find the moment of inertia about an axis AA which passes through the centre of mass of two particles m1 - Physics - System Of Particles And Rotational Motion

Question

find the moment of inertia about an axis AA which passes through
the centre of mass of two particles m1 and m2 at a distance r from
each other

Ujjval Chauhan · Accepted Answer

Dear student

Let the centre of mass is at position R from mass m1 then R=m1×0+m2×rm1+m2=m2×rm1+m2and distance of centre of mass from m2 will be =r-R=r-m2×rm1+m2=m1×rm1+m2So the moment of inertia of the system I=m1m2×rm1+m22+m2m1×rm1+m22I=r2m1m22+m12m2m1+m22I=m1m2m1+m2r2

find the moment of inertia about an axis AA which passes through the centre of mass of two particles m1 and m2 at a distance r from each other.