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 wW, What will be the angular velocity wp of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (6) at a 60° angle to the vertical, (c) vertically downward? (a) What will wp be if the person reaches up and stops the wheel in part (a)? See Sections 3-6 and 3-9.

Step-by-step solution

Step 1 of 5</p>

Initially, the total angular momentum about the vertical axis of rotation is zero.

As there is no torque, the total angular momentum of the platform and wheel about this vertical axis must be zero and will remain conserved.

Step 2 of 5</p>

(a) Hence when the axis of the wheel points up,

Where the negative sign indicates that the platform is rotating in the opposite direction of the wheel.

Step 3 of 5</p>

(b) When the axis points to the vertical, the component of the wheel's angular velocity about the vertical is

We have,