Centripetal Force Explained
What centripetal force is, the formula F = mv²/r, what provides it in cars, planets and fairground rides, why “centrifugal force” feels real, and examples.
Key takeaways
- Centripetal force is the net inward force that keeps an object moving in a circle.
- F = mv²/r: faster speed or tighter turns need much more force.
- Gravity, friction or tension can provide it; it isn’t a separate kind of force.
On this page
An object moving in a circle is always changing direction, which means it’s accelerating, even at constant speed. The force that causes this inward acceleration is called centripetal force.
The formula
F = m v² ÷ r
- m = mass (kg)
- v = speed (m/s)
- r = radius of the circle (m)
Centripetal acceleration: a = v² ÷ r
Double the speed and the force needed quadruples; halve the radius and it doubles.
What provides centripetal force?
| Situation | Force providing it |
|---|---|
| Car turning a corner | Friction between tyres and road |
| Planet orbiting the Sun | Gravity |
| Ball on a string | Tension in the string |
| Roller coaster loop | Normal force from the track plus gravity |
Centripetal force isn’t a new kind of force; it’s whatever real force points toward the centre.
Why do you feel pushed outward?
In a turning car, you feel thrown outward. In fact, your body tends to keep moving in a straight line (inertia) while the car turns beneath you. The outward “centrifugal force” is a way of describing that feeling from inside the car. See Newton’s first law.
Worked example
A 1,200 kg car turns a corner of radius 50 m at 15 m/s: F = 1,200 × 15² ÷ 50 = 5,400 N. If friction can’t provide that, the car skids; see friction explained.
For planets and satellites, gravity provides the centripetal force; see gravity explained.
Frequently asked questions
Is centripetal force a real force?
It’s the name for the net inward force, provided by real forces like friction, tension or gravity.
What happens if centripetal force disappears?
The object continues in a straight line, tangent to the circle.
What’s the difference between centripetal and centrifugal force?
Centripetal is the real inward force; centrifugal describes the apparent outward effect felt in a rotating frame.
Sources
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