A student at rest is handed a bicyle wheel pointed sideways, as shown in figure

Question

A student at rest is handed a bicyle wheel pointed sideways, as shown in figure 16a. In this orientation the wheel has no z component of angular momentum. Once the student has the wheel, the z component of the angular momentum of the student plus the wheel is conserved. Explain what will happen if the student orients the bicycle wheel up as shown in Figure 16b, so that the bicycle wheel is rotating counterclockwise as seen from above. student will start rotating counterclockwise, as seen from above, to conserve the total angular momentum of the student+wheel system student will not rotate, because the angular momentum of the wheel does not change student will start rotating clockwise, as seen from above, to conserve the total angular momentum of the student+wheel system Explain what will happen if the student orients the bicycle wheel down as shown in Figure 16b, so that the bicycle wheel is rotating clockwise as seen from above student will not rotate, because the angular momentum of the wheel does not change student will start rotating counterclockwise, as seen from above, to conserve the total angular momentum of the student+wheel system student will start rotating clockwise, as seen from above, to conserve the total angular momentum of the student+wheel system

Explanation / Answer

In Figure (16b) the bicycle has a positive z component of angular momentum lz = mvr and the student has none. Thus the total angular momentum of the wheel and student is :-
(lz) total = (lz) bicyclewheel + (lz)student

            = +mvr + 0 = +mvr

The special thing that happens when you stand on a freely rotating platform is that you cannot change your own z component of angular momentum. If no one off the platform passes or tosses in some angular momentum, your z component of angular momentum is conserved and there is no way you can change
it.

Have the student turn the bicycle wheel upside down as shown in Figure (16 c). Now of the bicycle wheel is pointing down so that the bicycle wheel now has a negative z component of angular momentum
(lz)bicyclewheel = – mvr
Since the total (lz)of the student and bicycle wheel must be conserved, the student must gain a positive
z component of angular momentum
(lz )student = + 2mvr
so that the sum remains + mvr.

when the student turns the bicycle wheel over is that she starts rotating counter clockwise; she gains a positive z component of angular momentum. If at any time she turns the wheel back up, she will stop rotating.

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