Angular Momentum Chair
The principle of conservation of angular momentum can be demonstrated using a swivel chair
and some 'dumbell' weights. Since such equipment is very non-specialist, this exhibit is rather
attractive in being popular with children and adults, while being inexpensive to obtain.
The simplest demonstration is that of letting a volunteer sit in the chair, with their legs reaching out,
and holding weights in their arms, initially at arms' length. The chair is then set spinning by the demonstrator, and on a signal, the volunteer is asked to pull his/her legs and arms in. The resulting
increase in the spin of the chair can be very impressive. In fact, in some cases, it is better to fix the
chair to the floor, or else have a soft landing area around the chair!
The effect is explained in three steps as follows.
Firstly, the angular momentum of the complete person/chair/dumbell system is proportional to the product of the moment of inertia and angular velocity of the system.
Secondly, the moment of inertia is proportional to the
square of the distance from the axis of rotation to each bit of mass in the system.
The result is that when the volunteer pulls in their legs and arms, the moment of inertia shoots down
in value, since the distances to rather heavy bits of the system (namely the person's limbs, and the
dumbells) is suddenly reduced.
Thirdly, since angular momentum is conserved, the drop in
inertia must be accompanied by a rise in the angular velocity, and so the system spins faster.