A person sits on a frictionless stool that is free to rotate but is initially at

Question

A person sits on a frictionless stool that is free to rotate but is initially at rest. The person is holding a bicycle wheel (I = 3 kg*m2) that is rotating at 8 rev/s in the clockwise direction as viewed from above, and the moment of inertia of the person-wheel-stool system is 9 kg*m2. 1.What is the magnitude of the angular momentum of the rotating wheel? 2. What is the magnitude of the angular velocity of the PWS? 3. What is the magnitude of the angular momentum of the PWS? 4. What is magnitude of the angular momentum of the system?

Explanation / Answer

1.

Iw = moment of inertia of wheel = 3 kgm2

Ww = angular velocity of wheel = 8 rev/s = 8 x 2 x 3.14 rad/s = 50.24 rad/s

Angular momentum of wheel = Lw = Iw Ww = 3 x 50.24 = 150.72 clockwise

2.

Wpws = angular velocity of PWS

Ipws = momwnt of inertia of PWS = 9 kgm2

Using conservation of angular momentum

Lw = Lpws

150.72 = Ipws Wpws

150.72 = 9 Wpws

Wpws = 16.75   counterclockwise

3)

Angular momentum of PWS system = Lpws = 150.72 counterclockwise

4)

angular momentum of the system = L = 0

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