# how to solve moment of inertia questions

509 Points
12 years ago

The moment of inertia (denoted as "I") is the measure of an object's resistance to changes in its rotation speed. It plays the same role in rotation motion as mass does in linear motion. For a point with a mass "m," the moment of inertia is calculated using the following formula: I = mr^2. "r" is the distance between the point and the rotation axis. The moment of inertia of a body depends on the object's shape (i.e., it is different for a rod and cylinder) and the point of rotation. As an example, calculate this parameter for the point mass and a solid cylinder.

## Instructions

• 1

Multiply the mass and square of distance to the rotation axis to calculate the moment of inertia of the point mass.
For example, the mass is 2 kg and the distance is 2 m. Hence, I = mr^2 = 2 kg x 2 m x 2 m = 8 kgm^2.

• 2

Navigate to the moment of inertia list (see Resources) and find a formula that corresponds to the object shape and the rotation point.
In the example with the solid cylinder, you would find that I = 1/2 x mR^2. Note that R is the cylinder radius.

• 3

Calculate the moment of inertia using the formula from Step 2. For example, the cylinder mass is 3 kg and its radius is 0.5 m. The moment of inertia would be:
I = 1/2 x 3 kg x 0.5 m x 0.5 m = 0.375 kgm^2.