Two gear wheels are such that, when they are engaged, their angular speeds are inversely proportional to their radii. One has a radius a and moment of inertia pa² about its axis of rotation. The other gear wheel has radius b and moment of inertia qb² . The first is rotating with angular speed  when it engages with the second which is initially at rest.
i) By considering the change in angular momentum of each wheel separately, find the impulse between the teeth of the gear wheels when they engage.
ii) Find the angular speed of each wheel.
iii) Why is the angular momentum not conserved?
iv) Find the energy lost when the gears engage.