Ch 17 Notes – Part 2

1. Ch 17 Notes – Part 2 17.4 Rotation About a Fixed Axis • When a body rotates about O, the mass center G moves on a circular path • Therefore we can best use normal and tangential axes • (aG)t = rGα • (aG)n = 2rG

2. Ch 17 Notes – Part 2 17.4 Rotation About a Fixed Axis • Ft = m(aG)t = mrGα • Fn = m(aG)n= m2rG • MG =IGα • But, • Io = IG + mrG2 by the parallel axis theorem • So, Mo = Ioα α

3. Example 17.9

4. Example 17.9 (continued)

5. Example 17.9 (continued)

6. Example 17.10

7. Example 17.10 (continued)

8. Example 17.10 (continued)

9. Example 17.11

10. Example 17.11 (continued)

11. Example 17.11 (continued)

12. Example 17.12

13. Example 17.12 (continued)

14. Example 17.12 (continued)

15. 17_FP007

16. 17_FP008

17. 17_FP009

18. 17_FP010

19. 17_FP011

20. 17_FP012

21. Ch 17 Notes – Part 2 17.5 General Plane Motion • Fx = m(aG)x = mrGα • Fy=m(aG)y • MG =IGα α

22. Ch 17 Notes – Part 2 17.5 General Plane Motion • Or, considering a point P, other than G: • Fx = m(aG)x • Fy=m(aG)y • MP =(MP), where (MP) = Iα + maG(or its components) about P α

23. Ch 17 Notes – Part 2 17.5 General Plane Motion • If you have a uniform disk of circular shape that rolls on a rough surface without slipping, (Mk)IC becomes IICα by the PAT, so MIC = IICα α

24. Example 17.13

25. Example 17.13 (continued)

26. Example 17.13 (continued)

27. Example 17.14

28. Example 17.14 (continued)

29. Example 17.14 (continued)

30. Example 17.15

31. Example 17.15 (continued)

32. Example 17.15 (continued)

33. Example 17.16

34. Example 17.16 (continued)

35. 17_FP013

36. 17_FP014

37. 17_FP015

38. 17_FP016

39. 17_FP017

40. 17_FP018

41. 17_P104-105