# Problems with calclulating power

1. Jan 14, 2013

### losbellos

Hej Guys,

I have seen on wikipedia, that power = Force x velocity, and this is fine but when they explain the same for circular moving force then they use power = Force (x arm) x Angular velocity (rads/sec). This cannot be, the velocity actually cannot be represented by only angular velocity, it needs the radius as well. For example distance = velocity x time = angular velocity * radius * time. So in this way the equation power = Force x velocity (for linear moving force) and for circular moving force the power will be = arm x force x angular velocity x radius .. in circular considering that the force is always perpendicular to the arm. If not then power would be > force x sin (Angle of force-arm) x arm x angular velocity x radius.

example considering the force and velocity as a point on a circle or a line...
circle circumference = 62.83m
powerL = force * vel = 100N * 14.13675 = 1413.675 watts
powerC = force * angular velocity * radius = 100N * 1,4137 rads * 10.0m = 1413.7 watts
so out of calculation error PowerC = PowerL

angular velocity != velocity so even in rotational systems it cannot be used alone without the radius. This way the power = torque x angular velocity is not true. To prove this like above one maybe divide the circle to line segments where the a value = force x arm x velocity x distance can be calculated for each segments, considering the torque, and these segments added will be much different from the torque x angular speed (rads/sec) x distance segments together. Naturally there will be some difference based on the number of segments. The more segments the closer it will be. Again torque x velocity != torque x angular velocity (rads/sec). The result is only same if the other equation is power = force x arm x angular velocity x radius = torque x angular velocity x radius.

Am I right?
Thx.

Last edited: Jan 14, 2013
2. Jan 14, 2013

### ZapperZ

Staff Emeritus
First, stop using Wikipedia especially if you are using it as your PRIMARY source.

Secondly, "Power" is defined as the amount of energy expanded or supplied per unit time. This means that you need to find the time rate of energy available or produced. That is the general principle.

Thus, find the rotational energy of the system per its time period.

Zz.

3. Jan 14, 2013

### 256bits

losbellos
POWER
Linear system P = F v , Power = force times velocity
rotational system P = T ω , Power = torque times angular velocity(rad/sec)

( if you want to analyze, simplistically ; knowing T = F r, then P = F r ω = F v )

Also, you stated
Check your units to see if they come out correctly as something resembling power.

Last edited: Jan 14, 2013
4. Jan 14, 2013

### losbellos

Well they mean mechanical power. I usually deal with newtons. Can you direct me to a good guider to torque and other other calculations regarding force moving in circular path, using arms? I mean real validated source.

But by the way 1 joule is also 1 Nm(lets say second as well) and 1 watt second, so they all unit of different types of power aren't they? The time in my example is always 1 second to make it simple... I edited my post to make it more understandable.

5. Jan 14, 2013

### losbellos

Its not true, because you consider the r only once. You need it once for the torque and then one more time for the velocity because r x ω = velocity. Just see my example. I cannot state that the velocity I am doing linear is not the same the as the velocity travels on a circle. Both velocity travels the same distance by the time... circular or linear it doesn't matter. So defining velocity by angular speed is invalid, unless the r multiplies.. Its like you try to consider the circular move without actually the arm. We say torque because it have an arm and the force. That makes torque but this torque rotates with a speed. For the speed I need the r again, because velocity = ω x r . Without it, its like you consider only the force and you leave the arm out of the calculation. Thats not valid.

Last edited: Jan 14, 2013
6. Jan 14, 2013

### 256bits

Torque and energy might have to same units but you have to keep the concepts seperate, and the units are designated so to avoid confusion.

torque is the unit newton-meter , N-m
energy is the unit joule

A torque of 1 N-m applied rotationally through a full revolution will require 2∏ joules of energy.

Last edited: Jan 14, 2013
7. Jan 14, 2013

### 256bits

You can argue about it all you want until the cows come home, but you are incorrect.
In any case in your calculation you have used r only once.
so you seem to be saying one thing but nonetheless, doing the calculations correctly.

