# Moment of force or torque [closed]

Is the moment of force taken in a clockwise and anticlockwise fashion? Why then do we curl our fingers and check it?Explain the equivalence or similarity between the two.

• This doesn't really seem like an engineering question, and I don't really understand what you mean by "Is the moment of force taken in a clockwise and anticlockwise fashion? " – JMac Aug 14 '17 at 19:59
• @JMac this is a exam question from the look of it – joojaa Aug 14 '17 at 22:18

A moment has a direction, which you can imagine when you look at the direction of the force and the axis you're calculating the moment from. Depending on which direction you're looking at it from, however, it can be seen as either clockwise or counter-clockwise. To remedy this confusion, we use the right-hand rule to identify whether a moment is positive or negative around an axis, instead of as clockwise or counter-clockwise.

A moment is positive when, curling the fingers of your right hand in the direction of the moment around the axis, your thumb points in the positive direction of the axis. Accordingly, it is negative when your thumb points in the opposite direction.

The right-hand rule is just a convention; it could very well be the left-hand rule that defines a positive direction. However, as far as I know, the right-hand rule is the leading convention. It is also used for angular velocity and magnetic fields, among other things.

• Right hand rule is just a convention. We could equally well choose to use a left handed coordinate system based definition. – joojaa Aug 14 '17 at 22:20
• I was wondering if I should have addressed that or not. It's a convention, but it's the leading convention, as far as I'm aware. – Andrew Elliott Aug 14 '17 at 22:27
• It should allways be mentioned. One day you will encounter a person using the opposite convention. – joojaa Aug 14 '17 at 22:31
• @joojaa is correct, you will meet people who use the opposite convention. There is some internal finite element software in my company where Mx and Mz use the right hand rule, but My uses the left hand rule. This allows the software to use tension as positive for Fx but sagging as positive for My. It's completely idiotic in my view. – AndyT Aug 15 '17 at 9:48

The right hand rule dictates what a positive moment is. For a planar force, a positive moment is along the +z axis (out of the plane). Also a positive rotation is also along the +z axis (out of plane). See diagrams below on the left for what positive moments and rotations looks like: On the right are the exact same moments and rotations, just expanded out by components.

The rule for the moment of a force $\pmatrix{F_x & F_y}$ located at $\pmatrix{x&y}$ is $$M = x\,F_y - y\,F_x$$

Similarly for motions the velocity if a point located at $\pmatrix{x&y}$ while being rotated by $\omega$ is

$$\pmatrix{v_x & v_y} = \pmatrix{ -y\, \omega & x\, \omega}$$

These are kind of hard to remember, so you kind of have to visualize it to come up with these.

Alternatively use the 3D versions, which are much simpler

$$\vec{M} = \vec{r} \times \vec{F}$$

and

$$\vec{v} = \vec{\omega} \times \vec{r}$$

where $\times$ is the vector cross product, applied as 3D vectors. Here again you have to memorize that position comes before force in the 1st expression, but after rotation in the 2nd one.

PS. In the UK, they do use the left-hand-rule with a different permutation of vectors (zyx instead of xyz) in order for the result to be the same.

• Your top right diagram is wrong. Fx, as drawn, will cause a positive moment about the Z axis, not negative. – AndyT Aug 15 '17 at 9:44
• I dispute your 'in the UK' statement - I'm in the UK, and right-hand set is by far the most common case. I don't doubt that there is some application of a left hand set in the UK, but not more so than anywhere else. We drive on the left, but we don't routinely use left hand coordinate sets or rotations conventions. – achrn Aug 15 '17 at 10:50
• Also, the bottom right diagram is wrong - v.y = x w only if v.x is zero (and conversely), and as AndyT notes, your v.x direction arrow and sign convention are not mutually compatible. – achrn Aug 15 '17 at 10:52
• @achrn I have taken A' level GCE physics in the 80's and we definitely used the left-hand rule. – John Alexiou Aug 15 '17 at 14:14
• @AndyT - I realized that. The expression assumes a positive value for $F_x$, but the diagram shows a negative value. I should have drawn the force line with a positive direction (1st quadrant) instead of the second. In such a case if the line is passing with a CCW fashion about the origin then the moment is positive, and if it is CW then it is negative. – John Alexiou Aug 15 '17 at 14:19