Centre of Mass — Chapter Summary

The centre of mass is

The centre of mass is the point whose motion represents the motion of the entire system. If external force acts on a system, the system moves as if it

For two particles of masses m1

For two particles of masses m1 and m2 at position vectors r1 and r2, the centre of mass is given by the weighted mean of their position vectors. It li

For n particles

For n particles, the centre of mass is the mass-weighted average of all their position vectors. In Cartesian form, each coordinate is found by adding

For a continuous body

For a continuous body, the centre of mass is found using integration over small mass elements. The vector form is the mass-weighted integral of positi

A uniform rod has mass evenly

A uniform rod has mass evenly distributed along its length, so its centre of mass lies at the midpoint. For a rod with non-uniform mass per unit lengt