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Unformatted text preview: 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 m r ( t ) . (1) Theorem A: Momentum and the Center of Mass Motion Because P ( t ) = X m r ( t ) = d dt X m r ( t ) = d dt h M 1 M X m r ( 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 systems 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 -th particle within the system experiences two forces in general: a force F ( e ) ( 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 r ( t ) = F ( e ) ( t...
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