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 ωW. Take the ωW direction counterclockwise when viewed from above. Part A

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

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

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

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

answer is given below

Explanation:

first we use here conservation of angular momentum in the vertical direction that is express as

angular velocity platform =  clock-wise     ..........................1

so the net angular momentum = 0

and

here when vertical angular momentum will be 0   than

here  angular velocity of the platform will be

ωP =  clock-wise       ..........................2

and

the angular velocity of the platform

ωP =    anti-clock-wise        ............................3

and

when here Platform will stop than

ωP = 0      ............................4

so as that conserve the angular momentum

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