What Is the Angular Velocity Converter?
Angular velocity (ω) measures how fast an object rotates or revolves relative to another point, expressing the change in angle per unit time.
While tachometers and motors standardly display RPM, physics formulas for centrifugal force (F = m·ω²·r) and power (P = τ·ω) require radians per second.
How Does the Angular Velocity Converter Work?
One full revolution spans 360° or 2π radians (~6.28318 rad).
Converting RPM to rad/s: multiply by 2π and divide by 60 seconds (factor ≈ 0.1047198).
Angular Velocity Converter Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Angular velocity ω in radians per second equals rotational frequency multiplied by 2π radians per complete turn.
How to Use the Angular Velocity Converter
- Input the rotational speed.
- Select whether your measurement is in RPM, rad/s, °/s, or Hz.
- Read output across engineering and scientific kinematic units.
Step-by-Step Example Calculation
Electric Motor at 3,000 RPM
Input Values:
Understanding Your Result
Standard 60 Hz 2-pole induction motors turn at roughly 3,600 synchronous RPM (377 rad/s).
Rotational frequency in Hertz equals RPM ÷ 60.
Factors That Affect the Result
- Radius: Linear surface tangential velocity increases with radius according to v = ω · r.
- Gearing: Mechanical gear ratios scale angular speed inversely with torque.
When Should You Use This Calculator?
- Calculating motor mechanical power from torque (P = τ · ω).
- Sizing drone propellers, turbine blades, and automotive flywheels.
Assumptions & Limitations
- Assumes steady-state constant rotational velocity.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Uses exact mathematical constants π and 60 seconds per minute.