Moment of inertia

Intermediate

Rotational inertia: resistance to angular acceleration.

Key relationI = Σm r²

I = Σmr² measures the resistance to angular acceleration. Mass far from the axis counts a lot (r²). It is the rotational analogue of mass.

Worked example

Two 1 kg masses at 0.5 m on a rod: I = 0.5 kg·m².

Common mistake

I depends on the axis chosen.

In more detail

Moment of inertia, I = Σmr², measures how hard it is to change an object's rotation. It depends on the mass distribution and the chosen axis.

Flywheels use large moment of inertia to store rotational energy smoothly.
Gymnasts reduce their moment of inertia to spin faster.
Figure skaters and divers change their moment of inertia to control how fast they spin.

Is moment of inertia the same as mass?

No. It depends on how mass is distributed relative to the axis, not just total mass.

What are the units?

Kilogram metres squared.

Does moment of inertia depend on the axis?

Yes. The same body has different moments of inertia about different axes, so always state the axis used.