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Mechanical Engineering Dynamics ME 201 Lecture #35 Moment of Inertia

This lecture covers Moment of Inertia, Parallel Axis Theorem, and Radius of Gyration for composite bodies. Learn how to apply equations for translation and rotation motion, discuss slipping vs. tipping, and explore general applications of motion equations.

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Mechanical Engineering Dynamics ME 201 Lecture #35 Moment of Inertia

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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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