A student sits motionless on a stool that can turn frictionf

A student sits motionless on a stool that can turn friction-free about its vertical axis (total rotational inertia I). The student is handed a spinning bicycle wheel, with rotational inertia I_wheel, that is spinning about a vertical axis with a counterclockwise rotational velocity omega_0. The student then turns the bicycle wheel over (that is, through 180degree). Estimate, in terms of omega_0, the final rotational velocity acquired by the student.

Solution

As the student sits motionless on the stool initially, the net angular momentume before he is handed over the wheel is zero.

Now, the moment the student is handed the wheel which is rotating in the anti-clockwise direction, his stool will start rotating in the opposite direction so that the net angular momentum of the stool plus wheel system remains zero.

However, as he tips the wheel over, the direction of momentum of the wheel gets flipped, as a result of which the stool will start rotating in the anti-clockwise direction now so as to maintain the net angular momentum to be zero.

As the angular velocity of the wheel is o, we can form the equation for the net angular momentum and then resolve to determine the angular velocity of the student.

I(wheel) x o = I x  

or = I(wheel)  o / I

Therefore the required angular velocity is Iw* o/I