Free · Rotational and periodic motion calculators 🌎

Circular Motion: Period, Speed & Inward Acceleration

Relate period, cycle frequency and angular rate, or add radius to calculate tangential speed and centripetal acceleration.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A period of 2 seconds means frequency 0.5 Hz and angular speed π rad/s. At radius 1 m, tangential speed is π m/s and inward acceleration is π² m/s².

f = 1/T; ω = 2π/T; v = ωr; a = ω²r

Worked example

Enter these known values and leave the other values blank.

Time for one complete revolution
2 sec
Revolutions per second
0.5 Hz
Angular speed magnitude
3.1416 rad/s

Assumptions and limitations

  • This model describes uniform circular motion with positive radius and positive finite period. All displayed rates are magnitudes.
  • Nonzero motion is required for a finite period. A stationary object does not have a finite revolution period in this model.
  • Centripetal acceleration changes velocity direction even when speed is constant. It does not include tangential acceleration from changing speed.
  • Frequency in hertz counts turns per second, while rad/s measures radians per second. One turn is 2π radians.

Common questions

Why is acceleration nonzero at constant speed?

Velocity includes direction. Circular motion continuously changes that direction, requiring acceleration toward the center.

Does RPM mean radians per minute?

No. RPM counts revolutions per minute. Multiply by 2π/60 to obtain radians per second.

References

Bookify rejects zero or negative rates and periods in the finite, revolving-motion model. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor.

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