# sys - internal force on the ith particle M A = Σ i F net...

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Dynamics of a N-particle system Consider a system of N particles. The mass of this system may be written, M Σ i m i , where the sum on i runs from i = 1 to i = N. For this system we define a new vector called the center of mass position vector , R (1/M) Σ i m i r i . Differentiation of R gives the velocity and acceleration of the center of mass and the total momentum of the system P , V d R /dt = (1/M) Σ i m i v i and A d V /dt =(1/M) Σ i m i a i . P M V = Σ i m i v i Using Newton’s second law in the sum in A we may make the replacement, m i a i = F i,net . Therefore, M A = Σ i F i,net .

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We write, F i,net = F net i,ext + F net i,int , where we have separated the net force into the net external and net
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Unformatted text preview: internal force on the ith particle. M A = Σ i F net i,ext + Σ i F net i,int . The last sum vanishes on using Newton’s third law, and we have M A = Σ i F net i,ext = F net,ext This last result may also be written F net,ext = d P /dt = M A = Md V /dt = Md 2 R /dt 2 , where P is the momentum of the system. This result is really the same as that for a single particle. In conclusion, the center of mass moves as a particle of mass M, position R , velocity V , momentum P , acceleration A , acted on by F net,ext . Examples[in class]...
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## This note was uploaded on 07/29/2011 for the course PHY 2048 taught by Professor Chen during the Spring '08 term at UNF.

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sys - internal force on the ith particle M A = Σ i F net...

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