Calculate the moment of inertia of common shapes about their principal axis.
Moment of inertia depends on where mass sits relative to the axis, not just how much there is. A ring has twice the inertia of a solid disc of the same mass and radius because all its mass is at the rim. Flywheels put mass at the rim to maximise inertia per kilogram, while rotating machinery does the opposite to minimise spin-up torque.
Moment of Inertia
I = k m r², where k is the shape factor (½ for a disc, 1 for a ring, ⅖ for a sphere)
I = k m r², where k is the shape factor (½ for a disc, 1 for a ring, ⅖ for a sphere) Moment of inertia depends on where mass sits relative to the axis, not just how much there is. A ring has twice the inertia of a solid disc of the same mass and radius because all its mass is at the rim.
Flywheels put mass at the rim to maximise inertia per kilogram, while rotating machinery does the opposite to minimise spin-up torque.
This calculator takes 3 inputs: Mass, Radius, Shape. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.