Torque and Inertia

Moment of Inertia Squares Radius

The moment of inertia of a point mass is I = m * r^2, so mass farther from the axis counts quadratically more toward rotational inertia. The arithmetic is exact only for the stated point mass and radius in the ideal rigid-body model. Real systems add distributed mass, axis choice, friction, flexing, calibration, and measurement uncertainty.

Point-mass inertia uses mass times radius squared. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Moment of inertia squares the radius

A 2 kilogram point mass at radius 3 meters contributes 18 kilogram meter squared.

I=2×32=18 kg m2I=2\times3^2=18\ \mathrm{kg\,m^2}
Moment of inertiaPoint masses at radius set inertia.r=3 mm=2 kgr=3 mI=18 kg*m^2

The radius is not a linear weight

The radius 3 is squared before it multiplies the mass.

32=93^2=9
Moment of inertiaPoint masses at radius set inertia.r=3 mm=2 kgr=3 mI=18 kg*m^2