2. What if our system is the whole universe?
No “surroundings”, so the angular momentum principle says:

3. The angular momentum of the universe is conserved.
System

4. For any choice of system:
Angular momentum is transferred between system and surroundings. Never created, never destroyed.

5. If the system has no interactions with the surroundings, there are no external torques on the system, so:
System
Surroundings

6. If the system has no interactions with the surroundings, there are no external torques on the system, so:
System
Surroundings

7. Symmetry of physical laws
Emmy Noether’s theorem (1915)
Conserved quantity
Momentum
Energy
Angular momentum
Symmetry of physical laws
Translation
Time
Rotation

8. Conservation of angular momentum
角动量守恒

9. Any external torques acting on the skater are small, and we will ignore them.
Angular momentum principle (around skater’s COM):

10. The skater spins faster when she pulls her arms in.
Where does the extra energy come from?

11. Example: A bullet fired into a door
A police officer fires a bullet into the center of a door. The bullet gets stuck inside the door.
What is the angular speed of the door just after it is hit by the bullet? A
m = 0.01 kg
d = 1.0 m
v = 400 m/s
M = 15 kg

12. Gyroscope 陀螺仪
This change in the direction of the rotation axis is called precession.
We can understand it using the angular momentum principle:

13. The initial angular momentum is in the x direction.
The torque acting on the gyroscope around the pivot (point A) is:
in the y direction. y x

14. Angular momentum principle:y y x x