# problems with calclulating power

by losbellos
Tags: calclulating, power
P: 335
 Quote by losbellos hej, well, őőőőő I dont what to say. again as you state, tangential speed is equal to ω x r this the velocity. - ω x r what is the power. Power is Force x velocity. true BUT HEJ THERE IS AN ARM THERE!!!! SO THE FORCE WILL BE... So power is P = Force x arm length < (BECAUSE YOU CANT TAKE THIS AWAY FROM IT) x ω x r . If it would be force only then you would disregard the arm... But we cant do that.... Because it is an arm and it makes the force much stronger on the smaller circle. Nobody doubts it I hope! So this is why i don't understand why we say p = T x ω ... You understand my problem with this? Force acting there call it torque or not it forces the cylinder to rotate... Force basically travels there and keeps the cylinder rotating with certain velocity.
You are wrong. There isn't much discussion about it. The force is the same whether or not there is an arm. The torque will be different depending on the length of the arm. If I apply a force of 1N to a lever, it is 1N no matter where I push. Depending on how far from the pivot I push, it will have a different torque, but the force is 1N. Torque is not force. We are not calling a force a torque for fun. We are calling torque a torque. Spend a little time thinking/reading about torque and then come back with questions.

As a side note, I feel like your tone is little too confident since nobody agrees with you and you don't have any sources. I think most people are more likely to discuss this if you ask questions without assuming that you are correct.
 P: 18 got no clue what to say, when I think that you guys acknowledge it that If I have an arm and use my muscles on the end and the force will be less on the other end of the arm because its is less than 1 meter.. then I am sorry, must be some sort of planetary influence taking over the physics forum.. I am sorry I find an other community. take care!!!
PF Patron
 P: 335 Okay, let me try to make this clearer (please excuse typos, I've had a few beers) Consider a lever. There is a pivot at $x=0$ and the arm of the lever is 2m long. Assume that the lever extends from zero to $x=2$. Now, lets say we have a mechanism of some sort that can exert a force of 1N. If we apply that at the mid point (always at right angles to the arm in order to keep this as simple as possible), the torque will be $\tau=1N\cdot1m=1Nm$. If you measure the force at the end of the lever, the TORQUE will be the same and therefore $F=\frac{\tau}{r}=\frac12N$. So the measured force is less, but the torque, which is NOT the same as the force, is the same. Now we want to consider the power. To keep things simple, lets assume that applying the force of 1N allows this lever to move at a constant velocity $v=1m/s$ (maybe it is in some viscous liquid or whatever, the specifics aren't important). So we apply this force and we find that $P=Fv=1N\cdot 1m/s=1W$. Since the torque and angular velocity are constant and defined as $\tau=Fr,\ \omega=\frac{v}{r}$, this is the same as saying $P=\tau\omega=1Nm\cdot 1s^{-1}$. If somebody else attempts to extract energy at the far end of this lever, by my calculations the power will be $P=\frac12\cdot 2m/s=1W$ since the force is one half that of the midpoint and the velocity (linear) is twice that of the midpoint. This clearly shows that the work extracted from the end point in any given time interval is equal to the work put in. By your calculations, the power is $P=\tau r\omega$ which gives the same power as input but at the end of the lever $P=1Nm\cdot 2\cdot 1s^{-1}=2W$. So, by your calculation, every second this simple lever allows one to freely extract twice as much energy as one puts in. This would solve a lot of problems if it were true, but it is not.
 P: 72 The best way to see this (IMO) is this: If you accept (or look up a proof) that rotational K.E. is given by $0.5Iω^{2}$, and that $T = I dw/dt$. If you think about the change in rotational K.E. : $d(0.5Iω^{2})/dt = Iω dw/dt = Tω$