How this calculator works
Uniform circular motion has constant speed but continuously changing velocity direction. One period covers a circumference, so the speed is circumference divided by period. Radius links the rotational variables to linear speed and acceleration. These relationships describe a fixed circular path and do not account for changing angular speed.
Formula
f = 1/T; omega = 2 pi f; v = omega r; a_c = v²/r = omega² r.
Worked example
A 1 m radius path with a 2 s period has frequency 0.5 Hz and angular speed pi rad/s. A 6 m/s speed on radius 2 m gives 3 rad/s and 18 m/s² radial acceleration.
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Frequently asked questions
Is constant speed zero acceleration?
No. The velocity vector changes direction, which produces inward acceleration.
Where is mass?
These are kinematic relationships. Multiply acceleration by mass to find the required radial force.
What if the object is stationary?
Its period is infinite. This calculator requires positive rates to report a finite period.