Sit on a revolving chair, holding gym weights or a large unopened tin of baked beans in each hand, and hold your arms out straight.
Ask one of your students to gently push the chair so that you revolve slowly. After making a slow revolution bring your hands into the centre.
You should find that you noticeably speed up. If you are going too fast, hold you hands out horizontally again and you will slow down.
You can also try this using a playground roundabout. Stand on the roundabout, holding on with both hands, and lean backwards. Ask someone to give you a gentle push. You will revolve quite slowly. Now lean inwards and you will increase speed dramatically. Lean outwards to slow down.
Angular momentum is the product of angular velocity and the moment of inertia. The angular velocity is the speed at which you rotate, measured in degrees per second. The moment of inertia is dependent on the mass of an object and how that mass is distributed. If the mass is a long way from the rotation axis then the object has a large moment of inertia. Therefore, when you are holding the tins at arm's length, you have a large moment of inertia. When you move the tins towards the centre, the moment of inertia decreases. In order to conserve angular momentum the angular velocity has to increase, and you speed up.