The sum of moments of all the particles in a system about its center of mass is always______

Step-by-step solution

Assume a system of three particles having mass m 1 ,   m 2  and   m 3   located at a distance of r 1 ,   r 2   and   r 3   from the centre of mass. If centre of mass of the system is at origin, r → = m 1 r 1 → + m 2 r 2 → + m 3 r 3 → m 1 + m 2 + m 3 = 0   then, m 1 r 1 → + m 2 r 2 → + m 3 r 3 → = 0 Sum of moments of particles in a system about centre of mass is, τ com = m 1 r 1 a + m 2 r 2 a + m 3 r 3 a = a m 1 r 1 + m 2 r 2