Conservation of Angular Momentum

Sit on the chair and rotate the umbrella using the circular handle. The chair rotates in the opposite direction. Any rotating object will have a property called angular momentum which is a constant at any given time. The total angular momentum of this system was zero before we rotated the umbrella. As the umbrella rotates, there is a change in its angular momentum.

To counter that, the base rotates in the opposite direction so that the total angular momentum is again zero.

The model here basically has a rotating platform. A chair connected to an umbrella structure is fixed to this rotating platform. This umbrella can be set into rotation using the ring provided.

To observe the working of this model, one has to sit on the chair and set the umbrella part to rotate. The platform and hence the person sitting on the chair start rotating in the direction opposite to that of umbrella.

All rotating systems have a characteristic property known as angular momentum which depends on the mass and mass distribution of the system and also the velocity with which the system is rotating about an axis. If the net torque 'c' acting on the system i.e., the force acting at a distance from the axis of rotation is zero, the angular momentum of the system remains unaltered.

The same angular momentum can also be expressed as the product of moment of inertia of the system (I) and the angular velocity (w) about the axis of rotation. This product remains a constant when the net torque ‘c’ is zero. This can happen when a change is ‘I’ is compensated by a change in ‘w’. Even when the system comprises of different parts with different I and W, total angular momentum i.e. the sum of all InWn terms remains a constant.

The moment of Inertia of the system is the rotational inertia of the system which is a measure of the ease with which the system can be set into rotation. This depends on the mass of the system, the way it is distributed and the axis about which it has to be rotated.

Another quantity involved in the product IW is the angular velocity W. This is a vector quantity which is taken to be positive if the rotation is in counter clockwise direction and negative for clockwise rotation.

The system here can be treated like a combination of two parts 1) The umbrella part and 2) The platform with chair.

If I1, I2 and W1, W2 are taken as the moment of inertia and angular velocities of part 1 and 2 respectively, then the initial total angular momentum can be given as I1W1+I2W2. Since W1 = 0 and W2=0, this sum will also be zero when the system is undisturbed.

When the umbrella part is rotated in some direction, W, is no more equal to zero and the product I1W1 also gets some value.

As a result, the platform rotates in opposite direction so that I2W2 has a magnitude exactly same as I1W1 but with opposite sign so that their sum is once again zero.