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Torque, speed and power are one relationship

Power is torque times rotational speed. Two of the three fix the third, so a motor rated in kilowatts tells you the torque only once you know the speed it turns at. Slow the same power down and the torque rises.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

In beta. This lesson was written for Hone and has not yet been checked by a licensed engineer. Practice material, not professional advice. What that means.

What it is for

It is the relationship behind every drive selection, and the one people work around rather than through. Somebody asks for 'a bigger motor' when what they actually need is the same power geared down, because the problem was never power, it was torque at low speed.

How to think about it

Write the three quantities down and see which two you have. Use radians per second, not revolutions per minute: the formula is in radians, and converting at the start prevents the commonest error in the whole subject.

Worked example

Power = torque x angular speed.
P in watts, T in newton metres, omega in rad/s.
rev/min to rad/s: multiply by 2 pi and divide by 60.
Do this first, every time.
Same power, half the speed, double the torque.
Which is what a gearbox sells you.
A motor plate gives power AND speed for this reason.
Neither alone tells you the torque.

Your turn

A shaft delivers 20 N·m at 100 rad/s. Write the power in watts.

P = 20 x 100 =  W

The trap

Putting rev/min straight into the formula. It is out by a factor of about 9.55 and the answer still looks like a sensible number of watts.

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