Angular Velocity to Linear Speed Calculator
Convert between angular velocity and linear (tangential) speed at a given radius.
Also calculates centripetal acceleration.
Angular velocity describes how fast an object rotates (radians per second or RPM). Linear velocity describes how fast a point on that rotating object moves in a straight line. The relationship between them depends on the radius.
The Formula:
v = ω × r
Where:
- v = linear velocity (m/s)
- ω = angular velocity (radians per second)
- r = radius from the center of rotation (meters)
Converting RPM to rad/s:
ω (rad/s) = RPM × (2π / 60) = RPM × 0.10472
Worked Example:
A car wheel with radius 0.33 m (13-inch wheel) spins at 800 RPM on a highway:
ω = 800 × 0.10472 = 83.8 rad/s
Linear velocity = 83.8 × 0.33 = 27.6 m/s = 99 km/h
Practical Applications:
| Application | Typical Angular Velocity |
|---|---|
| Car wheel at 100 km/h | ~800 RPM |
| Hard drive platter | 5,400–7,200 RPM |
| Jet turbine | 10,000–25,000 RPM |
| Dental drill | 300,000–500,000 RPM |
| Earth rotation | 0.00417°/second = 1 rev/day |
Centripetal Acceleration:
A point on a rotating object also experiences inward acceleration:
a = ω² × r = v² / r
At the rim of a 0.33 m wheel doing 800 RPM: a = 83.8² × 0.33 = 2,318 m/s² ≈ 236g
Practical Tips:
- When calculating tire speed, use the loaded radius (slightly smaller than unloaded radius)
- Belt and pulley systems use this formula to calculate output speed from input speed
- A larger radius always produces higher linear velocity for the same angular velocity
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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