Torque can’t exist for rigid objects

I am fairly certain deformation is not, in fact, required for torque to exist in rigid objects under Newtonian mechanics.
Here is a concrete example with all forces laid out that demonstrate how an uowards force is applied to leftmost point of the object while the external force is applied on the right:
suppose we have 3 points that do not lie on the same axis with the same mass: O, A, B
O is our fixed axis, A is the leftmost point, B is the rightmost point.
Suppose A has coordinates (-1, 1) O has coordinates (0, 0), B has coordinates (1, 0)

Suppose there is a flrce Fa between O and B, Fb between O and A, Fo between A and B (those forces have a positive sign if they repell points), as well as an external force acting on B downwards: F and the force of the axis of rotation: T that acts in an unknown direction

knowing that O is fixed in place we get: T+Fa+Fb=0 in vector form
knowing that A and B stay the same distance away from the origin, we get that their acceleration is perpendicular to the lines OA and OB respectively
so we get that projection of total force on those axes is 0, specifically:
A: Fb+Fo/sqrt(2)=0; B: Fa+Fo/sqrt(2)-F/sqrt(2)=0
we also know that since distance between A and B is unchanging that the tangential component of the acceleration must be the same:
Fo/sqrt(2)=-Fo/sqrt(2)-F/sqrt(2)

so, we get that
Fo=-F/2
Fb=F/(2sqrt(2))
Fa=3F/(2sqrt(2))
T=-Fa-Fb in vector form

This way, everything is fine. Point A moves up because force Fb pushes it outwards while force Fo pulls it to the right.
The total torque on the system is generated by T and F
No contradiction is reached.

As others already pointed out, the paper appears to have several mistakes.
I don't see any mistake in this concrete 3 point argument that works under Newton's mechanics, has external forces be applied along the lines between 2 objects and describes rotation of a rigid body consisting of 3 same mass points.

Obviously that model doesn't work when special relativity is taken into account and is technically not correct as real life objects aren't truly rigid, but it is internally consistent.

If anyone finds an error in my comment or finds some fact non-trivial and needing explanation, please let me know. But as of right now, I am convinced that the claim of the video is incorrect or presented in a misleading manner.

One issue I see with these simulations, is the assumption of a simple cubic crystal structure. This crystal structure is uncommon among most solids, and is known to create weak shear strength in materials and weaknesses of non-axial loads, due to the weak diagonal bonds between atoms. Much more common crystal structures are face centered cubic (FCC), body centered cubic (BCC), and hexagonal close-pack (HCP). These crystal structures have higher packing factors than simple cubic, and are much better at supporting shear and moment loads, due to diagonal bonds between atoms, creating "cross-bracing" in the crystal structure.

Years ago, when I was just getting serious about studying math and physics, I spent countless hours over the course of (probably) weeks trying to derive some torque laws for rigid bodies, only assuming Newton’s Laws.

I learned it was pretty straightforward for non-rigid objects, but the rigid case literally kept me up at night.

I had forgotten all about it until I saw the title of this video. Great work as always ❤

Then how will a perfectly rigid object behave? I think without that explanation, this video's argument will be incomplete

The animations were fun, but I thought they were going to demonstrate that torque doesn't work on perfectly rigid bodies, not just repeat it doesn't many times.

I'm still not convinced that an object must deform for torque to make sense.

The algorithm brought me here

I think I got it. The analogy of the springs helped me to understand why a hypothetical perfectly rigid body can't have torque. If I understanded correctly, is because when you applied a downward force to a tool, the other end of the tool must have an upward force, just like when you stretch a spring outward, there's an inward force because of the flexibility. Likewise, when you use lug nuts wrench and use a pipe to have more torque, the flexibility of the material gives an opposite force: you move the pipe downward, and the other end of the pipe moves upward. I can imagine if it were possible a perfectly rigid tool, you can apply whichever big force to the tool that it move give any torque, just like when you use a really tiny wrench, but just imagine an infinite small wrench, it won't have torque at all. Well, this is my first time learning this, so I might be wrong, but I think I got it.

