Library / Foundations: Physics / FPH-23
Foundations: Physics
Speed in circular motion
Speed of a point on a rotating body from frequency and radius.
- Ref
- FPH-23
- Rev
- v1
- Field
- Foundations: Physics
- Result
- v [m/s]
ω in rad/s, f in Hz, r radius in m. Radial acceleration a = v²/r = ω²r.
A point further from the axis travels a longer circle in the same time, so it moves faster.
Calculator
m/s
Hz
m
- Angular speed ω31.42 rad/s
- Radial acceleration ω²r296.1 m/s²
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.
Speed (m/s) current value 9.425 m/s
fFrequencyKey driver
0.188942
rRadius
0.314157
- Rim speed limits the size and speed of flywheels, propellers and discs.
- Doubling the radius at the same f doubles the speed and doubles the acceleration.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| f Frequency | 0.1 to 500 Hz | 0.1885 | 942.5 | 942.3 | +10% | +10 % |
| r Radius | 0.01 to 5 m | 0.3142 | 157.1 | 156.8 | +10% | +10 % |
Sweep of Frequency
| Frequency (Hz) | Speed (m/s) |
|---|---|
| 0.1 | 0.1885 |
| 0.29 | 0.5466 |
| 0.8409 | 1.585 |
| 2.438 | 4.596 |
| 7.071 | 13.33 |
| 20.5 | 38.65 |
| 59.46 | 112.1 |
| 172.4 | 325 |
| 500 | 942.5 |
Sweep one variable
Speed (m/s)Hover, touch, or use the arrow keys on the chart
Variables and how each one contributes
v
Speed
What the equation gives you. Everything else feeds it.
f
Frequency
Revolutions per second. Directly proportional.
r
Radius
Distance from the axis. Directly proportional.
Worked example with the values above
- ω = 2πf = 2π × 5 = 31.42 rad/s.
- v = ωr = 31.42 × 0.3.
- v = 9.425 m/s.
Assumptions and limits
- Uniform rotation.
- Radius measured from the axis.
Common mistakes
- Using rpm directly as f.
- Forgetting 2π.
Statistics and uncertainty
Speed and radius errors combine in quadrature; radius of large rotors is usually known to under 1%.
Where it is used
- Tip speed of rotors and propellers.
- Centrifuge and flywheel checks.
Maths you need
- Frequency: rev per second
- Radians: 2π per revolution