Uniform Circular Motion Calculator (Centripetal Force, Angular Velocity, Period)
Enter mass, radius, and speed (or angular velocity) to calculate the centripetal force, angular velocity, period, and frequency of uniform circular motion (F = mv²/r = mω²r).
Usage Tips
- Speed (v) and angular velocity (ω) are related by ω = v/r, so you only need to know one of them to calculate everything else. If your source value is in RPM, convert it to rad/s first with rpm × 2π ÷ 60.
- Centripetal force keeps changing the direction of motion — it does not speed the object up along its path. In uniform circular motion, the speed itself stays constant while only the direction keeps changing.
- Increasing the radius (r) while keeping speed (v) fixed reduces the centripetal force in inverse proportion (F = mv²/r). Conversely, doubling the speed at a fixed radius quadruples the centripetal force — a common mistake is assuming it only doubles.
- Frequency (f) is the number of full revolutions per second and is the reciprocal of the period (T). To compare with a motor's RPM rating, multiply f by 60 to get revolutions per minute.
Frequently Asked Questions
Side Note — The Newton–Hooke Dispute Over Universal Gravitation
The concept of centripetal force in uniform circular motion also played a key role in understanding the motion of celestial bodies. Isaac Newton reasoned that the Moon keeps orbiting the Earth in a roughly circular path because Earth's gravity acts as the centripetal force, and he extended this insight to planetary motion in general to derive the law of universal gravitation.
Interestingly, the idea that the strength of gravitational attraction falls off with the square of the distance was independently conceived not only by Newton but also by his contemporary Robert Hooke, leading to a famous priority dispute between the two. Hooke had hinted at the idea in a letter to Newton, but it was Newton who ultimately worked out the full mathematical treatment — using the centripetal force equation to derive the elliptical planetary orbits described by Kepler's laws.
Today, the concept of centripetal force extends far beyond orbital mechanics: it is routinely applied in engineering fields ranging from designing roller coasters at amusement parks, to setting the spin speed of a washing machine's drum, to calculating the tire friction needed for a car to safely take a curve.