# Angular velocity

How fast something turns, measured in radians per second. One full turn is 2 pi radians.

Physics (university) · Part 04: Rotation and gravity · Card 1 of 11 · Last updated 2026-10-19

## Analogy

The second hand of a clock sweeps a steady angle each second.

## Example

**Wheel at 60 rpm**

60 rev/min = 1 rev/s
omega = 2 pi x 1
omega = 6.28 rad/s

## In practice

A wheel turning at 60 revolutions per minute spins at about 6.28 rad/s.

## Practice

### Flashcards

- **How many radians are in one full turn?** 2 pi radians, about 6.28.

## Questions people ask

### How do I convert rpm to rad/s?

One revolution is 2 pi radians, and one minute is 60 seconds. Multiply the rpm value by 2 pi and divide by 60. For example, 300 rpm gives 300 x 6.28 / 60, which is about 31.4 rad/s. A quick rule is rpm times 0.105.

### Why do physicists use radians instead of degrees?

Radians link angle directly to arc length: arc length equals radius times angle. That makes formulas such as v = r omega clean, with no extra constants. With degrees you would need a conversion factor each time. One radian is about 57.3 degrees.

## Related concepts

- [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)
- [Torque](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-4)
- [Moment of inertia](https://studyvisually.com/learn/science/physics-university/physics-university-part-4/physics-university-part-4-concept-5)

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