An object moving in a circle is always changing direction, so it is accelerating towards the centre even at constant speed. The force that causes this is the centripetal force, F = mv² ÷ r.
This calculator gives the centripetal force and acceleration, the angular velocity and the time for one full turn. The force comes from something real: tension in a string, friction on a car's tyres, or gravity for a satellite.
| Mass (m) | 0.5 kg |
| Speed (v) | 4 m/s |
| Radius of the circle (r) | 1 m |
| Centripetal force (N) | 8 |
| Centripetal acceleration (m/s²) | 16 |
| Angular velocity ω (rad/s) | 4 |
| Time for one revolution (s) | 1.5708 |
| Revolutions per minute | 38.1972 |
The string must pull with 8 N; the stone goes round 38.1972 times a minute.
Try this example →| Mass (m) | 1,000 kg |
| Speed (v) | 15 m/s |
| Radius of the circle (r) | 50 m |
| Centripetal force (N) | 4,500 |
| Centripetal acceleration (m/s²) | 4.5 |
| Angular velocity ω (rad/s) | 0.3 |
| Time for one revolution (s) | 20.944 |
| Revolutions per minute | 2.86479 |
Friction must supply 4,500 N to take a 50 m curve at 15 m/s (54 km/h).
Try this example →Centripetal force is a real force pointing towards the centre. The 'centrifugal force' you feel pushing you outwards in a turning car is not a real force; it is your body's inertia trying to keep moving in a straight line.
F = mv² ÷ r, or F = mω²r using angular velocity.
Always towards the centre of the circle.
The gravitational pull of the Sun.
The object moves off in a straight line along the tangent to the circle.