Angular Velocity Converter
Convert angular velocity units — radians per second, degrees per second, RPM, and more. Free online angular velocity converter for physics, mechanics, and engineering.
Understanding Angular Velocity
Angular velocity measures how fast an object rotates or revolves. You express it in radians per second (rad/s), degrees per second, or revolutions per minute (RPM). Angular velocity describes rotational motion analogous to linear velocity.
Angular velocity is a vector quantity with direction along the rotation axis. Right-hand rule determines direction: curl fingers in rotation direction, thumb points along angular velocity vector.
Angular Velocity Formulas
ω = Δθ / Δt
Definition: Angular velocity equals change in angle divided by change in time. Omega (ω) represents angular velocity.
v = ω × r
Linear velocity: Tangential velocity equals angular velocity times radius. Connects rotational and linear motion.
ω = 2 × π × f
Frequency relationship: Angular velocity equals 2π times frequency in Hz. One revolution equals 2π radians.
Example: A motor spinning at 3,000 RPM has ω = 3,000 × 2π / 60 = 314 rad/s.
Common Angular Velocity Conversions
| rad/s | deg/s | RPM | rad/min |
|---|---|---|---|
| 0.000291 | 0.0167 | 0.00278 | 0.0175 |
| 0.0175 | 1 | 0.167 | 1.05 |
| 0.105 | 6 | 1 | 6.28 |
| 1 | 57.3 | 9.55 | 60 |
| 104.7 | 6,000 | 1,000 | 6,283 |
Rotational Speed Reference
| Application | Speed (RPM) | Speed (rad/s) |
|---|---|---|
| Earth Rotation | 0.0007 | 0.000073 |
| Ceiling Fan | 100-300 | 10-30 |
| Car Engine (idle) | 600-1,000 | 60-100 |
| Car Engine (max) | 6,000-8,000 | 600-800 |
| Hard Disk Drive | 5,400-15,000 | 565-1,570 |
| Dental Drill | 200,000-400,000 | 20,000-40,000 |
| Jet Engine Turbine | 10,000-20,000 | 1,000-2,000 |
Practical Applications
Electric Motors
Motor speed ratings specify RPM at rated load. AC induction motors run at synchronous speed minus slip. 4-pole 60 Hz motors run at approximately 1,750 RPM.
Centrifuges
Laboratory centrifuges separate samples by density. Speed ranges 1,000-30,000 RPM. Relative centrifugal force (RCF) depends on both speed and rotor radius.
Gyroscopes
Gyroscopes maintain orientation using high-speed rotors. Navigation gyros spin at 10,000-24,000 RPM. MEMS gyros measure angular velocity for stabilization.
Wind Turbines
Large wind turbines rotate slowly, 10-20 RPM. Gearboxes increase speed to 1,500-1,800 RPM for generators. Tip speed ratio optimizes energy extraction.
Frequently Asked Questions
How do you convert RPM to rad/s?
Multiply RPM by 2π/60 or approximately 0.1047. One revolution equals 2π radians. One minute equals 60 seconds. So rad/s = RPM × 2π / 60.
What is the difference between angular velocity and angular frequency?
Angular velocity describes physical rotation. Angular frequency describes oscillation in radians per second. Both use rad/s units but represent different phenomena.
How do you measure angular velocity?
Tachometers measure RPM directly. Optical encoders count rotations. Gyroscope sensors output angular velocity. Stroboscopes freeze rotating objects for visual measurement.
What is critical speed?
Critical speed occurs when rotation frequency matches natural frequency. Resonance causes excessive vibration. Rotating machinery must operate below or above critical speeds.
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