.Understanding Torque: Forces, Rotation, and Equilibrium

[beginner16]

hi

If two equal forces in oposite direction act on an object in translational equilibrium it will just rotate and continue to be in translational equilibrium.No matter where on the body two forces are applied?

As simple as possible please: How did we come up with
torque= F * distance_between_two _forces

Can you tell me why formula is correct no matter where the rotation axis is located?
What if body has no rotation axis,if it is just your regular book or something like that?


Could these two forces actually represent the sum of many forces applied on multiple points on the body,or must there be only two forces?

thank you for your time

 

[Pyrrhus]

Why don't you prove it?

Start with a rigid solid and put two forces with same magnitude but opposite directions, then calculate the moment of each force at a point O and add them.

 

[beginner16]

prove what?There are 5 questions I asked,and in any case I'm not shure I know what you are talking about

 

[andrevdh]

Use this drawing to "proof" the formula.

 

[beginner16]

I did proof but still have two questions

M=F( r1*sin(a) + r2*sin(b) )=F*d

d=F*r1*sin(a) + r2*sin(b)

What if body has no rotation axis,if it is just your regular book or something like that?Could these two forces actually represent the sum of many forces applied on multiple points on the body,or must there be only two forces?

 

[Pyrrhus]

What if body has no rotation axis,if it is just your regular book or something like that?

What do you mean? could you provide an example?

Could these two forces actually represent the sum of many forces applied on multiple points on the body,or must there be only two forces?

There can be many forces acting on solid body, this is just an special case, where you can rewrite them as a couple or as those forces, it depends on the case. Also, the concept of couple it's important in order to develop the statically equivalent relations, all systems in equilibrium can be reduced to a resultant force and resultant couple, etc..

 

[beginner16]

What do you mean? could you provide an example?

Well if the two forces are applied on a book around what would the book rotate.Around its center of mass or does it depend on where on the body the two forces are applied.If it would rotate around center of mass...why?

There can be many forces acting on solid body, this is just an special case, where you can rewrite them as a couple or as those forces, it depends on the case. Also, the concept of couple it's important in order to develop the statically equivalent relations, all systems in equilibrium can be reduced to a resultant force and resultant couple, etc..

But if those two forces are infact net forces,then how do you decide where the point of contact will be since depending on point of contact between a body and a force,the torque between force couples could vary?

 

[Pyrrhus]

Well if the two forces are applied on a book around what would the book rotate.Around its center of mass or does it depend on where on the body the two forces are applied.If it would rotate around center of mass...why?

It' will rotate around any axis that is perpendicular to the plane the two forces are in. This is because the moment about any point for a couple it's the same.

But if those two forces are infact net forces,then how do you decide where the point of contact will be since depending on point of contact between a body and a force,the torque between force couples could vary?

What do you mean? Couples are free vectors, they can be put anywhere on the solid body.
What i was saying is if you consider Varignon's Theorem, and if you have a finite numer of vector forces concurrent to one point and then another set of vector forces concurrent to another point, and if you calculate the resultant force of each of both sets, and the resultant force of each set has the same magnitude, but opposite direction (thus being in the same plane), then you indeed can form a couple out of these two set of forces.

 

[Pyrrhus]

I was thinking a little more about your question, yes a Couple could be the statically equivalent system for a system of many forces acting in different points, coplanar o not.

 

[beginner16]

It' will rotate around any axis that is perpendicular to the plane the two forces are in. This is because the moment about any point for a couple it's the same.

But what axis will it rotate around if the object in question is a book?Or a shoe...

 

[Pyrrhus]

It depends, but for most engineering puposes we care about the centroidal axis.