Question

Two point masses m1 and m2 are separated by a massless rod of length L.
a) Write an expression for the moment of inertia about an axis perpendicular to the rod and passing through it at a distance X from mass m1 .
Calculate d/dx and show that I is at a minimum when the axis passes through the center of mass of the system.

Answer 1

Explanation:

we need to express the moment if inertia relative to the axis S passing through point O.

The moment of inertia due to a point mass m is

IM= mr^2

when m is the mass and r the distance from the mass to the axis. In such fashion,the moment if m1 and m2 to S

Total moment of inertia.

I sist= i1+i2

finally the moment if interia of the rod and masses relative to S is,

I sist=mx^2+m(L-x)^2