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