Math

Moment of Inertia Calculator

Find the moment of inertia for common rigid shapes.

Parameters Live Compute
Calculated Output
Moment of inertia 0.25
Formula: I = k·m·(r or L)²
Step-by-Step Breakdown
1. Values used:
2. Mass = 2
3. Radius = 0.5
4. Length (rods) = 1
5.
6. Moment of inertia = Radius / Mass = 0.5 / 2 = 0.25
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Moment of inertia measures how hard it is to change a rotating object's spin — the rotational analog of mass.

The math behind it

Each shape has a standard coefficient: I = k·m·r² (or k·m·L² for rods). More mass farther from the axis means a larger moment of inertia.

Worked Example

Solid cylinder, m = 2, r = 0.5 → I = ½·2·0.25 = 0.25.

Frequently Asked Questions

Why does shape matter?

Mass distributed farther from the rotation axis resists angular acceleration more.

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