What Is Centrifugal Force?
Whirl a bucket of water over your head fast enough and the water stays in the bucket — even at the top, upside down. The outward push that seems to slam everything toward the outside of a curve is what we call centrifugal force.
Strictly speaking, physicists classify it as a fictitious force: nothing is actually pushing outward. What is really happening is inertia — every object wants to travel in a straight line, so when something forces it around a bend (a string, a road surface, a spinning drum), the object pushes back against whatever is turning it. That resistance shows up as an apparent outward force in the rotating frame of reference, and it is very measurable. Engineers rely on it to size centrifuges, design banked curves, test astronaut tolerances and build amusement rides.
The Centrifugal Force Formula
Using the object's linear speed $v$ along the circle:
[
F = \frac{mv^{2}}{r}
]
Where:
- F is the centrifugal force in newtons (N)
- m is the mass of the object in kilograms (kg)
- v is the speed along the circular path in metres per second (m/s)
- r is the radius of the path in metres (m)
If you know the angular speed $\omega$ (in radians per second) instead, use the equivalent form:
[
F = m\omega^{2}r
]
Both formulas are the same statement, because $v = \omega r$: substitute once and $m(\omega r)^2 / r$ collapses to $m\omega^2 r$. Notice that velocity enters squared — double the speed and the force quadruples.
Worked Example: A Ball on a String
A 5 kg ball swings in a circle of radius 2 m at 10 m/s:
[
F = \frac{mv^{2}}{r} = \frac{5 \times 10^{2}}{2} = \frac{500}{2} = 250 \text{ N}
]
Now confirm it with the angular-speed form. The angular speed is $\omega = v/r = 10/2 = 5$ rad/s:
[
F = m\omega^{2}r = 5 \times 5^{2} \times 2 = 5 \times 25 \times 2 = 250 \text{ N}
]
Both routes agree: 250 N, about 5.1 g on the ball — the same pull a fighter pilot feels in a hard manoeuvre. Try entering these numbers above; the calculator reproduces them exactly.
Centrifugal vs Centripetal: Two Sides of One Turn
Students mix these up constantly, so here is the clean split:
| Centripetal force | Centrifugal force | |
|---|---|---|
| Direction | Toward the centre | Apparent push outward |
| Real or fictitious | Real (tension, friction, gravity…) | Fictitious (inertia viewed from the rotating frame) |
| Formula | Same magnitude: $mv^2/r$, directed inward | Same magnitude: $mv^2/r$, directed outward |
| Example | Friction gripping a car's tyres through a bend | The sideways slide you feel across the seat |
They are always equal in size and opposite in direction. The inward force is the cause; the outward feeling is the effect you experience from inside the turn.
Where the Squared Velocity Bites
Because $v$ is squared, small speed changes create huge force changes:
| Speed on a 50 m bend (same car) | Relative force |
|---|---|
| 50 km/h | 1× |
| 70 km/h | ≈ 2× |
| 100 km/h | 4× |
This is exactly why speed limits drop sharply before tight curves: the grip available from the tyres is fixed, but the demanded force grows with the square of your speed. The same logic sets spin speeds in washing machines and laboratory centrifuges — a modest radius spun very fast generates enormous separating forces.
Quick Recap
- Centrifugal force is the apparent outward push in a rotating frame, caused by inertia.
- Formula: $F = mv^2/r$, or equivalently $F = m\omega^2 r$ with $v = \omega r$.
- Velocity enters squared: twice the speed means four times the force.
- Centripetal pulls inward (real); centrifugal seems to push outward (fictitious) — equal in magnitude.
- Use the calculator above to check any mass–speed–radius combination and see the g-force instantly.
Once you have the force on a rotating body, the RPM to G-Force Calculator is a natural next step for exploring spin-driven loads.