Physics Calculator
Circular Motion
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Calculate Circular Velocity and Centripetal Acceleration easily. Enter your values and get instant step-by-step solutions.
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Circular Velocity
Find the speed of an object moving in a circular path
✅ Result
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Step-by-Step Solution
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Circular Velocity (v)
The speed of an object moving along a circular path. It depends on the radius and the time taken to complete one full revolution.
v = 2πr / T
Also written as: v = ωr
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Centripetal Acceleration (a)
The acceleration always pointing toward the center of the circle. It keeps the object moving in a circular path instead of a straight line.
a = v² / r
Also written as: a = ω²r
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Key Facts
Important things to remember about circular motion
1
Even at constant speed, circular motion has acceleration — because direction keeps changing.
2
Centripetal acceleration always points toward the center of the circle — never outward.
3
The force causing centripetal acceleration is called Centripetal Force: F = mv²/r
4
Angular velocity: ω = 2π/T — relates to how fast the angle changes per second.
5
One full revolution = 2π radians. Period T is the time for one complete circle.
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Variables & Symbols
All symbols used in circular motion formulas
| Symbol | Meaning | Unit | Description |
|---|---|---|---|
| v | Circular Velocity | m/s | Speed along the circular path |
| r | Radius | m | Distance from center to object |
| T | Time Period | s | Time for one full revolution |
| a | Centripetal Acceleration | m/s² | Acceleration toward center |
| ω | Angular Velocity | rad/s | Rate of change of angle |
| f | Frequency | Hz | Revolutions per second (f = 1/T) |
| π | Pi | — | ≈ 3.14159 |
| F | Centripetal Force | N | F = mv²/r (needs mass m) |