According to wiki,
In rigid body mechanics, force couples are free vectors, meaning their
effects on a body are independent of the point of application.
I'm having some trouble understanding this statement. Consider the following scenarios:
Here, $O$ is the center of mass of the solid and uniform bar. Here, $|\underline{u}|=|\underline{v}|=5N$. Here, $\underline{u}$ and $\underline{v}$ constitute a force couple.
Scenario 1:
The two forces will have no resultant force, but they will have a resultant torque.
Scenario 2:
Here, since $\underline{u}$ and $\underline{v}$ are free vectors according to wiki, I've moved them such that they are facing each other directly. Now, there will be no resultant force nor will there be a resultant torque.
My question:
- According to wiki, scenario 1 and scenario 2 should have the same
effect on the bar. However, the effects are different. So, isn't
wiki wrong?
Best Answer
In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of the point of application.
You have misinterpreted the Wiki statement.
Given a couple, two equal magnitude, parallel, non-linear forces, it does not matter where those two forces act on the body as long as the couple, $Fd$ anticlockwise in this case, stays the same.
You to deal with the couple as a whole.
One last point.
The torque on the body as a vector in all cases is $\tau_{\rm couple} = F\,d\,\hat z$ where $\hat z$ is a unit vector pointing out of the screen and note there is no mention of the forces, separation, position etc.