Free · Rotational and periodic motion calculators 🌎

Circular-Motion Force, Acceleration & Angular Speed

Solve circular-motion relationships for force, acceleration, speed, radius or mass, with angular-speed unit conversion.

  • Formula & worked example
  • Private in your browser
  • No signup
Go to tool

Calculator inputs

Loading calculator…

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

For mass 2 kg, radius 4 m and speed 8 m/s, centripetal force is 32 N, acceleration is 16 m/s² and angular speed is 2 rad/s.

F = mv²/r; a = v²/r; angular speed ω = v/r

Worked example

Enter these known values and leave the other values blank.

Mass (m)
2 kg
Radius (r)
4 m
Tangential speed
8 m/s
Angular speed
2 rad/s
Inward centripetal force magnitude
32 N
Centripetal acceleration (a)
16 m/s²

Assumptions and limitations

  • Mass and radius are positive; speeds, acceleration magnitude and force magnitude are nonnegative.
  • These are instantaneous radial relationships for circular motion. Tangential acceleration and its force component are not included.
  • Radians per second, cycles per second and revolutions per minute differ by exact factors of 2π and 60.

Common questions

Does centripetal force point outward?

No. It is the net inward radial force required for circular motion.

What happens if speed doubles?

At unchanged mass and radius, radial force and acceleration become four times larger.

References

Bookify allows the zero-speed limit with zero angular speed, force and radial acceleration. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor. The pound-force uses the exact international pound and standard gravity instead of the rounded captured factor. The poundal uses exactly one international pound-foot per second squared. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor. The light-year uses exactly 299792458 m/s times a 31557600-second Julian year, replacing the rounded reference factor.

Explore rotational and periodic motion calculators 🌎 or browse all physics calculators.