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Ch 17 Notes – Part 2

Explore the intricacies of rotational motion with this comprehensive guide. Understand concepts like fixed axis rotation, normal and tangential axes, rotational inertia, and the parallel axis theorem. Learn how to apply these principles to solve complex problems in mechanics. This resource covers examples and exercises to help you enhance your understanding of rotational dynamics. Whether you're a student or a physics enthusiast, this guide will deepen your knowledge of rotational mechanics.

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Ch 17 Notes – Part 2

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  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

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