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Power, torque and speed

The power transmitted by a shaft is linked to the torque and the angular velocity. This is useful when choosing a motor size or converting between torque and power at a known speed, for example for a motor or a pump.

P = M\omega

power from torque and angular velocity

\omega = \dfrac{2\pi n}{60}

angular velocity from speed

Symbols

$P$	power	W
$M$	torque	Nm
$\omega$	angular velocity	rad/s
$n$	rotational speed	rpm

Example

A torque of 100 Nm at 300 rad/s:

$P = 100\cdot 300 = 30\,000$ W $= 30$ kW.

Always convert speed (rpm) to

\omega

(rad/s) before using

P = M\omega

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Part of Machine Design: Machine elements.