Problem 11.9 A person stands on a platform, initially at rest, that can rotate f

Question

Problem 11.9

A person stands on a platform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is IP. The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia IW and angular velocity W. Take the W direction counterclockwise when viewed from above.

Part A

What will be the angular velocity P of the platform if the person moves the axis of the wheel so that it points vertically upward?

Express your answer in terms of the variables IP, IW, and W.

Part B

What will be the angular velocity P of the platform if the person moves the axis of the wheel so that it points at a 60 angle to the vertical?

Express your answer in terms of the variables IP, IW, and W.

Part C

What will be the angular velocity P of the platform if the person moves the axis of the wheel so that it points vertically downward?

Express your answer in terms of the variables IP, IW, and W.

Part D

What will P be if the person reaches up and stops the wheel in part A?

Express your answer in terms of the variables IP, IW, and W.

Explanation / Answer

Part A:

Using the conservation of angular momentum in vertical direction;

angular velocity of platform = [W*IW] / IP clock-wise

So, the net angular momentum = 0.

Part B:

The vertical angular momentum should be zero.

So, angular velocity of the platform, P =  1/2 * [W*IW] / IP clock-wise

Part C:

the angular velocity of the platform, P = [W*IW] / IP anti-clock-wise

Part D:

Platform will stop, P = 0, so as to conserve the angular momentum.

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