I have one minor complaint which is that there is sometimes a really high pitched whistling with /s/ sounds, which I think could be EQd away

While it is totally ok to model a system of particles constrained by spring forces to gain insight into deformation, the claim that it is necessary in order to explain torque, moments, and force couples is as laughably incorrect as the paper cited here in the comments. Truly a "don't believe everything you see on the internet" moment

Please make more videos on electronics

I feel the need to touch those non-rigid objects.

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.

Do you guys have a video explaining why hot gasses are less dense?

thanks ❤

I was waiting for a simulation of a theoretically perfectly rigid object, demonstrating it breaking torque

I wonder if this is why ATG's Engine Sim always has really strange numbers

Eugene, your voice is so feminine. And robotic.

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.

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

Now that the video title has me thinking about it, can we really call any object with size "rigid" considering the causal speed limit?

This is beautiful. The fact that physics can break into smaller pieces, even the simplest phenomenon that we think we comprehend.

With enough force, everything is a spring

Thank you Eugene ✌🏿

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

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

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?

Double the points agai- NAUR PLEASE NA-

I still don't see why it's impossible for rigid objects. I know they can't exist, but if you could somehow force their existance, I don't see why they wouldn't follow Newton's equations.

Congratulations, your flexible thinking is enabling you to steer in right direction.

These animations are consistently brilliant and convey novel ideas in a tangible way, thank you!

Maybe some more philosophical video relating to the existence of God? or any deity/higher power?

I don't think your conclusion is correct because it doesn't account for the diagonal forces

Einstein would say the limit of rigidity is that which creates a speed of sound approaching the speed of light/information

Hey that's what Vsauce was talking about in the safety third interview !

what does a rigid object "not working properly" look like exactly?

Conservation of angular momentum can definitely be programmed accurately into rigid body physics simulations, but it requires quite a bit of calculus.

Eugene I want your permission to recreate your videos in Hindi language. I want your videos to reach more indian students. As I know they are not very familiar with English. And your videos have very much potential for knowledge which they can easily grab upon. Your animation is very approachable to the concept at very basic and easy to understand. And our students really need this.
Thanks for all of your contributions towards students who lack resources and connectivity.

Suppose the spring constant is k. As k approaches infinity the body approaches being perfectly rigid. You can increase k such that it is indistinguishable from perfectly rigid.

Infinity is not a number. Infinity minus 1 is not less than infinity. One can't say that something is different at infinity vs infinity minus 1. How could one demonstrate that the situation would be different at k = "infinity" vs k = 10^100000000000000000 N/m.

There is no physical thing that has been measured or proved to be infinite. Infinity is not a determinable real physical thing.

That paper by Daniel J. Cross has at least one error. In equation 2b the 'T' should be multiplied by r1/r2.

So - sorry, not sorry - This video is bogus.

(Nice graphics and nice narration voice though.)

I Get mad ,at this Universe, evertime I bust my Brains, and figure it Out, you give me the Answer afterwards.I thought you we're my friend.hahah crazy

A video explaining how the Higgs field gives mass to objects would be appreciated. But
beyond the usual analogy of substance resistance, which is more like an aether theory with a perfect rest frame. Us who are watching your videos want more.
Thanks for your videos.

It would be great if you could explain how exactly energy bends spacetime. Einstein do not say a word about this cause he had no idea why!

I'm in my masters year of Physics and I have literally never understood Torque better than I do now after seeing this video. God I love springs.

And that is why torque is a pain for rigid body simulations. Because we can't just rely of linear motion laws.

Hallo, thank You.

Yes, I have it!
The mass elements above and below the pivot can move more freely around the pivot, and less freely toward/ away from it.
Every time you insert an spring element between the pivot and the force, the force is "turned" more to more effectively pull the elements above the pivot and push those below.
The side with fewer spring elements between the force and the pivot will lose.