Where
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M = S mi A = acceleration of COM
Fext = sum of all external forces acting on system of particles Instead of treating extended bodies as single particles , we can now treat them as systems of particles .
We can obtain the translational component of their motion , i . e . the motion COM of the system , by taking the mass of the whole system to be concentrated at the COM and all the external forces on the system to be acting at the centre of mass .
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When a bomb explodes in a parabolic path , different fragment goes in different path with complex trajectories , but COM continues to travel in the same parabolic path .
Example - A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor . If the child gets up and runs about on the trolley in any manner , what is the speed of the CM of the ( trolley + child ) system ?
Solution – In this case if we take ( trolley + child ) as a system , there is no external force involved . The force involved in running of child ( friction ) becomes internal , so the speed of CM of this system remains constant .