Torque does not do work, ie cause acceleration. Power does that. Power is a product of force and movement. Try to undo a wheel nut that seized and you have applied loads of torque but done no work unless it moves.
Work is measured in J which is force (N) newton) applied thru one metre (m) metre). In order to do work you need to use energy (J) joules).
Power is the rate at which energy is consumed. Simply energy per time (W) watts).
Acceleration is change of velocity per time (m/s) metre/second). Acceleration is the net result of all forces (N) acting on the object.
Velocity is speed with direction of motion (m/s). If not going in a straight line and/or speed isn’t constant means acceleration.
Let’s get back to power: since we know power uses energy, which in turn is work per time. Power = J / time. And work is force per distance. Power = N • distance / time
But wait, distance per time is velocity, so power = N • velocity. And again force is mass times acceleration we get power = mass • acceleration • velocity.
Power = torque • velocity.
As you can see you can’t have one without the other, everything intervenes.
Real world example, you are trying to move in 6 gear from standstill, what happens, it doesn’t move, because torque is too low. And when you shift to 1st you increase torque, but input power stays the same.
Regarding your nut. No work has been done on a nut, but energy has been spent so work is done, just elsewhere, say your dewalt or your muscles.
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Edited by TomasLT, 04 January 2018 - 10:10 AM.