I have been asked to compare the power required to turn a 80mm dia. bar at 100rpm to that of an 80mm dia. at 200 rpm. I'm not too sure how to go about this... I have made the presumption that I'm using steel which can be machined at 15cm^3/min per kilowatt.

I know that 100rpm will produce 25m/min by using:

S=(TTd/v)/1000..... so 200rpm will equal 50m/min

Just can't get my head round calculating and comparing the power........

I have been asked to compare the power required to turn a 80mm dia. bar at 100rpm to that of an 80mm dia. at 200 rpm. I'm not too sure how to go about this... I have made the presumption that I'm using steel which can be machined at 15cm^3/min per kilowatt.

I know that 100rpm will produce 25m/min by using:

S=(TTd/v)/1000..... so 200rpm will equal 50m/min

Just can't get my head round calculating and comparing the power........

It's possible to do those things with zero power since angular momentum of a closed system and if the bar has no torque on it then it takes zero power. There has to be a counter torque acting in order for the bar to exert power since power is the energy transfered per unit time. Where is the energy transfer in your question?

Work done
A=Fs
s=ra,
where a is angle [rad].
Power is
P=A/t=Fra/t=Frw,
where w is angular speed [rad/s].
Or
M=Fr
P=Mw.
Asuming that M=const or F=const
P1/P2=w1/w2.

Ypu didn't define s, r and a. If Work done is W = F*ds where "* represents the dot product. Here where F abd ds are perpendicular so therefore F*ds = 0.