1. Rotation (转动)

3. Neutron star (中子星), spinning 30 times a second

4. Spiral galaxy, spinning once every 50 million years

5. Even electrons spin (but how…? Do they have a radius?)

6. More about multiparticle systems

7. System of particles
There is a special position (位置) in a system of particles that moves as if
all of the system’s mass was concentrated (集中) at that point.
Environment
System

8. System of particles This position is called the center of mass (质心).
Environment
This position is called the
center of mass (质心).
We often just call it the COM.
System

9. Even though the diver’s body is rotating (转动) in a complicated way, his center of mass moves just like a single particle would.
Path followed by center of mass

10. Definition of the center of mass:

11. Now, differentiate this equation with respect to time :

12. Now, differentiate this equation with respect to time :
(assuming… what?)
The total momentum of an object is equal to its total mass times its center of mass velocity.

13. Path followed by center of mass
Momentum principle:
Path followed by center of mass

14. Example: Hockey pucks (冰球)

15. Example: Hockey pucks (冰球)
After pulling for a short time Δt, which of the following is true?
(Use the momentum principle.)
Puck 1 moves faster than puck 2
Puck 2 moves faster than puck 1
Both pucks have the same velocity

16. Example: Hockey pucks (冰球)
After pulling for a short time Δt, is there any difference between the pucks’ energy?
How much work was done by the hand in each case?
What types of energy does each puck have?

17. Separation of kinetic energy
[For solid objects (刚体), we assume no vibration.]

18. A rigid body, rotating with constant period T around a fixed axis.
Angular speed
A rigid body, rotating with constant period T around a fixed axis.

19. Angular speed
Greek letter omega

21. where r is the distance to the axis of rotation.

22. Example: Playing a CD ω
As a CD rotates, it must pass over the laser (激光) at a constant linear speed of v = 1.2 m/s.
So the angular speed ωof the CD must keep changing as the laser moves from the inside to the outside.

23. ωstart r1 Example: Playing a CD
At the start, the laser is a distance r1 = 2.3 cm from the center.
Since v = 1.2 m/s , what is ωstart? r1

24. ωend r2 Example: Playing a CD
At the end, the laser is a distance r2 = 5.9 cm from the center.
Since v = 1.2 m/s , what is ωend? r2