A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). If this system of masses rotated about the Z-axis perpendicular to the X-Y plane, then the moment of inertia of this system is:

The moment of inertia of this system is 68 kilogram-square meters.

Explanation:

We have two particles rotating about the z-axis, which is orthogonal to xy plane, the moment of inertia of the system (), measured in kilogram-square meters, is determined by the following formula:

(1)

Where:

- Mass of the i-th particle, measured in kilograms.

- Distance of the i-th particle from axis of rotation, measured in meters.

By Pythagorean Theorem we calculate each distance:

If we know that , , and , then the moment of inertia of the system is:

(1b)

The moment of inertia of this system is 68 kilogram-square meters.