Torque is defined about a point?

[miko1977]

Hello guys

My question is simple but it really bugs me! Why we must define a torque about a POINT? In most of the textbooks i checked they define torque about an Axis. In wikipwdia though it is defined about a point. As a matter of fact it mentions:
"Torque is defined about a point not specifically about axis as mentioned in several books."
What is the diffrence between the two definitions?!

 

[ModusPwnd]

Try this...

Take the axis of your situation and calculate the torque about various points on it. What is the different between calculating with respect to the different points on the axis?

 

[conquest]

Hi,

As far as I know torque N is defined as:

N=r x F

Where F is the force and r is the vector from the origin to place the force attaches. (i.e. where you apply the force). Obviously you can superpose forces to get sums of torques.

In this definition no axis is explicitely named. There is a point that is explicitly named (namely the origin). Thus the torque is defined about the origin (a point).

However the reason for this definition is exactly that the torque vector gives you a measure of the rotation the force will cause and also the axis of the rotation. The magnitude gives you the measure (not in the measure theoretic sense of the word) and the direction gives you the axis of rotation.

This is actually not completely true because the torque could be 0. In that case we really can't speak of any axis at all since the vector doesn't really specify any direction. So we need to define the torque around a point for that case.

 

[miko1977]

Sorry my friend! I don't understand what you are trying to say. Can you explain please?

 

[miko1977]

Hi my friend.

Thanks for the explanation, it enlightened me! I don't fully understand your last statement though.

 

[conquest]

Hi,

Good

If it's still a bit fuzzy here's a summary (point (1) was made before me and it's the important one).The two points raised were essentially:(1) (goes for points with nonzero torque) Per point the axis of rotation varies, but you could definitely have two points with the same axis of rotation. Thus specifying an axis does not specify a point, but specifying a point automatically specifies an axis.

(2) When the Torque is zero the vector is the zero vector but there are infinitely many lines in Euclidian 3-space that go through any point in particular (0,0,0). So you need two points to specify a line (axis). If there is no Torque there is no line, but we should still be able to find out that torque is zero. So trying to define torque everywhere by only giving an axis would imply torque is non-zero everywhere which need not be the case.

 

[miko1977]

Great explanation! Thanks.

 

[Studiot]

There is some confusion about what is meant by torque and moment that has existed since the terms were first introduced nearly two centuries ago.

Exact definitions have varied depending upon which source you read or quote.

Personally I prefer to reserve torque for the twisting action about an axis for two reasons.

Firstly because that is consistent with engineering use for torsion and for shaft torque in a machine.
This allows the revolution angle to exceed 360 so torque can be referred to engine speed in rpm or whatever.
Using torque for torsion allows moment to be reserved for bending.
Finally using torque about an axis allows the transfer of twisting action along a shaft as in say a screwdriver.

go well