Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

What is the difference between torque and moment? I would like to see mathematical definitions for both quantities.

I also do not prefer definitions like "It is the tendancy..../It is a measure of ...."

To make my question clearer:

Let $D\subseteq\mathbb{R}^3$ be the volume occupied by a certain rigid body. If there are forces $F_1,F_2,....,F_n$ acting at position vectors $r_1,r_2,...,r_n$. Can you use these to define torque and moment ?

share|improve this question
    
Possible duplicates: physics.stackexchange.com/q/16389/2451 and links therein. –  Qmechanic Feb 19 '13 at 13:16
    
I upvoted all answers. Since, I am getting different answers I accepted the one that seems most reasonable to me. –  Amr Feb 19 '13 at 18:53
add comment

5 Answers

up vote 8 down vote accepted

The moment of a vectorfield $\vec{v}$ at a position $\vec{r}$ is equal to $$\vec{r}\times\vec{v}.$$ So torque is simply a special case where the vectorfield we look at is the force field, $\vec{v} = \vec{F}$. Another way of saying this is that torque is the moment of force.

share|improve this answer
    
Thank you for referring to the big picture. The terminology looks alright for me. As far as I understood, this is just a redundancy in terms. I have been told before that torque is different from moment of a force. Is this true ? –  Amr Feb 19 '13 at 17:50
1  
There might be some slight differences, but they probably stem from technical jargon (so no real physical difference). From what I've read (on this website among others), the term "torque" is usually preferred when speaking of the moment of a couple of forces (so when 'twisting' rather than 'rotating'). The term "moment" is used in any other general case. Personally I think it is an unnecessary distinction and source of confusion. I'm not a native English speaker and in my language we don't have this problem. :) –  Wouter Feb 19 '13 at 18:24
    
In addition, what is the moment of rotational velocity? It is linear velocity $\vec{v} = \vec{r}\times\vec{\omega}$. In fact, both forces and rotations act along a line, the position of which is given by $$ \vec{r} = \frac{\vec{v}\times\vec{\omega}}{|\vec{\omega}|^2} \\ \vec{r} = \frac{\vec{\tau}\times\vec{F}}{|\vec{F}|^2}$$ Do you see the similarity? –  ja72 Nov 27 '13 at 18:54
add comment

While the formulas are similar, Torque relates to the axis of rotation driving the rotation, while moment relates to being driven by external force(s) to cause the rotation. Moment is a general term and when used in context of rotational motion is pretty much the same.
Torque is $\vec{F} \times \vec{r}$. As @Apurba said, $\sum{\vec{F}}$ may not be zero. Moment = Magnitude of Force x Perpendicular distance to the pivot.

share|improve this answer
add comment

Torque is $\vec{F} \times \vec{r}$ but in this case $\sum{\vec{F}}$ may not be equal to zero. Where as in case of moment the two equal force acts in tow different side, So $\sum{\vec{F}} = 0$. I think this is the difference.

share|improve this answer
    
Thus, every moment is a torque –  Amr Feb 19 '13 at 11:22
add comment

moment is turning effect produced by a force . while torque is due to rotation of body.

share|improve this answer
2  
Neither of these brief definitions provides enough detail to be useful in any way. –  Brandon Enright May 16 '13 at 7:05
    
and what's the difference between "turning" and "rotation" ? –  Amr Nov 8 '13 at 18:40
add comment

Moment is bending due to linear force and the distance from the axis is perpendicular whereas in torque rotation takes place beyond 360 degrees.

share|improve this answer
add comment

protected by Qmechanic Nov 27 '13 at 19:32

Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.