How to Calculate the Moment of Inertia of a Square Plate for Rotation

Moment of inertia is the resistance of an object to change rotation speed. Moment of inertia has the same function for the rotation motion as mass does in the linear motion. Moment of inertia of a square plate depends upon its mass, the dimensions and the point of rotation. Particularly, the rotation axis can go either through the plate center or along the plate edge.

Things You'll Need

• Calculator
• Scale
• Metric ruler

Instructions

1. Weigh the plate on a scale or obtain the mass of the plate elsewhere. For example, the mass of the plate is 1.3 kg.

2. Measure the side of the square plate or obtain this dimension elsewhere. For example, the side of the plate is 30 cm or 0.3 m.

3. Calculate the square of the plate's side length and then multiply the product by the mass of the plate. In our example, 0.3 m x 0.3 m x 1.3 kg = 0.117 kg m^2.

4. If the rotation axis goes through the plate center, divide the value obtained in Step 3 by six to calculate the moment of inertia. In our example, it is 0.117 / 6 = 0.0195 kg m^2.

   If the rotation axis goes axis along the plate edge, divide the value obtained in Step 3 by three to calculate the moment of inertia. In our example, it is 0.117 / 3 = 0.039 kg m^2.

References

• "Classical Mechanics", J.R. Taylor, University Science Books, January, 2005.

Resources

• Moment of Inertia of Objects