Two point masses a 6 kg mass and an 18 kg mass are connected by a mass less rod 6 meters long. calculate the distance of the center of mass from the 18 kg mass. calculate the moment of inertial about an axis located at the center of mass that is perpendicular to the rod.

The center of mass is given by:

∑mx/∑m

m is the mass of each object

x is the position of each object

We will assign x = 0m to the 18kg mass, therefore x = 6m for the 6kg mass.

∑mx/∑m = (18×0+6×6)/(18+6) = 1.5m

The center of mass is located 1.5m away from the 18kg mass.

The total moment of inertia of the system about the center of mass is given by:

I = ∑mr²

I is the moment of inertia

m is the mass of each object

r is the distance of each object from the center of mass

We know r = 1.5m for the 18kg mass and the rod is 6m long, therefore the 6kg mass must be r = 4.5m from the center of mass.

I = 18(1.5)² + 6(4.5)²

I = 162kg×m²