Question

A small mass m on a string is rotating without friction in a circle. The string is shortened by pulling it through the axis of rotation without any external torque, Fig. 8–39. What happens to the tangential velocity of the object?

(a) It increases.

(b) It decreases.

(c) It remains the same.

FIGURE 8-39

MisConceptual Questions 10 and 11.

Short answer

The correct option is (a).

Step-by-step solution

Angular momentum

For angular momentum conservation, if the radius of the rotational path decreases, the moment of inertia decreases, and the rotational speed increases.Tangential speed is proportional to the angular speed; hence, the tangential speed increases.

The small mass is m.

Explanation

When you pull the string, the radius of the circular path decreases, and the moment of inertia of the mass also decreases. As there is no external torque, the angular momentum is conserved.

To maintain the conservation of the angular momentum of the mass, the angular velocity increases when the moment of inertia decreases.

Now, the tangential velocity of an object is proportional to the angular velocity. Therefore, the tangential velocity of that object also increases.