1. Lecture 8 Vector Mechanics for Engineers: Dynamics MECN 3010 Department of Mechanical Engineering Inter American University of Puerto Rico Bayamon Campus Dr. Omar E. Meza Castillo omeza@bayamon.inter.edu http://www.bc.inter.edu/facultad/omeza

2. Lecture 8 MECN 3010 Inter - Bayamon 2 Tentative Lecture Schedule TopicLecture Kinematics of a Particle 1,2,3,4 Kinetics of a Particle: Force and Acceleration 5 Kinetics of a Particle: Work and Energy 6 Planar Kinematics of a Rigid Body 7 8

3. Lecture 8 MECN 3010 Inter - Bayamon Force and Acceleration Topic 5: Planar Kinematics of a Rigid Body 3 "Lo peor es educar por métodos basados en el temor, la fuerza, la autoridad, porque se destruye la sinceridad y la confianza, y sólo se consigue una falsa sumisión” Einstein Albert

4. Lecture 8 MECN 3010 Inter - Bayamon Chapter Objectives  To introduce the methods used to determine the mass moment of inertia of a body.  To discuss applications of these equations to bodies undergoing translation, rotation about a fixed axis, and general plane motion. 4

5. Lecture 8 MECN 3010 Inter - Bayamon 17.1 Mass Moment of Inertia 5

6. Lecture 8 MECN 3010 Inter - Bayamon 17.1 Mass Moment of Inertia: Procedure for Analysis 6

7. Lecture 8 MECN 3010 Inter - Bayamon Parallel-Axis Theorem: If the moment of inertia of the body about an axis passing through the body’s mass center in known, then the moment of inertia about any other parallel axis can be determined by using the parallel-axis theorem. 17.1 Mass Moment of Inertia 7

8. Lecture 8 MECN 3010 Inter - Bayamon Radius of Gyration: Occasionally, the moment of inertia of a body about a specified axis is reported in handbooks using the radius of gyration, k. This is a geometrical property which has unit of length. When it and the body’s mass m are known the body’s moment of inertia is determined from the equation Composite Bodies: Composite Bodies: 17.1 Mass Moment of Inertia 8

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17. Lecture 8 MECN 3010 Inter - Bayamon 17.2 Planar Kinetic Equations of Motion  Equation of Translational Motion This equation is referred to as the translational equation of motion for the mass center of a rigid body. It states that the sum of all the external forces acting on the body is equal to the body's mass times the acceleration of its mass center G 17

18. Lecture 8 MECN 3010 Inter - Bayamon 17.2 Planar Kinetic Equations of Motion 18

19. Lecture 8 MECN 3010 Inter - Bayamon 17.2 Planar Kinetic Equations of Motion  Equation of Translational Motion 19

20. Lecture 8 MECN 3010 Inter - Bayamon 17.2 Planar Kinetic Equations of Motion 20

21. Lecture 8 MECN 3010 Inter - Bayamon 17.2 Planar Kinetic Equations of Motion 21

22. Lecture 8 MECN 3010 Inter - Bayamon 17.2 Planar Kinetic Equations of Motion 22

23. Lecture 8 MECN 3010 Inter - Bayamon 17.2 Planar Kinetic Equations of Motion  General Application of the Equations of Motion 23

24. Lecture 8 MECN 3010 Inter - Bayamon 17.3 Equations of Motion: Translation  Rectilinear Translation 24

25. Lecture 8 MECN 3010 Inter - Bayamon 17.3 Equations of Motion: Translation  Curvilinear Translation 25

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31. Lecture 8 MECN 3010 Inter - Bayamon 17.4 Equations of Motion: Translation  Equations of Motion : Rotation about a Fixed Axis 31

32. Lecture 8 MECN 3010 Inter - Bayamon 17.4 Equations of Motion: Translation  Equations of Motion : General Plane Motion 32

33. Lecture 8 MECN 3010 Inter - Bayamon Homework6  Blackboard 33