8. Jan 14, 2013

### losbellos

I think not, its 1 joule if the rotation is done by one second. Even though Nm doesn't have time value assigning it that the torque did "work" for one sec (for one revolution) then it will be one joule. Otherwise it is not known. It could be 10 sec or 5 sec or anything therefore I cannot say 2Pi joule. Also why would i use radians instead of velocity?

For simplicity lets consider the arm and the force as a point. This force point rotates around the center of the circle on the cirle. It wont matter that it rotates or moving on a linear path,velocity is what defines the power. So why I should use angular speed instead of velocity.
Its like I want to degrade the output power because its moving circular. Seeing the prove above, that divide a circle into points or lines it would result very different values...

9. Jan 14, 2013

### 256bits

10. Jan 14, 2013

### losbellos

I explain there the force moving on a circle it doesnt matter that it is considered as a torque or else. This is what I am tryin to say. I will explain the problem in a graphic then maybe it will be clearer why I would say that Power including torque would be T x ω x r

11. Jan 14, 2013

### losbellos

So here is a diagram explains the problem.
There is an arm in between A and B points.
This arm is attached to the smaller circle which rotates with 3.21 m/s. This rotation is due the force being applied at the end of the arm at B point.

Now lets start with the forces; The torque at point A would be arm length x force x sin (angle in between arm and force) . THe torque is 6.84m x 100N x sin(147.995
) = 362.5 NM

Basically at that point 362NM "rotates" with 3.21 m/s or with 1.04 rad. So the power would be P=T x ω by the physics but hej, this force - because torque is basically a force with a support arm - why would I use uu instead of velocity. And why ω would be different in this sense from the actual velocity? What is the reason for this? So why not use instead P = ω x r x T Can you explain this to me ?

Also this torque force could be just a liner move of force with velocity, must be same... (lets not consider the angle of the force or consider it always parallel to the arm)

12. Jan 14, 2013

### losbellos

So actually here it would be valid to say that power in other way would be: Power = Force x Distance / Time . This way the 362 N moves 1 meter in one second. So the power is 362Watts.
Well since I don't point exactly out where the force actually acting so I consider the arm as a One ARM lifter (dont know it in english) and consider the weight I have to lift and the rotation point on the other side at A point and the Force at B point. So just simply multiply with the length of the arm.

13. Jan 14, 2013

### losbellos

14. Jan 14, 2013

### 256bits

A point on the circumference of the smaller circle rotates at a tangential velocity of 3.21 m/s

are you using the correct arm length from the axis of rotation to point B. There are no dimensions so impossible to tell.

i think you mean 1.04 rad/sec, the angular velocity.

correct

One reason is that it is easier to do calculations using ω. All points on a body rotating about an axis have the same angular velocity ω. The tangential velocity of points vary from a value 0 at the axis to a value v = r ω at the circumference.
For your problem, Point A and B have the same angular velocity ω ( rad/s ), but the tangentiial velocity v ( m/s ) of A is less than that of B.

Check the units and you will see that ωrT does not come out as watts, or power.

15. Jan 14, 2013

### DrewD

Perhaps you should think about it coming from the linear definition.
We define $P=Fv$, but in a rotational setting, $v=r\omega$ so we find that $P=Fr\omega$. But now we notice that $Fr=\tau$ so we must have $P=\tau\omega$ and not $P=\tau\omega r$ as you said.

The reason for using torque and angular velocity is, as 256 says, it is often easier to use if you know that a system is rotating. It is significantly easier when you have a constant angular velocity. In this case, using the linear velocity is complicated since it is continuously changing.

16. Jan 14, 2013

### 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.

17. Jan 14, 2013

### losbellos

I don't know where else to talk about it so please don't stop the discussion about it.

18. Jan 14, 2013

### losbellos

19. Jan 14, 2013

### DrewD

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.

20. Jan 14, 2013

### losbellos

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!!!