Angular Velocity Calculator
The Angular Velocity Calculator converts a rotational speed in RPM into angular velocity, then uses the radius to find tangential speed and centripetal acceleration. The formula used is: ω = RPM × 2π/60; v = ω × r; a_c = ω² × r.
Formula
ω = RPM × 2π/60; v = ω × r; a_c = ω² × r
Example Calculation
Inputs
- Rotational speed: 3000 RPM
- Radius: 0.3 m
At 3000 RPM, ω = 3000 × 2π ÷ 60 ≈ 314.16 rad/s. With a 0.3 m radius, the tangential speed is ω×r ≈ 94.2 m/s and the centripetal acceleration is ω²×r ≈ 29,609 m/s².
Frequently asked questions
How do you convert RPM to rad/s?
Multiply revolutions per minute by 2π/60, because one revolution is 2π radians and a minute is 60 seconds. So ω = RPM × 2π/60.
What is tangential speed?
It is how fast a point on the rim moves along its circular path: v = ω × r, where r is the radius.
What is centripetal acceleration?
It is the inward acceleration that keeps a point moving in a circle: a_c = ω² × r.
What units should I enter?
Enter rotational speed in RPM and the radius in metres. Results are in rad/s, m/s, and m/s².
How accurate are the results?
They are computed exactly from the inputs and rounded only for display.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.