Calculating Power from Torque and Rotor Speed

[littlesohi]

Homework Statement

An electric motor runs at 24 rev/s and supplies a torque of 50.3 Nm. What is the power P delivered by this motor?

Homework Equations

The Attempt at a Solution

I just know that power is work/second. I don't know how I can relate the torque, rotor speed and power! Pleaseee help :(

 

[Delphi51]

That is tricky! It should be okay to think of the motor lifting a weight of 50.3 N at a distance of 1 meter from the center of the shaft. Can you figure out how fast it is moving the weight from that 24 rev/s?

There is a way to do the rest more elegantly with formulas, but at what I think is your level of physics, I would recommend you consider a small time, say 0.1 second.
Figure out how far the weight is lifted in that time.
Figure out how much work is done in lifting it that far.
Then use your power formula on those figures.

 

[littlesohi]

So basically by dividing the "weight" of the 50.3 by the rotos speed I will get how much speed it will actually take to move that weight? Is that right??

 

[Delphi51]

"how much speed it will actually take to move that weight" doesn't make sense to me. The thing is, it makes 24 complete turns per second so it has a definite speed you must take into account. Think 24 times the circumference divided by one second. From that you can figure out how far it is lifted in the arbitrary time of 0.1 s. Maybe better to use 0.001 s so you don't get sidetracked thinking about non-vertical motion. This arbitrary time should cancel out in the whole calc.

 

[SteamKing]

Instead of all this hand waving about lifting a weight in a certain amount of time, there is a simple formula which relates torque and angular velocity to power output. A simple Google search should find this formula.

 

[Delphi51]

True, but is the only objective to find the answer?
I think the OP will have a much better learning experience figuring it out a step at a time with the familiar basic formulas. Then, perhaps, he or she will take time to derive the linear formula for power as a function of force and velocity using the same technique, only with algebra instead of numbers. The last step, using the formula you mentioned, I would say is simply going too far into the abstract. There are enough formulas to remember already!