Calculator
Example Data Table
| Case | Mass | Radius | Speed | Formula | Force |
|---|---|---|---|---|---|
| Small rotating object | 2 kg | 0.8 m | 6 m/s | F = mv²/r | 90 N |
| Vehicle on curve | 1200 kg | 50 m | 15 m/s | F = mv²/r | 5400 N |
| Lab turntable | 0.5 kg | 0.25 m | 4 rad/s | F = mω²r | 2 N |
Formula Used
The main centripetal force formula is:
F = m × v² / r
Here, F is centripetal force, m is mass, v is linear speed, and r is radius.
Angular form:
F = m × ω² × r
Distance around a circular path:
d = v × t or d = 2πr × revolutions
Other useful relations are v = ωr, a = v²/r, T = 2π/ω, and f = 1/T.
How to Use This Calculator
- Select the calculation mode that matches your unknown value.
- Enter the known values in the available fields.
- Choose the correct unit beside each value.
- Leave unused fields blank.
- Press the calculate button.
- Read the result table above the form.
- Use the CSV or PDF button to save the result.
Understanding centripetal motion
Centripetal force acts toward the center of a circular path. It does not point along the path. It changes direction, not necessarily speed. A car turning on a curve, a stone on a string, and a satellite in orbit all need inward force. Without that inward pull, the object moves in a straight line.
Why distance matters
Distance in circular motion can mean two useful values. The radius is the distance from the center. The path distance is the length traveled around the circle. Both values affect the answer. A larger radius lowers required force when speed stays fixed. A longer travel time increases path distance when speed stays fixed.
Speed, radius, and force
The main relation is simple. Force grows with mass. Force also grows with the square of speed. So doubling speed makes force four times larger. Radius works the other way. A wider turn needs less inward acceleration at the same speed. This is why sharp turns feel stronger than wide turns.
Angular motion option
Some problems use angular speed instead of linear speed. Angular speed tells how fast the angle changes. The calculator converts revolutions per minute, degrees per second, and radians per second. It then finds linear speed using radius. This helps with rotating wheels, centrifuges, motors, and lab turntables.
Practical interpretation
Use the result as a model. Real systems may include friction, banking angle, air drag, tension limits, or measurement error. For classroom work, show the chosen formula and units. For lab work, record each input and compare trials. Small unit mistakes can create very large force errors.
Good calculation habits
Start with SI units when possible. Check that mass is positive. Check that radius is not zero. Use enough significant digits for intermediate steps. Round only the final answer. If the result seems too large, inspect speed first. Speed has the strongest effect because it is squared.
Using the results
The calculator also reports acceleration, period, frequency, circumference, and revolutions when enough data is available. These extra values help you check the physical picture. They also show whether a selected speed or radius is realistic for a safe turn or rotating device in practice before building or testing equipment safely.
FAQs
What is centripetal force?
Centripetal force is the inward force that keeps an object moving in a circular path. It always points toward the center of the circle.
What does radius mean here?
Radius means the distance from the center of rotation to the moving object. It is not the total distance traveled around the circle.
Can this calculator find distance traveled?
Yes. It can find path distance from speed and time. It can also find distance from radius and revolutions.
Which units should I use?
You may enter common units. The calculator converts them to SI units before solving. Final core results are shown in SI units.
Why does speed affect force so much?
Speed is squared in the formula. If speed doubles, required centripetal force becomes four times larger when mass and radius stay the same.
Can angular speed be used instead of linear speed?
Yes. Use angular speed when the problem gives rotation rate. The calculator converts it into linear speed using the radius.
Is centripetal force a separate kind of force?
No. It is a role played by another force. Tension, friction, gravity, or a normal force can provide centripetal force.
Why is my result very large?
Check your speed and radius units first. A small radius or high speed can greatly increase centripetal force.