1. 1 Lecture #4 Angular Momentum And moment of inertia And torque And Central force Moment of Inertia Difference between it and CM Worked examples :10

2. 2 Analogies between Linear and Angular motion equations :45

3. 3 Relating Angular Momentum and Torque :50

4. 4 Angular Momentum and Central Forces :45 If doing an integral, usually need to rewrite, for example:

5. 5 Derivation of moment of inertia and “B” :45 Completely general For object perpendicular to rotation axis

6. 6 Moment of Inertia vs. Center of Mass For a multi-particle discrete mass-distribution For a continuous mass-distribution. :45

7. 7 Parallel Axis Theorem :55 CM Axis 1 (through CM) Axis 2 (Parallel to axis 1) a

8. 8 Derivation of parallel axis theorem :45 O’ O

9. 9 Moment of Inertia worked problem :60   Calculate the moment of inertia and kinetic energy of a wire of uniform mass-density lambda, mass M,  and length L. A) If rotated about axis at midpoint at angular velocity   B) If rotated about axis at endpoint at angular velocity   L

10. 10 Moment of Inertia worked problem #2 :60 Show moment of inertia of a sphere (about it’s CM) is 2/5MR^2 by proper integration in spherical coordinates!

11. 11 Worked Example L3-1 – Discrete masses Given m 1 to m 10 m  = m m  = 3m y x y x O1O1 O2O2 1 unit 2 units Calculate Given origin O1O1 For homework given O 2 :30

12. 12 Lecture #4 Wind-up. We are done w/ chapters 1 and 3, read all. Assignment includes Taylor /Supplement / Lecture probs. :72