Moment of Inertia of Systems Practice Problems

Coins can be treated as discs. A dummy coin has an inner uniform solid disc with a diameter of 120.0 cm and an area density of 4.00 g/cm², which is encircled by a concentric ring with inner and outer diameters of 120.0 cm and 160.0 cm and an area density of 2.50 g/cm². Find the coin's moment of inertia around an axis that passes through its center and is perpendicular to its plane.

Two little balls are bonded to the ends of a uniform bar. The balls can be thought of as point masses and have masses of 0.200 kg each, but the bar is 3.00 m long and has a mass of 5.00 kg. Find the combination's moment of inertia about an axis parallel to the bar across both balls.

A rectangle measures 30 cm by 50 cm. Point masses weighing 420 g are fitted on each of the four corners. Assume the connecting rods between the point masses have negligible mass. Find the moment of inertia of the system about an axis perpendicular to the square and passes through i) one of the corners and ii) the center of the short edge (point p).

You oversee projects for a business that produces goods. A thin, uniform rod measuring 60.0 cm in length and weighing 0.400 kg is one of the machine parts being assembled on the assembly line. One of your engineers has suggested that you bend the rod at its center into a V-shape with a 30.0^o angle at its vertex in order to lessen the moment of inertia. What would this bent rod's moment of inertia be at its vertex, which is an axis perpendicular to the plane of the V?

Two little balls are attached to the ends of a uniform bar. The mass of the 2.00 m long, 4.00 kg long bar is greater than that of the individual balls, which are point masses with masses of 0.300 kg each. Find the combination's moment of inertia about an axis passing between one of the balls and the bar that is perpendicular to it.

There are two tiny balls affixed to the ends of a uniform bar. The balls can be thought of as point masses and have masses of 0.300 kg each, whereas the bar is 2.00 m long and has a mass of 4.00 kg. Find the combination's moment of inertia around an axis that passes through the middle of the bar and is perpendicular to it.