How to Find the Moment of Inertia of Particle A With Respect to the X Axis

The moment of inertia of an object is a measure of how difficult it is to rotate it around a fixed axis. The moment of inertia is the rotational equivalent of mass, the measure of how difficult it is to accelerate an object linearly. The formula for the moment of inertia of a point mass is mR^2, where m is the mass of the object, and R is the distance from the point it is rotating about.

Instructions

1. Calculate the distance from the particle to the x-axis. This can be done by taking the positive square root of the sum of the squares of the y and z coordinates.

   For example, a point with coordinates (7m, 3m, 4m) would have a distance of the square root of (3m)^2+(4m)^2, which is the square root of 25m^2, which is equal to 5m. "M" is the symbol for a meter.

2. Find the mass of the particle. This should be given in the problem.

3. Multiply the square of the distance obtained in Step 1 by the mass of the particle. This is the moment of inertia. If a particle had a mass of 5kg and had the distance given in the Step 1 example, it would have a moment of inertia of 5kg*25m^2 = 125*kg*m^2.

References

• Georgia State: Moment of Inertia