# The direction of moments (no specific problem, just a confusion)

• slayerjacket
In summary, the direction of a moment in two dimensional statics problems can be determined using the right hand rule or by setting up a determinant with the position and force vectors in a cartesian coordinate system. For 2-dimensional problems, the moment vector will always be either into or out of the paper.
slayerjacket
Hi.

For whatever reason I'm really struggling with figuring out the direction of a moment in two dimensional statics problems. How can I tell if it's CW or CCW? The right hand rule just confuses me even more and I cannot find any explanation that breaks it down simply enough for me to understand.

I thought I understood it in that I could just base the direction of the moment on the quadrant it was located in, but that doesn't seem to be consistent. I feel like I'm just missing something very fundamental about the way moments work in relation to their corresponding point and it's throwing me off entirely. Please help! Explain like I'm five!

The moment or torque on a particle a distance r from the origin of your coordinate system is given by

τ = r x F

where τ is the torque vector,
r is the position vector from the coordinate system origin to the particle,
and F is the force vector applied to the particle.

The right-hand rule says, "hold your right hand so the 4 fingers all point in the direction of r; hold the thumb up so it forms a right angle to the fingers; now curve the fingers around towards the direction of F, and the thumb will point in the direction of τ."

If this confuses you, you can always revert to using a cartesian coordinate system:

r = rx i + ry j
F = Fx i + Fy j

then set up the determinant with
i j k in 1st row,
rx ry rz in second row
Fx Fy Fz in third row.

If you are working with 2-dimensional statics problems, such that all beams/girders/trusses/etc. lie on the x-y-pane of the paper, the direction of the moment vector will always be either into the paper or out of the paper. You can use rude man's explanation of the right hand rule to determine of the direction of a given moment is into or out of the paper.

## 1. What is the direction of moments?

The direction of moments is the direction in which a force acts on an object, causing it to rotate around a pivot point. It is usually described using the right-hand rule, where the direction of the moment is perpendicular to both the force and the distance vector from the force to the pivot point.

## 2. How is the direction of moments determined?

The direction of moments is determined by the cross product of the force vector and the distance vector from the force to the pivot point. The resulting vector will be perpendicular to both vectors and its direction will indicate the direction of the moment.

## 3. Are there different types of moments with different directions?

Yes, there are two types of moments: clockwise and counterclockwise. The direction of the moment will depend on the direction of the force and the direction of rotation around the pivot point. A clockwise moment will rotate an object in a clockwise direction, while a counterclockwise moment will rotate an object in a counterclockwise direction.

## 4. Can the direction of moments change?

Yes, the direction of moments can change if the direction of the force or the distance vector changes. Additionally, the direction of the moment can change if the pivot point changes. However, the magnitude of the moment will remain the same as long as the force and distance vectors remain unchanged.

## 5. Why is understanding the direction of moments important?

Understanding the direction of moments is important in order to analyze and predict the motion of objects under the influence of forces. It is also crucial in engineering and design, as it allows for the design of stable and efficient structures that can withstand external forces and moments.

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