Angular velocity calculator
A rotating part has one angular speed and as many surface speeds as it has radii.
rpm
Angular velocity
314.159 27rad/s
- Rotational frequency
- 50 Hz
- Surface speed
- 31.415 927
- Centripetal acceleration at that radius
- 9869.6044 m/s2
- In g
- 1006.42
- Time per revolution
- 0.02 s
Show the working
- Rotational speed = 3000
- Radius = 0.1
- Angular velocity = 3000 * 2 * pi / 60 = 314.159
- Rotational frequency = 3000 / 60 = 50
- Surface speed = 314.159 * 0.1 = 31.4159
- Centripetal acceleration at that radius = 314.159^2 * 0.1 = 9869.6
- In g = 9869.6 / g0 = 1006.42
- Time per revolution = 3000 > 0 ? 60/3000 : 0 = 0.02
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- omega = 2 pi x rpm / 60
- v = omega r
- a = omega^2 r
A grinding wheel at 3000 rpm and 100 mm radius runs at 31 m/s and pulls nearly 1000 g at the rim.