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Motion of Centre of Mass

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Motion of centre of Mass

The centre of mass of a system of particles moves as if the entire mass of the system were concentrated at the centre of mass and all the external forces were applied at that point. Velocity of centre of mass of a system of two particles, m1 and m2 with velocity v1 and v2 is given by,

`"V"_("cm") = ("m"_1"v"_1 + "m"_2"v"_2)/("m"_1+"m"_2)`

Acceleration of centre of mass, acm of a two body system is given by,

`a_(cm) = ("m"_1"a"_1 + "m"_2"a"_1)/("m"_1 + "m"_2)`

If no external force acts on the body, then the centre of mass will have constant momentum. Its velocity is constant and acceleration is zero, i.e., Mv = constant.

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