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

[Femme_physics]

I recently fall upon this principle while trying to do this 3D mechanics exercise.

http://img193.imageshack.us/img193/1416/legitwheel.jpg

Looking from a side view (only z and y axes), this should be about right:

http://img28.imageshack.us/img28/5758/momentsq.jpg

Ignore the question marks. I know it's right. Now does this mean that the sum of all moments on the center of perfect wheels is always 0?

 

[Fewmet]

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.

 

[Femme_physics]

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"

Nothing about "angular rotation"

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.

 

[Studiot]

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

 

[Doc Al]

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"

Nothing about "angular rotation"

You are told that the shaft undergoes uniform circular motion.

 

[Femme_physics]

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!