Question

For a system of n particles, show that if the total angular momentum about the centroid is nonzero at some time, then it is not possible at any time for all the particles to come together at a single point.

Answer 1

Angular momentum of a particle= m*r*v sin, where m is mass, r is position, v is velocity and is the angle between r and v.

According to law of conservation of angular momentum,if there is no net external torque acting on a system, then total angular momentum of the system is conserved.

Initially, the system of n particles was having non zero angular momentum about the centroid.

Assume that they come together to a point A. Then, the centroid of the system of particles is also at point A. Now, about the centroid, position r for each particle is zero. So, angular moemntum for each particle about the centroid is zero, which implies , total angular momentum of the system of particles is zero. This violates the law of conservation of angular momentum.

So, the particles cannot come together at a single point.