How Centrifugal Force is Calculated
When an object moves in a circle, it requires a force directed towards the centre to keep it on its circular path. This inward force is called the centripetal force. From the perspective of the rotating object itself, there is an apparent outward force of equal magnitude, known as the centrifugal force.
F = mv²/r or equivalently F = mω²r
Where:
- F = centrifugal/centripetal force (newtons, N)
- m = mass of the object (kilograms, kg)
- v = linear (tangential) speed at the radius (metres per second, m/s)
- r = radius of circular motion (metres, m)
- ω = angular velocity (radians per second, rad/s)
The two formulas are equivalent because linear speed and angular velocity are related by v = ωr. Substituting into F = mv²/r gives F = m(ωr)²/r = mω²r.
Worked Example
A 2 kg object travels in a circle of radius 0.5 m at a linear speed of 10 m/s. What is the centrifugal force?
| Step | Calculation | Result |
|---|
| Mass | m = 2 kg | 2 kg |
| Radius | r = 0.5 m | 0.5 m |
| Speed | v = 10 m/s | 10 m/s |
| Force | F = mv²/r = 2 × 10² / 0.5 | 400 N |
| G-force | a = v²/r = 100/0.5 = 200 m/s² → 200/9.81 | 20.39 g |
This matches the calculator's default output: 400 N, 0.40 kN, and 20.39 g.
RPM to Angular Velocity Conversion
If you know the rotational speed in RPM (revolutions per minute), convert to angular velocity using:
ω (rad/s) = RPM × 2π / 60
For example, 300 RPM = 300 × 2π / 60 = 31.42 rad/s. The centrifugal force is then F = mω²r.
Practical Applications
Centrifugal force calculations appear in many engineering and everyday contexts:
- Centrifuges: Laboratories use high-speed centrifuges to separate materials. A sample 0.1 m from the axis at 10,000 RPM experiences roughly 11,000 g.
- Vehicle cornering: When a car turns, passengers feel an apparent outward push. Engineers size tyres and suspension based on the centripetal force needed to hold the car on the curve.
- Rotating machinery: Turbine blades, flywheels, and washing machine drums must be designed to withstand the centrifugal stresses at operating speeds.
- Amusement rides: The outward feeling on a carousel or loop-the-loop is centrifugal force. Ride engineers calculate maximum g-forces to ensure passenger safety.
- Satellites and orbits: A satellite in orbit is in free fall towards Earth; the centripetal acceleration of its orbit equals the local gravitational acceleration.
G-Force
G-force expresses acceleration as a multiple of standard gravity (g = 9.81 m/s²). The centripetal acceleration is a = v²/r (or a = ω²r), and the g-force is simply a/9.81. Fighter pilots can sustain around 9 g briefly; sustained exposure above 5 g causes blackout in most people without a pressure suit. Industrial centrifuges routinely operate at tens of thousands of g.
Related Calculators
Sources and method: Newton's second law of motion and classical circular motion theory as given in Halliday, Resnick and Krane, Physics (5th ed.). Standard gravity g = 9.80665 m/s² (BIPM). Conversion 1 lbf = 4.44822 N.
This calculator applies to uniform circular motion in a single plane. It does not account for non-uniform rotation, relativistic effects, or three-dimensional orbital mechanics. For engineering applications involving high-speed rotating machinery, consult a qualified mechanical engineer.
