What is the Moment of Inertia?

The Moment of Inertia (MOI), often denoted by the symbol I, is a physical quantity that measures an object's resistance to rotational acceleration. Just as mass is a measure of an object's resistance to linear acceleration (inertia), the moment of inertia depends not only on the amount of mass but also on how that mass is distributed relative to the axis of rotation.

How to Use This Calculator

This Moment of Inertia calculator is designed to provide quick and accurate calculations for common geometric shapes. To use the tool, simply select the shape of the object you are analyzing, such as a solid sphere, cylinder, or rectangular plate. Enter the mass in kilograms and the required dimensions (radius, length, or width) in meters. Clicking the calculate button will instantly generate the result along with a detailed step-by-step breakdown of the formula used.

Common Formulas

Different shapes have unique formulas for calculating rotational inertia:

• Solid Cylinder: I = ½mr²
• Solid Sphere: I = (2/5)mr²
• Thin Rod (center): I = (1/12)mL²
• Hollow Sphere: I = (2/3)mr²

Frequently Asked Questions

Q: What are the units for Moment of Inertia?
A: In the International System of Units (SI), it is measured in kilogram-square meters (kg·m²).

Q: Why does the distribution of mass matter?
A: Because the distance from the axis is squared in the formula (mr²), mass located further from the center of rotation increases the inertia much more significantly than mass located near the center.

Q: Can the moment of inertia be negative?
A: No, since mass and the square of the distance are both positive values, the MOI is always a positive scalar quantity.