Lecture 25 Translational motion the gravitational external force acts on the center of mass Rotational motion object rotates about center of mass Note that the mass may be accelerating Fixed Axis Rotation and Translation Example For straight line motion the bicycle wheels rotate about a xed direction and the center of mass translates 1 s x slipping 2 s x rolling without slipping 3 s x skidding Rolling without slipping s x R 0 v t v R v Rw The sign depends on the choice on linear coordinate system and rotational coordinate system Translational Motion of Center of Mass Newton s Second and Third Laws The momentum of a system remains constant unless the system is acted on by an external force in which case the acceleration of center of mass satis es Impulse changes center of mass momentum F I Fixed axis rotation about the center of mass of a rigid body The total external torque produces an angular acceleration about the center of mass is the moment of inertial about the center of mass is the angular acceleration about the center of mass is the angular momentum about the center of mass Angular Momentum for two dimensional rotation and translation The angular momentum for a translating and rotating object is given by Angular momentum arising from translational of center of mass The second term is the angular momentum arising from rotation about the center of mass Kinetic Energy of Rotation and Translation Kinetic energy of rotation about center of mass Translational kinetic energy Kinetic Translational Motion Velocity Vectors
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