1. Angular Momentum 角动量
M&I Chapter 11

2. Three fundamental principles
Momentum principle
Energy principle ?

3. Ferris wheel 摩天轮

4. Think about the Earth orbiting the Sun.
What is conserved during the orbit?

5. Think about the Earth orbiting the Sun.
What is conserved during the orbit?
Answer:
The translational angular momentum with respect to the Sun.
Angle between r and p

6. What is the direction of the vector ?
The direction depends on the direction of rotation.
It is perpendicular (垂直) to both and .

7. Your turn…

8. Your turn…
What is the direction of the angular momentum of the planet?

9. Comet

10. Angular momentum from the vector cross product
Translational angular momentum around a point A:
Magnitude:
Direction:

11. Your turn…

12. Your turn…

13. Your turn…

14. Your turn…

15. Your turn…
A comet orbits the Sun, in the xy plane. Its momentum is shown by the red arrow. What is the direction of the comet’s angular momentum about the Sun?

16. Example…
Earth orbiting around the Sun.

17. Rotational angular momentum
Let’s look at the bicycle wheel again.
What is the total angular momentum of the wheel around its center of mass? ω

18. Rotational angular momentum
Let’s look at the bicycle wheel again.
What is the total angular momentum of the wheel around its center of mass? ω

19. Rotational angular momentum
Let’s look at the bicycle wheel again.
What is the total angular momentum of the wheel around its center of mass? ω
The rotational angular momentum of a rigid body around its center of mass:

20. Rotational angular momentum
Let’s look at the bicycle wheel again.
What is the total angular momentum of the wheel around its center of mass? ω
The rotational angular momentum of a rigid body around its center of mass:
(If the body is planar, or symmetrical around its axis of rotation.)
对称的

21. Your turn…

22. QUIZ