Calculator Form
Use one geometry input and one solving method. The form keeps a single-column page layout, while the inputs shift to 3, 2, and 1 columns by screen size.
Example Data Table
| Scenario | Radius (m) | Input Method | Input Value | Velocity (m/s) | Acceleration (m/s²) |
|---|---|---|---|---|---|
| Small flywheel | 0.50 | RPM | 120 | 6.2832 | 78.9568 |
| Turntable edge | 1.20 | Period | 3.00 s | 2.5133 | 5.2638 |
| Rotating platform | 2.00 | Frequency | 0.75 Hz | 9.4248 | 44.4132 |
Formula Used
- Tangential velocity:
v = ωr - Angular velocity from period:
ω = 2π / T - Angular velocity from frequency:
ω = 2πf - Angular velocity from RPM:
ω = 2π(RPM / 60) - Centripetal acceleration:
ac = v² / r = ω²r - Period and frequency:
T = 1 / fandf = 1 / T - Circumference:
C = 2πr - Distance after n revolutions:
d = n × 2πr - Centripetal force:
Fc = mac - Kinetic energy:
KE = ½mv²
How to Use This Calculator
- Choose the solving method that matches the data you already have.
- Enter radius, diameter, or circumference in any supported unit.
- Fill only the value related to your selected method.
- Optionally add mass to estimate centripetal force and kinetic energy.
- Click Calculate Velocity to show the result above the form.
- Review the chart, example table, and formulas for interpretation.
- Use the CSV or PDF buttons to export the calculated result.
FAQs
1) What is velocity in circular motion?
It is the tangential speed of an object moving around a circular path. Its direction keeps changing, but the calculator reports the magnitude of that speed.
2) What is the difference between angular velocity and tangential velocity?
Angular velocity measures how fast the angle changes, usually in radians per second. Tangential velocity measures how fast the object travels along the path, usually in meters per second.
3) Can I calculate velocity from RPM?
Yes. RPM is converted into angular velocity first, then multiplied by the radius. This makes RPM one of the quickest ways to find tangential speed.
4) Why does a larger radius increase tangential speed?
At the same angular velocity, points farther from the center travel a longer arc each second. That larger path length produces a higher tangential speed.
5) Why does centripetal acceleration change with speed?
Centripetal acceleration depends on v² / r. Small increases in speed cause much larger increases in acceleration because velocity is squared in the formula.
6) Which geometry input should I enter?
Use whichever value you know best: radius, diameter, or circumference. The calculator converts that measurement into radius internally before performing the motion calculations.
7) Can this help estimate force on a rotating object?
Yes. If you provide mass, the calculator also estimates centripetal force and kinetic energy. That is useful for basic design checks and motion analysis.
8) What if I know revolutions completed over a time interval?
Choose the revolutions-over-time method. The calculator converts that information into angular velocity, then computes tangential speed and the remaining circular motion values.