Class 11 Physics Rotational Motion Motion of COM

Motion of COM

• The centre of mass of a system of particles moves as if all the mass of the system was concentrated at the centre of mass and all the external forces were applied at that point.

• MA = Fext (Since the contribution of internal forces is zero, because they appear in pairs and cancel

out each other)

Where

• 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.

• 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.

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