If you forget everything in this chapter, be proud that you at least remember this:

1. If you forget everything in this chapter, be proud that you at least remember this: • The Angular Momentum of any closed system is • always Constant, no ifs, ands, or buts.

2. Rolling Objects (without slipping) Kinetic Energy of a moving object Kinetic Energy of a rotating object Kinetic Energy of a rolling object (moving and rotating)

3. O. O. . P . P Friction on a Rolling Object F N Mg R  ( Mg

4. N  Mg sin  R  ( Mg

5. Torque about a Reference Point y  F F )  r O x

6. Angular Momentum of a Particle y  mv p = mv  r  O x r

7. Newton’s Second Law, with a twist System of Particles More about Angular Momentum    L = 

8. Angular Momentum of a rotating fixed body   Conservation of Angular Momentum     Even more about Angular Momentum Angular momentum of any closed system is always conserved

9. Angular Momentum must be conserved for this object rotating on a fixed axis Ifm=2.0 kg·m2 f=?? Iim=6.0 kg·m2 i=1.2 rev/s Ip=3.0 kg·m2

10. Looking at Kinetic Energy If=5.0 kg·m2 f=2.2 rev/s Ii=9.0 kg·m2 i=1.2 rev/s

11.  y x z Collisions with Angular Momentum M (  v m

12. y x z Collisions with Angular Momentum f=??

13.  y x  z 2 O. M (  v r Angular Momentum is constant m

14.  y x  z 2 O.

15.  y x  z 2 O.

16. Angular Momentum is always Constant