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Lecture21

Lecture21 - Motion of the CM Trajectory of the CM When a...

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Motion of the CM Motion of the CM cm a M F G G = ext net v P G G = total The CM is a good “representation” of the extended object. Internal forces among the parts may change the velocities and accelerations of the parts, but the velocity of the CM of a system remains constant unless it is acted on by an external force. Conservation of linear momentum Constant velocity of center of mass = Trajectory of the CM When a shell explodes, the CM keeps moving along the parabolic trajectory the shell had before the explosion. Reference frame of the CM Motion of a system of particles can be broken down to: 1. Motion of each particles relative to the CM 2. Motion of the CM relative to the lab In particular, for the kinetic energy: = i m K 2 lab , lab system, 2 1 + = 2 lab CM, CM , ) ( 2 1 G G 2 lab CM, lab CM, CM i, 2 CM i, 2 1 2 2 1 2 1 ii + + = ∑∑ G G 2 lab CM, 2 CM i, 2 1 2 1 Mv + = 0 CM CM, CM i, = = G G Velocity of the CM relative to the CM lab CM, CM system, lab system, + = lab CM, CM system, + = System of particles System of particles • The momentum of the system is the momentum of the center of mass • The kinetic energy of a system is the kinetic energy of the center of mass plus the kinetic energy of the parts of the system relative to the center of mass. Phy 221 2007S Lecture 21 N’s First Laws of C of M motion The velocity of the C of M of a system remains constant unless it is acted on by an external force. – Note: Internal interactions within the system do not alter this assertion. • By conservation of momentum does not change if there are no external forces. P v M cm G G = Phy 221 2007S Lecture 21 N’s Second Laws of C of M motion • The total external force on a system is equal to (the total mass)(acceleration of CofM) • Note however that how that net force is applied makes a difference in terms of what happens within the system. external tot cm F F a M G G G = =

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Phy 221 2007S Lecture 21 Lecture 21 Rotation of a Rigid body Phy 221 2007S Lecture 21 Today’s Lecture Today’s Lecture • Review circular motion • Energy of rotational motion • Moment of inertia Phy 221 2007S Lecture 21 Review of circular motion ; ; dd dt θ ω θω α == vR = y x s R Relation to linear quantities: s = R Description in terms of angular quantities (in radians!): tan aR = Centripetal acceleration 2 2 c v a tan c total Phy 221 2007S Lecture 21 The right-hand rule •In 3D ω is a vector defined by the right-hand rule •Curl fingers of right hand in the direction of motion.
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Lecture21 - Motion of the CM Trajectory of the CM When a...

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