Moment of Inertia Calculator
Calculate moment of inertia for common geometric shapes.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Select the shape, enter the mass and relevant dimensions (radius, inner/outer radius, or length depending on the shape). The calculator computes the moment of inertia about the specified axis.
About Moment of Inertia
Moment of inertia quantifies an object's resistance to rotational acceleration about a given axis. It is the rotational analog of mass in linear motion. The value depends on both the total mass and its geometric distribution. Objects with mass concentrated far from the axis (hollow shapes) have larger moments of inertia than those with mass near the axis (solid shapes). This concept is critical in mechanical engineering, flywheel design, and understanding rotational dynamics.
Frequently Asked Questions
What is moment of inertia?
Moment of inertia is the rotational equivalent of mass. It measures an object's resistance to changes in rotational motion. It depends on both mass and how that mass is distributed relative to the axis of rotation.
How does mass distribution affect moment of inertia?
Mass farther from the axis contributes more to the moment of inertia. A hollow sphere has a larger moment of inertia than a solid sphere of the same mass and radius.
What are the units of moment of inertia?
The SI unit is kilogram meters squared (kg m2). It appears in the rotational form of Newton's second law: torque = I times angular acceleration.