Moment of Inertia Calculator
Enter mass and radius to compute the moment of inertia of a solid disk or hoop about its central axis.
Input Data
Results
At a glance:The moment of inertia I (or rotational inertia) is a body's resistance to change in its rotational motion about an axis, analogous to mass in linear motion. For a solid disk (uniform cylinder) about its symmetry axis I = ½·m·r²; for a thin-walled hoop all mass is at radius r so I = m·r². In general I = ∫ r² dm. It depends on both mass and how that mass is distributed relative to the axis — mass farther from the axis contributes more. This calculator covers the common solid-disk case.
Formula
Solid disk: I = ½·m·r²
Thin hoop: I = m·r²
$$I = m r^2$$How to Use
- Enter the mass m (kg).
- Enter the radius r (m).
- The calculator returns the moment of inertia I.
Case Studies
Flywheel disk
m = 10 kg, r = 0.2 m.
I = ½×10×0.2² = 0.2 kg·m².
Stores rotational kinetic energy ½Iω².
FAQ
Why does a hoop have twice the inertia of a disk of same mass and radius?
In a hoop all mass sits at distance r from the axis (I = mr²); in a solid disk mass is spread from 0 to r, lowering the average r² to give I = ½mr².
What is the rotational analogue of F = ma?
τ = I·α, where τ is torque, I the moment of inertia and α angular acceleration — the rotational form of Newton's second law.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.