Question

Three objects are attached to a massless rigid rod that has an axis of rotation as shown. Assuming all of the mass of each object is located at the point shown for each, calculate the moment of inertia of this system.

Answer 1

I cannot see diagram.

First calculate center of mass,
x = (m1 x1 + m2x2 + m3 x3)/(m1+m2+m3)
y = etc.

Next define r as distance from center of mass, around which object will rotate.

I = sum (mi * ri^2) = m1 r1^2 + m2 r2^2 + m3 r3^2.

I is your moment of inertia around center of mass.

Around another point h away from c.m. add total mass times h^2 to this.