# Solving the Mystery of 3D Mechanics: Is the Sum of Moments 0?

• Femme_physics
In summary, the principle is that the sum of all moments around the center of a perfect wheel is always zero.
Femme_physics
Gold Member
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Femme_physics said:
Now does this mean that the sum of all moments on the center of perfect wheels is always 0?

Assuming the angular rotation of the wheel is zero, the the net torque is zero and the sum of the moments is zero.

Aren't A and C of different diameters? If so, the lever arms for T3 and T4 are different. That alters the diagram, but not the relationship.

It looks to me like you are treating the two wheels as one when seen in two dimensions. That would seem to assume that neither moves independently of the other. If they can spin freely the net moment need not be be zero.

Aren't A and C of different diameters? If so, the lever arms for T3 and T4 are different. That alters the diagram, but not the relationship.

You're right they're different diameters. It should be

http://img714.imageshack.us/img714/8756/bebebebebe.jpg

Ignoring the length of the vectors

Assuming the angular rotation of the wheel is zero, the the net torque is zero and the sum of the moments is zero.

I wasn't told anything about the angular rotation of the wheel. Actually, let me just write the question
"Shaft AD is supported by bearing D and B (the bearings don't have any pivotal forces) On the shaft are strap-wheels A and C. On the straps are acting forces as described in the drawing. The shaft is at uniform circular motion..
Given: Radius of wheel A is 50mm and radius of wheel C is 40mm"

It looks to me like you are treating the two wheels as one when seen in two dimensions. That would seem to assume that neither moves independently of the other. If they can spin freely the net moment need not be be zero.

I see what you mean. But based on the question my assumption was correct, right? Since they're both attached to the same rotating shaft.

Last edited by a moderator:

There must be more to this question than you have let on?

Femme_physics said:
I wasn't told anything about the angular rotation of the wheel. Actually, let me just write the question
"Shaft AD is supported by bearing D and B (the bearings don't have any pivotal forces) On the shaft are strap-wheels A and C. On the straps are acting forces as described in the drawing. The shaft is at uniform circular motion..
Given: Radius of wheel A is 50mm and radius of wheel C is 40mm"

You are told that the shaft undergoes uniform circular motion.

There must be more to this question than you have let on?

Yes posted just before you posted :)

You are told that the shaft undergoes uniform circular motion.

Ah, so that's the key! :) I see now! The principles of mechanics are seemingly infinite and interesting!

Thanks Doc, Fewmet, Studiot!

## 1. What is the concept of "sum of moments" in 3D mechanics?

The sum of moments is a key concept in 3D mechanics that refers to the total amount of rotational force acting on an object around a fixed point. It takes into account the magnitude, direction, and distance from the fixed point of each individual force acting on the object.

## 2. Why is it important to determine if the sum of moments is 0 in a 3D mechanical system?

Determining if the sum of moments is 0 is crucial in understanding the stability and equilibrium of a 3D mechanical system. If the sum of moments is 0, it means that there is no net rotational force acting on the object, indicating that the system is in a state of equilibrium.

## 3. How can one calculate the sum of moments in a 3D mechanical system?

The sum of moments can be calculated by taking the cross product of the force vector and the distance vector from the fixed point for each individual force acting on the object. The sum of these moments must be equal to 0 for the system to be in equilibrium.

## 4. What are some real-world applications of understanding the sum of moments in 3D mechanics?

The concept of sum of moments is crucial in various fields such as engineering, architecture, and physics. It is used to analyze the stability of structures and machines, design stable structures, and predict the behavior of objects under different forces.

## 5. What are some common mistakes that can lead to an incorrect sum of moments calculation in 3D mechanics?

One common mistake is not taking into account the direction of the force and distance vectors, which can result in incorrect calculations. Another mistake is not considering all the forces acting on the object, leading to an incomplete sum of moments calculation. It is important to carefully analyze and account for all forces and their respective distances to obtain an accurate sum of moments.

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