Angular Velocity to Linear Speed Calculator
Convert between angular velocity and linear (tangential) speed at a given radius.
Also calculates centripetal acceleration.
Linear Speed
For an object moving in a circle of radius r at angular velocity ω, the linear (tangential) speed is:
v = ωr = 2πfr
And the centripetal acceleration (directed toward the center) is:
a_c = v²/r = ω²r
Where:
- v = Linear (tangential) speed at the rim (m/s)
- ω = Angular velocity (rad/s)
- r = Radius of circular motion (m)
- f = Rotational frequency (Hz = rev/s)
- a_c = Centripetal acceleration (m/s²)
Converting RPM to rad/s: ω (rad/s) = RPM × 2π / 60
Practical examples:
| Application | Radius | RPM | Rim speed |
|---|---|---|---|
| Hard disk drive | 30 mm | 7200 rpm | 22.6 m/s |
| Car wheel | 0.3 m | 800 rpm | 25.1 m/s |
| Jet engine turbine | 0.5 m | 10,000 rpm | 524 m/s |
| Earth’s equator | 6371 km | 1 rev/day | 465 m/s |
Centripetal acceleration context: At Earth’s equator (rotation): a_c = 0.034 m/s² — only 0.35% of g. At fairground rides: 2–5 g typical.