1. Rigid body rotating around a point A
Linear motion

2. 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

3. 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

4. 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:

5. 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

6. Example:
A thin rod of mass M and length L has two small balls of mass m stuck to its ends.
The system rotates around its center of mass with angular speed ω.
What is the rotational angular momentum (around the center of mass)? ω M m m L ω

7. M m m L ω Example: What happens if we move the axis of rotation here?
Find the total angular momentum (around the new center of rotation). ω

8. Three fundamental principles
Momentum principle
Energy principle ?

9. Angular momentum principle
Greek letter “tau”
Instantaneous version:
where is the torque (力矩) around the point A.

10. Torque …and much easier here, further from the hinges.
It is hard to close the door by pushing here…

11. Calculating torque: method 1
Direction of torque from right-hand rule.
The component of the force perpendicular to r is F sin φ. Then

12. Calculating torque: method 2
“lever arm”

13. Calculating torque: method 3
Magnitude:

14. Example

15. Example

16. Example