Circular Motion Calculator
Calculate the centripetal acceleration, angular velocity, period and (optionally) centripetal force for an object moving in uniform circular motion. Handy for physics coursework, orbital-style problems and rotating machinery.
Enter Values
How to use this calculator
- Enter the linear speed v in metres per second.
- Enter the radius r of the circular path in metres.
- Optionally enter the object's mass m in kilograms to also get the centripetal force in newtons.
How it works
For uniform circular motion the centripetal acceleration is a = v²/r, the angular velocity is ω = v/r, and the period (time for one revolution) is T = 2πr/v. If a mass is supplied, the centripetal force needed to keep the object on the circle is F = m·v²/r, directed toward the centre.
Worked example
Worked example. An object moving at 10 m/s on a 2 m radius circle with a mass of 5 kg has a centripetal acceleration of 50 m/s², an angular velocity of 5 rad/s, a period of 1.26 s and a centripetal force of 250 N.
Common mistakes
- Entering a radius of zero — the path must have a positive radius.
- Confusing angular velocity (rad/s) with rotational speed in revolutions per minute.
- Assuming the speed changes; these formulas describe uniform (constant-speed) circular motion only.
Frequently asked questions
What is centripetal force?
It is the inward force required to keep an object moving in a circle, equal to m·v²/r and always directed toward the centre.
Do I have to enter a mass?
No. Mass is optional — leave it blank to get acceleration, angular velocity and period; add it to also see the centripetal force.
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Tip: Enter any known values to calculate the remaining results.
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