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King Fahd University of Petroleum & Minerals

King Fahd University of Petroleum & Minerals. Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 35. Objective. Moment of Inertia of a body Parallel Axis Theorem Radius of Gyration Moment of Inertia of Composite Bodies. Parallel Axis Theorem.

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King Fahd University of Petroleum & Minerals

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  1. King Fahd University of Petroleum & Minerals Mechanical Engineering Dynamics ME 201 BY Dr. Meyassar N. Al-Haddad Lecture # 35

  2. Objective • Moment of Inertia of a body • Parallel Axis Theorem • Radius of Gyration • Moment of Inertia of Composite Bodies

  3. Parallel Axis Theorem • The moment of inertia about any axis parallel to and at distance d away from the axis that passes through the centre of mass is: • Where • IG= moment of inertia for mass centre G • m = mass of the body • d = perpendicular distance between the parallel axes.

  4. Radius of Gyration

  5. Mass Center Example

  6. Objectives • Apply the Equation of Translation motion • Rectilinear Translation • Curvilinear Translation • Apply the equation of Rotation motion • The roll of the center of mass G • Discuss the slipping Vs. Tipping • Discuss the slipping Vs. freely rotating • Discuss the “wheely” Vs. Non-wheely

  7. General Application of the Equations of Motion Summation of moment in FBD = summation of the kinetic moment in K.D

  8. Rectilinear Translation

  9. Curvilinear Translation

  10. x N Discuss the slipping Vs. Tipping If x > 1.5 ft tipping If x < 1.5 ft slipping

  11. Slipping Vs. Freely rotating mg FA=msNA NA NB

  12. “Wheely” Vs. Non-Wheely Wheely : lift the front wheel off the ground NB=0

  13. Example 17-5

  14. Example 17-8 mBD=100kg mAB=mCD= Neglect q = 30o w = 6 rad/s TA= ? TB= ? aG=?

  15. Problem 17-43 mBNB NA NB m= 80 kg mB=0.8 NA=? NB=? When rear wheel locks for break a =? Deceleration aG

  16. Problem 17-43 a = 0 mBNB NA NB m= 80 kg mB=0.8 NA=? NB=? a =? When traveling at constant velocity and no break was applied

  17. Problem 17-44 mkNA NA NB=0 m= 80 kg NA=? NB=? a =? mk=? minimum When rider applies the front break and back wheel start to lift off the ground

  18. Rotation About a Fixed Axis

  19. Rotation About a Fixed Axis

  20. Ot Ox On Oy On Ot Pin Reaction Horizontal Reaction Vertical Reaction OR Normal Reaction Tangential Reaction

  21. Example 17-9 Start from rest q=? Number w=20rad/s Pine reaction

  22. Example 17-10

  23. Example 17-11 m=60 kg Radius of gyration kO=0.25 mb=20 kg a=? Drum a=?

  24. Example 17-12 W=50 Ib kG=0.6 ft w= 8 rad/s Pin reaction =?

  25. Frictional Rolling Problems - rolls without slipping - slides as it rolls

  26. Example 17-14 m = 8 Kg radius of gyration kG=0.3m. a=?.

  27. Example 17-15 W= 50-lb radius of gyration kG=0.70ft. aG=?.

  28. Example 17-16 m=100 kg IG=75 kg.m2 a=? The pole at rest

  29. Example 17-17

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