1. Angular Momentum

2. Inertia and Velocity  In the law of action we began with mass and acceleration F = maF = ma  This was generalized to use momentum: p = mv.

3. Moment of Momentum  To continue the analysis of rotational motion, we must also extend the idea of momentum. r p

4. Applying Torque  An external torque changes angular momentum.  L  L+rpsin  p

5. Spinning Mass  The moment of inertia is the analog of mass for rotational motion.  The analog for angular momentum would be: 

6. Angular Momentum Conserved  With no net external torque, angular momentum is constant. The angular momentum of an isolated system is conservedThe angular momentum of an isolated system is conserved

7. Internal Angular Momentum  A system may have more than one rotating axis.  The total angular momentum is the sum of separate vectors. L total = L s + L w = L w  LwLw L s = 0

8. Internal Movement  Internal torques cancel out.  Conservation requires that the sum stay constant. L total = L s + (- L w ) = L w L s = 2 L w  -L w L s = 2 L w

9. Conservation  With no external torque, angular momentum is constant.  L /  t = 0  L /  t = 0 L = constant L = constant  r  I = mr 2 m r/2 I = mr 2 /4 next