Question

A person standing on the ground is holding a spinning bicycle wheel. he reaches up and causes it to stop. Draw an angular momentum bar chart for the system of the person and the wheel. Comment on what provides any torques involved.

Answer 1

Because - assuming that the friction between the spinning platform and the bicycle wheel and their respective axes of rotation is irrelevant - angular momentum must be conserved.

Given your initial situation where the person is at rest and the wheel is spinning, the total angular momentum of your system will be that of the bicycle wheel, which is represented by a vector assuming a given orientation.

Now, if the person suddenly reverses the bicycle wheel, the vector which represents its angular momentum will also be reversed, assuming the same direction as before (along the same line) but pointing the opposite way.

Clearly this does not correspond to the initial angular momentum of the system - although the "value" of this momentum is the same as before (again, disregarding dissipative forces), we must remember that angular momentum is a vectorial quantity, not a scalar one.

So, what must happen in order that the total angular momentum be the same as the starting situation? The platform in which the person is standing must begin to rotate too, in a way that it not only "counterbalances" the wheel's momentum, but also that it restores the original angular momentum of the entire system.