Question

Suppose you are standing on the center of a merry-go-roundthat is at rest. You are holding a spinning bicycle wheel ove...

Suppose you are standing on the center of a merry-go-roundthat is at rest. You are holding a spinning bicycle wheel over yourhead so that its rotation axis is pointing upward. The wheel isrotating counterclockwise when observed from above.

For this problem, neglect any air resistance or frictionbetween the merry-go-round and its foundation.
Q.
Suppose you now grab the edge of thewheel with your hand, stopping it from spinning.
What happens to themerry-go-round?
It remainsat rest.
It begins torotate counterclockwise (as observed from above).
It begins torotate clockwise (as observed from above).
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Answer #1
Concepts and reason

The concepts of conservation of angular momentum and Newton’s third law are required to solve the problem.

First, check whether the merry-go-round will remain at rest or it will rotate. Then, determine the direction of rotation by using the conservation of angular momentum.

Fundamentals

According to conservation of angular momentum, the angular momentum of an object remains conserved unless it is acted upon by an external torque.

According to Newton’s third law for every action there is an equal and opposite reaction.

Suppose a person standing in the center of the merry-go-round and he is holding a spinning bicycle wheel.

Initially the wheel is rotating counterclockwise and to the stop the wheel from rotating, the person must exert a torque on the wheel in the opposite direction. Therefore, to conserve the angular momentum the wheel will exert an equal and opposite torque on the person. As there is no friction between the person and the merry-go-round, this opposite torque on the person will make the merry-go-round spin. Hence, the merry go-round will not remain at rest.

The person must exert a clockwise torque on the wheel to stop the wheel from rotating as the wheel is rotating counterclockwise. Therefore, to conserve the angular momentum the wheel will exert a counterclockwise torque on the person. As the person will spin counterclockwise, the merry-go-round cannot spin clockwise.

As the wheel is rotating counterclockwise and to the stop the wheel from rotating, the person must exert a clockwise torque on the wheel. Therefore, to conserve the angular momentum the wheel will exert a counterclockwise torque on the person which makes the person spin counterclockwise. As there is no friction between the person and the merry-go-round, this counterclockwise torque on the person will make the merry-go-round spin counterclockwise.

Hence, the merry go-round begins to rotate counterclockwise.

Ans:

The merry go-round begins to rotate counterclockwise.

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