1) Inertia and Kinetic Energy

Question 1

Explain why a roundabout speeds up when the user moves towards the centre of the roundabout.

Answer 1

• Angular momentum must be conserved.

- So if I decreases ω must increase.

Question 2

Explain where an increase of rotational kinetic energy of a roundabout would come from.

Answer 2

Work done as the user moves towards the centre.

Question 3

Explain how a diver moving his legs towards his chest causes the moment of inertia of the diver about the axis of rotation to decrease.

Answer 3

• I = mr^2.

- With legs close to his chest, there is more mass at a smaller r, so I is smaller.

Question 4

Explain in terms of angular momentum why the angular velocity of the diver varies during the dive.

Answer 4

• Angular momentum must be conserved.

- As I decreases, ω increases to maintain Iω constant

Question 5

State in words the quantities in rotational dynamics that are analogous to force and mass in translational dynamics.

Answer 5

• Force: Torque.

- Mass: Moment of Inertia.