What will be the value of r here.

[dE_logics]

Suppose I'm given a simple task to taking out the moment about a point -


o-------------------F

o is the fulcrum...and F is the place on which force applies (of course in the perpendicular direction) and r is the distance between the fulcrum and force.

If we take o as the origin, then r will be positive.

But what if we take the origin as somewhere on r?...what will be its sign then?

 

[tiny-tim]

Hi dE_logics!

If we take o as the origin, then r will be positive.

No, that doesn't make sense …

r is a vector (and so doesn't really have a sign), and so is the https://www.physicsforums.com/library.php?do=view_item&itemid=175", which is r x F

But what if we take the origin as somewhere on r?...what will be its sign then?

(see above, but it's worth adding …)

You would always take https://www.physicsforums.com/library.php?do=view_item&itemid=64" (torques) about the fulcrum anyway, because there's a reaction force there, of unknown size and direction,

and the only way of keeping that unknown force out of the equations is by taking moments about the fulcrum!

 

[dE_logics]

That reactive force on that fulcrum should be equal to the force applied...cause if this is not so, the body will not be in translational equilibrium.Initially I was thinking there would be no reactive force on the fulcrum.

But there are 2 cases...if the bar is mass less, then there has to be a normal reaction, cause as compared to a real body having mass, the normal reaction is given by its inertia...so there should be no application for force on the fulcrum, cause the normal reaction is given by the inertia.

In a mass less body, there is no inertia, so the normal reaction will be given by the fulcrum.

r is a vector (and so doesn't really have a sign), and so is the torque, which is r x F

But we came to that conclusion here -

https://www.physicsforums.com/showthread.php?p=2216723#post2216723

If this is not so, the F taken here should be its modulus.

 

[Born2bwire]

No, again, the torque is a vector and is the result of vectors and their operations.

 

[tiny-tim]

If this is not so, the F taken here should be its modulus.

Sorry, dE_logics, I've no idea what you're talking about.

r x F is a vector expression (ok ok … technically, it's two vectors making a psuedovector ).

 

[dE_logics]

Point is r and F should have their respective signs.

Cause...if suppose in a rotating bar, the direction (and so sign) of F will flip (as it rotates over time), but the torque and its sign remains the same (i.e clockwise or anticlockwise), so to balance the sign flip of F, r's sign should also be flipped...that is the only way, the torque's sign can be maintained.

That's what I mean here.

I don't know what is a psuedovector.

 

[dE_logics]

No, again, the torque is a vector and is the result of vectors and their operations.

Yeah...I agree with that, but that section of coordinate system is causing a problem.

 

[tiny-tim]

… the direction (and so sign) of F will flip …

Something's obviously bothering you, but I can't work out what it is …

what do you mean by "flip"? what is this F that's flipping?

 

[Born2bwire]

A vector does not have a sign, it has a magnitude and a direction. There is no sign flipping in terms of the force or displacement vectors. You need to treat these as vectors and understand how the vectors and their operations translate to scalar equivalents and not the other way around.

 

[dE_logics]

what do you mean by "flip"? what is this F that's flipping?

I mean the sign flip.

If you're observing a rotation, form your perspective the direction of F will change over time...since the torque or moment by force is not changing, there should be a compensation of the sign change in F...this compensation will be by r.

E.G -

and -

The torque exhibited by both of these is the same, but the direction force is opposite.

So the torque by one should be F*r and the other should be -F*r...i.e its direction should be opposite.

But obviously this does not happen...the r is there as the compensation, so actually this happens -

Torque by one : F*r, torque by other : -F*-r

This has been confirmed here -

https://www.physicsforums.com/showthread.php?p=2216723#post2216723

So there should be a sign of r...what will it be in the case as stated in the main question?

 

[dE_logics]

A vector does not have a sign, it has a magnitude and a direction. There is no sign flipping in terms of the force or displacement vectors. You need to treat these as vectors and understand how the vectors and their operations translate to scalar equivalents and not the other way around.

Ok...thanks!

 

[tiny-tim]

I mean the sign flip.

If you're observing a rotation, form your perspective the direction of F will change over time...since the torque or moment by force is not changing, there should be a compensation of the sign change in F...this compensation will be by r.

E.G -
…
So there should be a sign of r...what will it be in the case as stated in the main question?

I can see from your diagrams what you mean now …

but it's not "flipping", since F (and r) rotates continuously.

Anyway, your diagram shows an arrow at the head of F, but it also needs an arrow at the head of r …

the sign of F (and r) is irrelevant, but of course the direction matters, and F is always 90º clockwise from r, so r x F is always the same.

Forget about signs … always use arrows. ​

 

[dE_logics]

It all appears extremely confusing...need to work on vectors.