What causes rotation, a couple or a moment? (conceptual)

[Sarin]

Does a moment have any real (physical) significance or is it just a definition/ an aid to understand and calculate a couple. Is it that the rotation is actually caused by a couple!

I know we can resolve a force causing a moment about a point into a couple and an equal force acting at that point, but what i want to know is how does this actually happen in a real world scenario.

Also,
Say if there was a body (an extended bar or rod) in space so that no force would act on its centre of mass, then if a force F was applied on one of its ends what would happen and why?

forgive me if the question sounds stupid, but this concept has ben bugging me for a very long time now!

 

[D H]

Say if there was a body (an extended bar or rod) in space so that no force would act on its centre of mass, then if a force F was applied on one of its ends what would happen and why?

The object would undergo a linear acceleration per $m\vec a=\vec F$ and would undergo a rotational acceleration per $\mathbf I \,\dot{\vec\omega} = \vec r \times \vec F - \vec{\omega}\times (\mathbf I \,\vec{\omega})$ .

 

[_DJ_british_?]

The object would undergo a linear acceleration per $m\vec a=\vec F$ and would undergo a rotational acceleration per $\mathbf I \,\dot{\vec\omega} = \vec r \times \vec F - \vec{\omega}\times (\mathbf I \,\vec{\omega})$ .

In words, it's because you apply a force "on" the COM ie. linear acceleration, but a the same time, you apply a torque about the COM ie. rotational acceleration (unless the force is applied directly on the COM, then it's just linear).

 

[D H]

(unless the force is applied directly on the COM, then it's just linear).

A force doesn't need to be applied directly on the CoM (center of mass) to get pure translation. It just needs to be directed "in line" with the CoM. For example, in the case of a force applied at the end of a rod, there is no torque on the rod if the force is directed toward or away from the center of the rod (i.e., if the force is collinear with the rod).

 

[haruspex]

Does a moment have any real (physical) significance or is it just a definition/ an aid to understand and calculate a couple. Is it that the rotation is actually caused by a couple!

I know we can resolve a force causing a moment about a point into a couple and an equal force acting at that point, but what i want to know is how does this actually happen in a real world scenario.

These different views are equally real and produce the same answer. In many cases you can observe the cause of a force producing a moment, so it's natural to view that force as the reality. But in other cases exactly the same result could be produced by a combination of a torque and a linear force.

 

[Sarin]

DH, DJ british ? and Haruspex, thanks!
lol, and DH i think DJ british meant to say the same thing when he said "directly on the COM", please dun give him a hard time, haha.

OK i had been pondering over thisthe whole day, looked up some literature and i think i figured it out, one can even deduce this from the derivation of the "position of COM of a system".
Its just that it is very hard to imagine/ visualize the COM taking a translatory path (motion) when the force is not even acting on it/ directed towards it, i.e offset.

Anyways, I have another problem: a free body, say a bar (yet again), spins about the COM; but if we pivot a body at a point, then why does a force act on the pivot point simultaneously as a couple is generated.

I know one may argue since the forces are equal and opposite on the pivot point, they are as good as non existent (they cancel out each other), therefore it is the same thing. I know that!
I wan't to know how it happens in actuality, i.e if you pin a rod at one of it points, how is that point going to be under the influence of a force.

i know again a stupid question, my apologies.