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LinearMomentum

LinearMomentum - Linear Momentum Shina Tan Denition The...

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Linear Momentum Shina Tan Definition– The total linear momentum of any system is defined to be the vector sum of the linear momenta of all its constituent parts: 1 2 P = X α m α ˙ r α ( t ) . (1) Theorem A: Momentum and the Center of Mass Motion Because P ( t ) = X α m α ˙ r α ( t ) = d dt X α m α r α ( t ) = d dt h M 1 M X α m α r α ( t ) i = d dt [ M R ( t )] = M ˙ R ( t ) , we find P ( t ) = M ˙ R ( t ) . (2) Theorem A– The total linear momentum of any system is equal to its total mass times the velocity of the center of mass. In particular, if a system’s center of mass is not moving, its total linear momentum is zero, even though its individual parts may be moving. Theorem B: Rate of Change of the Momentum The α -th particle within the system experiences two forces in general: a force F ( e ) α ( t ) whose origin is external to the system, and the sum of forces acting on the particle by all other particles within the system: m α ¨ r α ( t ) = F ( e ) α ( t ) + X β f αβ ( t ) .

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