Ch 15 Notes – Part 2

1. Ch 15 Notes – Part 2 15.4 Impact • Central Impact • Oblique Impact • Line of Impact • Plane of Impact

3. Ch 15 Notes – Part 2 15.4 Impact

4. Ch 15 Notes – Part 2 15.4 Impact • Coeff of Restitution • e = (vB2 – vA2)/ (vA1 – vB1) • Plastic impact, e = 0 • Elastic impact, e = 1 • Can never achieve this exactly

5. 15_015b

6. 15_FP013

7. 15_FP014

8. 15_FP015

9. 15_FP016

10. 15_FP017

11. 15_FP018

12. Ch 15 Notes – Part 2 15.5 Angular Momentum • The angular momentum of a particle about point O is defined as the “moment” of the linear momentum about O. • (Ho)z = (d)(mv), where d is the moment arm or perpendicular distance from O to the line of action of mv

13. Ch 15 Notes – Part 2 15.5 Angular Momentum • Ho = r x mv • Ho = | i j k | • | rxryrz | • | mvxmvymvz|

14. Ch 15 Notes – Part 2 15.6 Relationship Between Force and Angular Momentum • Mo = Hodot = r x mvdot • The resultant moment about O of all the forces acting on the particle is equal to the time rate of change in the particle’s angular momentum

15. Ch 15 Notes – Part 2 15.6 Relationship Between Force and Angular Momentum • F = mvdot • F = Ldot • The resultant force acting on the particle is equal to the time rate of change in the particle’s linear momentum

16. Ch 15 Notes – Part 2 15.6 Relationship Between Force and Angular Momentum for a System of Particles • Mo = Hodot • The sum of the moments about O of all the external forces acting on a system of particles is equal to the time rate of change in the system’s angular momentum about O

17. Example 15.12

18. Example 15.12 (continued)

19. Ch 15 Notes – Part 2 15.6 Relationship Between Force and Angular Momentum • When the angular impulses acting on a particle or a system of particles during time t1 to t2 are zero, angular momentum is conserved. • (Ho)1 = (Ho)2

20. Example 15.9

21. Example 15.9 (continued)

22. Example 15.10

23. Example 15.10 (continued)

24. Example 15.10 (continued)

25. Example 15.11

26. Example 15.11 (continued)

27. Example 15.11 (continued)

28. Example 15.13

29. Example 15.13 (continued)

30. Example 15.14

31. Example 15.14 (continued)

32. Example 15.15

33. Example 15.15 (continued)

34. Example 15.15 (continued)

35. 15_023

36. 15_FP019

37. 15_FP020

38. 15_FP021

39. 15_FP022

40. 15_FP023

41. 15_FP024