Let's say I am using a long wrench to unscrew a tight bolt because the formulas developed in rigid body statics states that the moment arm should be longer for minimal force application. But how long till the force/torque travels to the bolt periphery, receives a reaction torque from the friction of the bolt fitting for real materials. We usually just learn rigid body physics and sort of hand-wavily say that oh that's what's happening in real bodies too (which it is albeit slightly differently). Of course I know rigid body concepts are good enough to develop confidence in understanding mechanics.
$\begingroup$
$\endgroup$
1
-
4$\begingroup$ Yes. There is no such thing as a pure toque. It is a mathematical construct. Real torque is always a pair of linear forces. $\endgroup$– John AlexiouCommented Jan 9 at 20:54
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
When you start to make a rigid body more "real," the usual approach is to break it up into a bunch of points which convey forces with one another. Atoms are pretty darn close to a bunch of points, so this simplification works well. When we think about it this way, forces and moments are really the same thing. It's just a set of forces applied to different points in the body.
So naturally, both forces and moments propagate the same way. They propagate at the speed of sound in that material, which is typically quite fast compared to the velocities we want to pay attention to. That's why the rigid body assumption is so effective.
It turns out that given a rigid body, you can derive all of the angular momentum formulae from the linear momentum formulae and vice versa. All you have to do is remember that the definition of a rigid body is that the distance between any two points does not change. Applying that rule over a bunch of points is sufficient to use one form of momentum to construct the equations for the other.
$\begingroup$
$\endgroup$
What you are describing is the propagation of stress waves inside an elastic body. The equations that govern a body's internal strains and stresses are agnostic to how the stresses arise from macroscopic effects such as forces and torques.
In addition, mechanical torque is always applied with a force pair (one or more pairs) and you have to have an underlying force to transmit it to a body mechanically. The concept of "pure torque" is a mathematical idealization where the location and orientation of the force pair are ignored. You cannot ignore either aspect of torque in real life if you want to be as detailed as possible.
answered Jan 9 at 21:00