Why Torque Can’t Exist for Rigid Objects
When we talk about torque, we are usually referring to the twisting force that is applied to an object to make it rotate. However, when it comes to rigid objects, torque simply cannot exist in the same way it does for non-rigid objects. Let’s explore why:
Rigid vs Non-Rigid Objects
Rigid objects are those that do not deform or change shape when subjected to external forces. This means that all the particles within the object move as a single entity when a force is applied. Non-rigid objects, on the other hand, can deform and change shape, allowing for torque to be applied in a more traditional sense.
The Definition of Torque
When we calculate torque, we use the formula:
τ = r x F
Where τ is the torque, r is the distance from the axis of rotation to the point where the force is applied, and F is the force applied. However, for a rigid object, all the particles move together as a single entity, making it impossible to determine an axis of rotation or a specific point where the force is applied.
Implications for Rigid Objects
Since torque is dependent on the distance from the axis of rotation to the point where the force is applied, rigid objects simply do not have the necessary elements for torque to exist. Without the ability to determine an axis of rotation or a specific point of force application, calculating torque for a rigid object becomes meaningless.
Conclusion
While torque is an important concept in physics, it simply cannot exist for rigid objects in the same way it does for non-rigid objects. The nature of rigid objects, with all their particles moving as a single entity, makes it impossible to calculate torque in a meaningful way. So next time you encounter a rigid object, remember that torque may not be a relevant concept to consider.
I have received a number of comments questioning whether we really need non-rigid objects. This is discussed in much more detail, with mathematics, in the paper at https://scholarship.haverford.edu/cgi/viewcontent.cgi?referer=https%3A%2F%2Fwww.google.com%2F&httpsredir=1&article=1494&context=physics_facpubs
Double the points agai- NAUR PLEASE NA-
Shear forces from friction don’t act along the line connecting surfaces unless you are zooming in and looking at none opposite sections of the surface?
The music was nice but understandable some people didnt like it. Science should have personality and I believe you have lots of personality in your videos
This entirely makes intuitive sense. If you think about a metal bar as a lever, why would it physically get more force with distance? I mean the atoms move the same distance and so on, but it works because each interaction is very strong
Thank you Eugene ✌🏿
With enough force, everything is a spring
This is beautiful. The fact that physics can break into smaller pieces, even the simplest phenomenon that we think we comprehend.
Now that the video title has me thinking about it, can we really call any object with size "rigid" considering the causal speed limit?
Newton's third law talks about inertial forces, you're talking about mechanical constraints. Of course the solution does not work if you change the problem. Rigidity changes how much a body deforms when a force is applied, not the force transmitted by the body
This was a nice demonstration, but the argument is incorrect. We can assume a perfectly rigid object as, instead of just saying "stiff connections", a bunch of masses connected by springs (as in your example), but with infinite spring stiffness. All the consequences of a deformable object approach still apply, the forces get transferred correctly, and torque works. Rigidity isn't incompatible with Newton's motion equations.
It would be better explained if you included a diagram like the one you have at 2:41, but actually two compared diagrams, one with a rigid joint and another with an ellastic (springy) joint. Instead of a momentum, imagine a force applied to one of the particles. In the rigid joint model, that would act as if it were only one body, but if we analyze the forces, the action and reaction force wouldn't be in the same line joining both bodies. That was the most important missing diagram for understanding, the other is more obvious, as the ellastic joint doesn't require to move the second body instantly as the first body where we applied the force, but that is determined by the spring whose force is depending only in the relative position of particles along it's axis.
Eugene, your voice is so feminine. And robotic.
I wonder if this is why ATG's Engine Sim always has really strange numbers
I was waiting for a simulation of a theoretically perfectly rigid object, demonstrating it breaking torque
what a underrated channel, i hope you get the recognition you deserve sir/mam. you are an amazing physicist and teacher, who can actually explicate and make others understand even the most complicated and abstract topics with great analogy, great definitions, and simulations, a lot of things are now clear and i can visualise it happening, my love for physics has immensely increased, thanks to your lucid explanations.
also, what do you exactly do professionally apart from youtube?are you physics professor or researcher under some institution?or an independent researcher?i would like to know that, as im interested in that field as well.
thanks ❤
Do you guys have a video explaining why hot gasses are less dense?
In your paper, you state that "because the internal forces in the rigid-body model do not obey the strong third law, they form a couple that generates a self-torque and thus angular
momentum." However, it is not very clear in your paper why they violate.
Would you mind explaining? Thanks.
I feel the need to touch those non-rigid objects.