Centripetal Force
Simple Explanation
Centripetal force is the net force, directed toward the centre of a circle, that is needed to produce centripetal acceleration and keep an object moving along that circular path. By Newton's second law, it equals mass times centripetal acceleration.
Why Do We Need It?
Something must always be providing this inward force — tension, friction, gravity, or a normal force — or the object cannot maintain circular motion and will instead move in a straight line (Newton's first law).
Formula
Centripetal Force
F = mv² / r
The net force directed toward the centre of a circular path that is required to keep an object moving in that circle.
- F
- — Centripetal force, in newtons (N)
- m
- — Mass of the object, in kg
- v
- — Speed along the circular path, in m/s
- r
- — Radius of the circular path, in metres
When to use it: Use to find the net inward force needed to keep an object of known mass moving in a circle of known radius and speed.
Worked Example
Finding required centripetal force
A 0.2 kg ball on a string moves in a horizontal circle of radius 0.8 m at 4 m/s. Find the tension in the string (assuming it provides all the centripetal force).
Why Does This Work?
Newton's second law (F = ma) applies just as much to circular motion as to straight-line motion — since the acceleration here is centripetal (v²/r, directed inward), the net force causing it must also be directed inward, with magnitude mv²/r.
Real-Life Example
Satellites orbiting Earth
A satellite stays in a stable circular orbit around Earth without any engine thrust.
Earth's gravity provides exactly the centripetal force needed to keep the satellite moving in its circular path — there is no separate 'centrifugal' force pushing outward; gravity alone supplies the inward force required, matching mv²/r for the satellite's orbital speed and radius.
Practice
A 1.5 kg object moves in a circle of radius 3 m at 6 m/s. Find the centripetal force needed.
MediumCommon mistake
Believing there is an outward 'centrifugal force' acting on the object itself — in an inertial (non-rotating) frame of reference, the only real force is the inward centripetal force; the outward sensation felt in a turning vehicle is due to inertia (the body's tendency to keep moving straight), not an actual outward force on the object.
Quick Review
- Centripetal force F = mv²/r, directed toward the centre, from Newton's second law.
- Real forces (tension, friction, gravity, normal force) provide the centripetal force — nothing pushes outward.
- Without enough centripetal force, an object cannot maintain its circular path.