence sense of rotational velocity is still negative (-ve).

When skater starts slowing it's rotational velocity is decreasing clockwise hence sense of it's rotational acceleration is positive (+ve).

* As angular momentum is directly proportional to moment of inertia and moment is inertia of wooden ball is large hence change in angular momentum hence in rotational motion of wooden ball is large and metal ball is least.

Ans - Metal sphere.