# Moment of inertia

How hard an object is to spin. It depends on mass and how far the mass sits from the axis, I = sum of m r squared.

Physics (university) · Part 04: Rotation and gravity · Card 5 of 11 · Last updated 2026-10-19

## Analogy

A figure skater with arms out is harder to spin than with arms in.

## Example

**Single mass**

I = m r^2
I = 2 x 0.5^2
I = 0.5 kg m^2

## In practice

A 2 kg mass at 0.5 m from the axis has I = 0.5 kg m squared.

## Practice

### Flashcards

- **What does a larger moment of inertia mean?** The object is harder to start or stop spinning.

### Interview questions

**A figure skater pulls her arms in. Explain the change in spin rate and kinetic energy.**

- Angular momentum is conserved
- Moment of inertia falls so omega rises
- Kinetic energy increases because the skater does work

## Questions people ask

### Why does a hollow cylinder roll slower than a solid one?

A hollow cylinder has its mass farther from the axis, so it has a bigger moment of inertia. More of the energy goes into spinning and less into moving forward. Down the same ramp, a solid cylinder reaches the bottom first.

### Does moment of inertia depend on the axis?

Yes. The same object has a different I about a different axis. A rod spun about its centre has I = ML squared over 12, but spun about its end it has ML squared over 3. Always state the axis before using a value.

## Related concepts

- [Angular momentum](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-7)
- [Angular velocity](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-1)
- [Centripetal acceleration](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-2)
- [Centripetal force](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-3)

Web page: https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-5
Study this card in the app: https://studyvisually.com/app/learn?category=physics-university&card=physics-university-part-4-concept-5