Calculator
Example data table
| Case | Radius | Given | Velocity | Notes |
|---|---|---|---|---|
| A | 0.50 m | ω = 12 rad/s | 6.00 m/s | Uses v = ωr |
| B | 0.25 m | T = 0.80 s | 1.96 m/s | Uses v = 2πr/T |
| C | 0.10 m | f = 5 Hz | 3.14 m/s | Uses v = 2πrf |
| D | 0.30 m | 900 rpm | 28.27 m/s | Converts rpm to ω |
| E | 0.40 m | aₙ = 36 m/s² | 3.79 m/s | Uses v = √(aₙr) |
Formula used
v = ωrwhereωis angular velocity andris radius.v = 2πr / TwhereTis the period per revolution.v = 2πrfwheref = 1/Tis the frequency.ω = 2πfandrpm = 60ffor rotational speed conversions.aₙ = v² / rgives centripetal (normal) acceleration.F = m aₙandv = √(F r / m)when force and mass are known.
How to use this calculator
- Select a calculation method that matches your known values.
- Enter the radius and the required input for that method.
- Pick units carefully to match your measurement system.
- Optionally add mass to compute centripetal force outputs.
- Press Calculate to show results above the form.
- Use CSV or PDF export buttons for documentation.
Circular motion velocity guide
1) Understanding tangential velocity
Tangential velocity is the instantaneous linear speed of a point moving along a circular path. Even when the speed is constant, the velocity direction rotates continuously, which is why circular motion always involves inward (centripetal) acceleration.
2) Key formulas and variable meanings
This calculator supports several equivalent relationships. Use v = ωr when angular velocity ω is known. Use v = 2πr/T when the period T is measured per revolution. Use v = 2πrf when frequency f is known. All three forms match because ω = 2πf and f = 1/T.
3) Typical units and conversions
Radius can be entered in meters, centimeters, millimeters, kilometers, feet, or inches, then converted internally to meters for consistent math. Angular speed may be given in rad/s, deg/s, or rpm. Period can be seconds, minutes, or hours; frequency can be Hz, per minute, or per hour.
4) Engineering and lab use cases
Use tangential speed to estimate belt surface speed, turntable rim speed, rotor tip speed, or wheel road speed. In labs, measure r and T to compute v, then compare against video tracking or sensor data. If you only know motor rpm, pick the rpm method and use the effective radius at the contact point.
5) Interpreting derived outputs
After solving v, the tool also reports ω, rpm, period, frequency, and centripetal acceleration aₙ = v²/r. If you provide mass, it estimates centripetal force F = m·aₙ. These extra fields help cross-check results and connect kinematics to dynamics. Speed is also shown in km/h and mph for quick reporting.
6) Common input mistakes to avoid
Ensure radius is the distance from center to the moving point, not the diameter. Keep T as time for one full revolution, not multiple turns unless you divide accordingly. When using rpm, remember it is revolutions per minute; the calculator converts it to rad/s automatically. Avoid zero or negative values.
7) Quick verification with sample numbers
As a sanity check, take r = 0.50 m and ω = 12 rad/s. Then v = ωr = 6.0 m/s and aₙ = v²/r = 72 m/s² (about 7.34 g). If your numbers differ wildly, recheck units and decimals before exporting.
FAQs
1) What is the difference between speed and velocity here?
Speed is the magnitude of motion along the circle. Velocity includes direction, which changes every moment. The calculator reports speed values and reminds you the velocity vector is tangent to the path.
2) Which method should I choose?
Use the method that matches what you measured: ω from sensors, T from timing one revolution, f from cycles per second, rpm from a motor spec, aₙ from accelerometers, or F and m from force and mass data.
3) Why does smaller radius increase acceleration?
Centripetal acceleration follows aₙ = v²/r. For the same tangential speed, dividing by a smaller r produces a larger aₙ. That is why tight turns feel harsher than wide turns at the same speed.
4) Can I calculate force without mass?
No. Force needs mass because F = m·aₙ. If you leave mass blank, the tool still computes aₙ from v and r, but it cannot convert acceleration into force.
5) How accurate are the unit conversions?
The page converts inputs to SI units internally, then converts results back to common units like km/h and mph. Accuracy is limited mainly by your measurements and rounding, not by the conversion factors.
6) What does the exported CSV or PDF include?
Exports include the computed speed, angular quantities, period, frequency, and centripetal acceleration. If mass is provided, force is included too. Use exports to paste values into reports, lab notebooks, or calculations.