Circular Motion Calculator

How it works

1. 1Enter the radius of the circular path and choose whether you know the linear speed or the angular speed.
2. 2The calculator converts inputs to SI, then derives all related quantities from the uniform-circular-motion equations.
3. 3Results show angular velocity ω, linear speed v, centripetal acceleration a = v²/r, period T = 2π/ω, and frequency f = ω/2π.

Use cases

• Analysing the forces on a car rounding a banked curve at a known speed.
• Designing a centrifuge and finding the centripetal acceleration at a given rotor radius and rate.
• Solving homework relating orbital period, speed, and radius for satellites or rides.

Frequently asked questions

How are linear speed and angular velocity related?

They are linked by the radius: v = ω·r, so ω = v ÷ r. For example, v = 10 m/s and r = 5 m give ω = 10 ÷ 5 = 2 rad/s.

How is centripetal acceleration calculated?

a = v² ÷ r. Using v = 10 m/s and r = 5 m: a = 100 ÷ 5 = 20 m/s². Equivalently a = ω²·r = 4 × 5 = 20 m/s².

How do period and frequency relate to angular velocity?

T = 2π ÷ ω and f = ω ÷ (2π) = 1 ÷ T. Continuing the example: T = 2π ÷ 2 ≈ 3.14 s and f ≈ 0.318 Hz — about 0.318 revolutions per second.