Library / Foundations: Physics / FPH-22
Foundations: Physics
Centripetal force
Inward force needed to move a mass in a circle.
- Ref
- FPH-22
- Rev
- v1
- Field
- Foundations: Physics
- Result
- F [kN]
For uniform circular motion the resultant radial force mv²/r points towards the centre. Also v = ωr and ω = 2πf.
Moving in a circle needs a constant pull towards the centre; the faster or tighter the turn, the bigger the force.
Calculator
kN
kg
m/s
m
- Radial acceleration v²/r8 m/s²
- Acceleration in g0.8158 g
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
Centripetal force (kN) current value 9.6 kN
vSpeedKey driver
0.024240
mMass
0.008160
rRadius
0.9696
- The force comes from friction, tension, gravity or a banked surface, depending on the situation.
- Halving the radius of a turn doubles the force needed at the same speed.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (kN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| v Speed | 1 to 100 m/s | 0.024 | 240 | 240 | +10% | +21 % |
| m Mass | 1 to 20,000 kg | 0.008 | 160 | 160 | +10% | +10 % |
| r Radius | 5 to 500 m | 0.96 | 96 | 95.04 | +10% | −9.09 % |
Sweep of Speed
| Speed (m/s) | Centripetal force (kN) |
|---|---|
| 1 | 0.024 |
| 1.778 | 0.07589 |
| 3.162 | 0.24 |
| 5.623 | 0.7589 |
| 10 | 2.4 |
| 17.78 | 7.589 |
| 31.62 | 24 |
| 56.23 | 75.89 |
| 100 | 240 |
Sweep one variable
Centripetal force (kN)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
F
Centripetal force
What the equation gives you. Everything else feeds it.
m
Mass
Mass moving in the circle. Directly proportional.
v
Speed
Speed along the circle. Squared: doubling speed quadruples the force.
r
Radius
Radius of the circle. Inversely proportional.
Worked example with the values above
- v² = 20² = 400.
- m v²/r = 1,200 × 400 / 50 = 9,600 N.
- F = 9.6 kN.
Assumptions and limits
- Uniform circular motion.
- Force directed towards the centre.
Common mistakes
- Thinking there is an outward force acting on the object.
- Using diameter for radius.
Statistics and uncertainty
Speed is squared, so a 3% error in speed gives about 6% in force.
Where it is used
- Vehicle cornering and banked track design.
- Rotating machinery loads.
Maths you need
- Newton’s second law: F = ma
- Circular motion: speed and radius