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 Inter - Bayamon MECN 3010 Tentative Lecture Schedule Topic Lecture 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 Planar Kinematics of a Rigid Body 8 2 Lecture 8 Inter - Bayamon "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 Topic 5: Planar Kinematics of a Rigid Body MECN 3010 Force and Acceleration 3 Lecture 8 Inter - Bayamon MECN 3010 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 Lecture 8 Inter - Bayamon MECN 3010 17.1 Mass Moment of Inertia 5 Lecture 8 Inter - Bayamon MECN 3010 17.1 Mass Moment of Inertia: Procedure for Analysis 6 Lecture 8 Inter - Bayamon 17.1 Mass Moment of Inertia 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. I r 2 dm d x ' y'2 dm m 2 m x '2 y'2 dm 2d x ' dm d 2 dm MECN 3010 m m I I G md 2 m 7 Lecture 8 Inter - Bayamon 17.1 Mass Moment of Inertia 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 I mk 2 or k I m MECN 3010 Composite Bodies: 8 Lecture 8 MECN 3010 9 Lecture 8 Inter - Bayamon MECN 3010 10 Lecture 8 Inter - Bayamon MECN 3010 11 Lecture 8 Inter - Bayamon MECN 3010 12 Lecture 8 Inter - Bayamon MECN 3010 13 Lecture 8 Inter - Bayamon MECN 3010 14 Lecture 8 Inter - Bayamon MECN 3010 15 Lecture 8 Inter - Bayamon MECN 3010 16 Lecture 8 Inter - Bayamon Inter - Bayamon 17.2 Planar Kinetic Equations of Motion MECN 3010 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 Lecture 8 Inter - Bayamon MECN 3010 17.2 Planar Kinetic Equations of Motion 18 Lecture 8 Inter - Bayamon MECN 3010 17.2 Planar Kinetic Equations of Motion Equation of Translational Motion 19 Lecture 8 Inter - Bayamon MECN 3010 17.2 Planar Kinetic Equations of Motion 20 Lecture 8 Inter - Bayamon MECN 3010 17.2 Planar Kinetic Equations of Motion 21 Lecture 8 Inter - Bayamon MECN 3010 17.2 Planar Kinetic Equations of Motion 22 Lecture 8 Inter - Bayamon MECN 3010 17.2 Planar Kinetic Equations of Motion General Application of the Equations of Motion 23 Lecture 8 Inter - Bayamon MECN 3010 17.3 Equations of Motion: Translation Rectilinear Translation 24 Lecture 8 Inter - Bayamon MECN 3010 17.3 Equations of Motion: Translation Curvilinear Translation 25 Lecture 8 MECN 3010 26 Lecture 8 Inter - Bayamon MECN 3010 27 Lecture 8 Inter - Bayamon MECN 3010 28 Lecture 8 Inter - Bayamon MECN 3010 29 Lecture 8 Inter - Bayamon MECN 3010 Lecture 8 Inter - Bayamon Inter - Bayamon MECN 3010 17.4 Equations of Motion: Translation Equations of Motion : Rotation about a Fixed Axis 31 Lecture 8 Inter - Bayamon MECN 3010 17.4 Equations of Motion: Translation Equations of Motion : General Plane Motion 32 Lecture 8 Inter - Bayamon MECN 3010 Homework6 Blackboard 33 Lecture 8