Centripetal Force (F = mv²/r)
Also known as circular motion force
Worked example: 1200 kg at 20 m/s, r = 100 m → F = 4800 N — press Try an example to run it live, then adjust anything.
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Falling around the Earth →
Grade 12Grade 12 Physics
Round the bend →
UniversityEngineering Mechanics
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Centripetal Force (F = mv²/r) explained
An object moving in a circle is accelerating even at constant speed, because its direction keeps changing — and sustaining that requires a net inward force of mv²/r. Swing a ball on a string and the string's tension supplies it; drive through a curve and tire friction does. A 1,200 kg car rounding a 50 m curve at 20 m/s needs = (1200)(20²)/50 = 9,600 N of sideways grip — nearly the car's own weight.
The v² is the part engineers respect: doubling speed quadruples the required force, which is why exit ramps post low advisory speeds and why racetracks bank their turns — banking tilts the road's normal force inward so friction isn't doing all the work. Solving for v takes the principal positive square root, since speed is a magnitude. And centripetal force is not a new kind of force; it's simply the name for whatever real force happens to point toward the centre.
Centripetal Force (F = mv²/r) formula
- = Centripetal force (N)
- = Mass (kg)
- = Speed (m/s)
- = Radius (m)
Missing one of these? Work it out first, then come back
- Centripetal force — Newton's Second Law, Work (W = Fd cos θ)
- Mass — Newton's Second Law, Kinetic Energy
- Speed — Speed, Distance & Time, Kinetic Energy
- Radius — Centripetal Acceleration (a = v²/r), Speed in Circular Motion (v = 2πr/T)