1. The Angular Momentum Principle for a Single Point Particle A So, if we define a new measure of twist about the center A, the net torque about A acting on the particle, we’ve established Note how it explains the behavior we observed in the preceding examples. The angular momentum principle

2. Clicker 1. Which case corresponds to largest torque? ABCABC 2. The direction of Torque in case B is: A) into page B) out of page C) it has no direction since it is zero Torque at angle

3. Example: momentum and angular momentum principles Use the momentum principle: Use the angular momentum principle: Falling object (nonrelativistic)

4. Conservation of angular momentum Example: Important: both L’s must be about the same point (axis)

5. A comet CLICKER: What is the direction of the torque on the comet in point B about the star due to gravitational pull? A)Into the page B)Out of the page C)It is zero B (nonrelativistic) Considering the comet at points 1 and 2,

6. Clicker A ball falls straight down in the xy plane. Its momentum is shown by the blue arrow. What is the direction of the ball's angular momentum about the origin? x y A) +y B) –y C) +z (out of the page) D) –z (into the page) E) zero magnitude

7. Clicker A planet orbits a star, in a circular orbit in the xy plane. Its momentum is shown by the red arrow. What is the direction of the angular momentum of the planet in respect to the star? A) same direction as B) opposite to C) into the page D) out of the page E) zero magnitude

8. Net torque caused by internal forces cancels out! m1m1 m2m2 m3m3 A Multiparticle System So, we’ve established that

9. The angular momentum principle for a multiparticle system Recall that we can express the total angular momentum of a system as the sum its translational and rotational (or spin) angular momenta. The angular momentum principle relative to the center of mass: