# Circular Motion Calculator

Calculate uniform circular motion properties: velocity, period, frequency, centripetal acceleration, and angular velocity.

## What this calculates

Uniform circular motion occurs when an object moves along a circular path at constant speed. Although the speed is constant, the velocity continually changes direction, requiring a centripetal acceleration directed toward the center. This calculator computes all key properties of uniform circular motion from the radius and either the period or tangential velocity.

## Inputs

- **Radius** (m) — min 0 — Radius of the circular path.
- **Known Value** — options: Period (s), Velocity (m/s) — Choose whether to input the period or the tangential velocity.
- **Period (T)** (s) — min 0 — Time for one complete revolution (used when Period is selected).
- **Tangential Velocity (v)** (m/s) — min 0 — Tangential speed of the object (used when Velocity is selected).

## Outputs

- **Tangential Velocity** (m/s) — v = 2πr/T
- **Period** (s) — Time for one complete revolution
- **Frequency** (Hz) — f = 1/T (revolutions per second)
- **Centripetal Acceleration** (m/s²) — a = v²/r = 4π²r/T²
- **Angular Velocity** (rad/s) — ω = 2π/T = v/r

## Details

For an object in uniform circular motion with radius r and period T, the key relationships are: v = 2πr/T (tangential velocity), f = 1/T (frequency), ω = 2π/T (angular velocity), and a = v²/r = 4π²r/T² (centripetal acceleration).

The centripetal acceleration always points toward the center of the circle. Without a centripetal force to produce this acceleration, the object would fly off in a straight line (Newton’s first law). The source of centripetal force varies: gravity for orbiting bodies, tension for a ball on a string, friction for a car rounding a curve, and the normal force for a roller coaster loop.

Circular motion analysis is essential in orbital mechanics (satellites, planets), rotating machinery (turbines, centrifuges), particle accelerators, amusement park ride design, and vehicle dynamics. Any system involving rotation or curved paths relies on these fundamental relationships.

## Frequently Asked Questions

**Q: What is uniform circular motion?**

A: Uniform circular motion is movement along a circular path at constant speed. The velocity is not constant because its direction continually changes. This change in direction requires a centripetal (center-seeking) acceleration even though the speed remains the same.

**Q: Is an object in circular motion accelerating?**

A: Yes, always. Even though the speed is constant in uniform circular motion, the direction of velocity is constantly changing. This change in direction is an acceleration (centripetal acceleration = v²/r) directed toward the center of the circle.

**Q: What is the difference between period and frequency?**

A: Period (T) is the time for one complete revolution, measured in seconds. Frequency (f) is the number of revolutions per second, measured in Hertz (Hz). They are reciprocals: f = 1/T and T = 1/f. A 2-second period means a frequency of 0.5 Hz.

**Q: How does radius affect circular motion?**

A: For a fixed period, a larger radius means higher tangential velocity (v = 2πr/T) and higher centripetal acceleration (a = 4π²r/T²). For a fixed velocity, a larger radius means lower centripetal acceleration (a = v²/r), making the curve gentler.

**Q: How is this related to satellite orbits?**

A: A satellite in circular orbit is in uniform circular motion where gravity provides the centripetal force. Setting gravitational force equal to centripetal force (GMm/r² = mv²/r) gives the orbital velocity v = sqrt(GM/r). Lower orbits are faster; higher orbits are slower.

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Source: https://vastcalc.com/calculators/physics/circular-motion
Category: Physics
Last updated: 2026-04-21