Moment of Inertia Calculator
Pick a rigid body shape, enter its mass and the relevant radius or length, and read the moment of inertia in kg x m^2 with the formula used.
How to use the moment of inertia calculator
- Choose the shape and rotation axis from the list.
- Enter the mass and either the radius or the length.
- Read the moment of inertia in kg x m^2 and the formula.
Examples
Solid cylinder
shape = solid cylinder, m = 5 kg, r = 0.2 m
I = 0.1 kg x m^2
Rod about its centre
shape = rod (centre), m = 3 kg, L = 2 m
I = 1 kg x m^2
Frequently asked questions
What is moment of inertia?
Moment of inertia measures how hard it is to change an object's rotation. It depends on the mass and how that mass is spread out from the axis.
Which shapes does the calculator support?
A solid cylinder or disk, a thin hoop or ring, a solid sphere, a hollow sphere, and a thin rod about its centre or about one end.
Why does a hoop have a larger value than a disk?
A hoop's mass sits at the rim, far from the axis, so I = m r^2. A disk spreads mass inward, giving the smaller I = 1/2 m r^2 for the same mass and radius.
What units should I use?
Use kilograms for mass and metres for the radius or length. The result is in kilogram metre squared, written kg x m^2.
Why is a rod about its end larger than about its centre?
Rotating a rod about its end keeps more mass far from the axis, so I = 1/3 m L^2, four times the 1/12 m L^2 value about the centre.
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