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Chapter 8: 8-13MCQ (page 198)

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, your angular velocity will

(a) increase.

(b) decrease.

(c) stay the same.

Short Answer

Expert verified

The correct option is (c).

Step by step solution

01

Conservation of angular momentum

In the absence of external torque, the angular momentum is conserved.For this problem, you should consider the masses and yourself as two different systems.

02

Explanation

When the masses drop, they move with the same angular velocity as you before hitting the ground. i.e., they leave your hand with their angular momentum.

So, in one view, you can think the mass decreases, which means the moment of inertia also decreases. Therefore, the angular velocity should increase.

However, the masses leave your hand with their angular momentum; so your momentum is conserved, and your moment of inertia will not change. Therefore, your angular velocity will not change.

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