# Kepler’s Second Law using the rotation of a stool

#### Apparatus and materials

Rotating stool or platform

Masses, 2 kg, 2

#### Health & Safety and Technical notes

Supervise students so they don't spin too quickly, or they may topple over.

A freely spinning music stool - or office chair - may be used for these demonstrations. It should be oiled before use.

#### Procedure

a Sit a student on the stool and ask them to hold a massive object, about 2 kg, in each hand with their arms stretched out sideways. Turn the stool so that it rotates fairly rapidly.

b Ask the student on the stool to draw in their arms, so holding the ‘planets’ tightly to their chest.

c Ask them to stretch their arms out again.

#### Teaching notes

1 This demonstration shows the conservation of angular momentum when the radius of the rotating mass is changed. As some parts of a spinning object are pulled in to make it more compact, then the object spins faster.

Newton gave a geometrical proof of Kepler’s Second Law, using changes of momentum (a vector). The Law is simply a statement of the conservation of angular momentum. The only force acting on a planet (gravity) is always directed towards the Sun.

2 Other examples if Kepler’s Second Law include the following:

• Suppose a high diver doing a somersault discovers half way down in his flight that he is going to hit the water feet first, when this is not his plan. He can double up, knees against the chest, and spin faster for a carefully judged time. To spin slower, the arms are spread out wide.
• A skater starts spinning slowly on one toe with arms stretched out and the body tilted. She then pulls herself upright with arms folded and spins very fast.
• The much more complicated movement of a falling cat, which always lands on its feet.

This experiment was safety checked in March 2008