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Circular motion and centripetal force calculator

Compute centripetal acceleration, force, period and angular velocity for an object moving in a circle.

Centripetal acceleration
50 m/s²
Centripetal force50 N
In g5.099 g
Angular velocity5 rad/s
Period1.2566 s
Revolutions per minute47.746 rpm

An object moving in a circle at constant speed is still accelerating, because its direction is changing. That acceleration points inward, toward the centre, and something has to supply the force that produces it.

a = v² / r = ω² r   F = m v² / r

There is no centrifugal force

The outward push you feel on a roundabout is not a force acting on you. It is your inertia — your body trying to continue in a straight line while the seat pushes you inward. In an inertial frame, the only real force is the centripetal one, supplied by friction, tension, gravity or a normal force depending on the situation.

Radius matters more than you expect

Acceleration goes as the square of speed but only inversely with radius. Halving the radius of a turn at the same speed doubles the force required. This is why a tight corner is far harder on tyres than a sweeping one at the same speed, and why a centrifuge is short rather than long — it is easier to reach high acceleration by spinning a small radius quickly.

Where the force comes from

  • A car turning: sideways friction between tyre and road, which has a hard limit.
  • A satellite: gravity, which is why orbital speed depends only on altitude.
  • A ball on a string: tension, which is why the string snaps above a certain speed.
  • A banked track: the horizontal component of the normal force, which is why banking lets a corner be taken faster than friction alone would allow.