The Angular Momentum Principle for a Single Point Particle

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

2. Torque at angle Clicker A B C 1. Which case corresponds to largest torque? 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

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

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

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

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

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. Multiparticle System m1 m2 m3 A Net torque caused by internal forces cancels out! So, we’ve established that

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