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 scholarship.haverford.edu/cgi/viewcontent.cgi?referer=https%3A%2F%2Fwww.google.com%2F&httpsredir=1&article=1494&context=physics_facpubs

"Bring me a *lever* long enough, and a *fulcrum* large enough, and I shall bend that lever"

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.

Nice not to have loud music at the same time as narration. So much easier to listen to.

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 ❤

As a Diesel mechanic, I routinely twist the maximum allowable torquage.

I can't believe she stopped that train car all by herself

I just like how the attractions and repulsions of particles can be simplified as springs.

This channel is invaluable

Universe: "that is my secret: there are no rigid objects"

Which software for the animation ?

wait... why does in a perfectly rigid object the strong version of Newton's 3rd law get violated? what is the effect of no elastic deformation?

Wow, this is very interesting! I never even thought about this concept, but it makes alot of sense.

As the spring constants are reduced further, not only is torque possible, but also twerk.

Seriously, this is seriously awesome physics videos! Thanks for the new video Eugene.

Amazing as always the animation helps so much.

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

I got A+ in physics and its mostly due to your videos. Thanks for helping students like me. Physics and Mathematics are now ny favorite subjects.

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.

I would love to know how this “distance to axis of rotation” effect works. I know such distance is directly proportional to torque; I just don’t know why that is the case. If the same force is applied to both sides of the object, how come one wins the battle just by virtue of being placed further away?

I'm having a difficult time accepting this. To fully understand it I think I need to see a visualization of how the force is distributed when applied to the theoretical rigid body.

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.

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

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.

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.

very enlightning. What is the simulation software? is it Gromacs?

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

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?

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

Thank you. Now I'll watch it.

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

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

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.

Simply awesome

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

So , If a force is applied on a perfectly rigid object (not along the centre of mass), then it'll act same as if the force is applied along centre of mass?

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.

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

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

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

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

But if you are going to assume that an object that can't exist does exist, then wouldn't you expect new physics along with it? If I understand the problem, the object can't stop or start rotation. Wouldn't acceleration in any direction run on to the same issue?

Please make more videos on electronics

Thanks for making these videos

what if the spring constant approaches infinity, won't that be a perfectly rigid body?

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

I guess it makes sense, what does infinite rigidity even mean when thinking of multiple particles instead of a single object? What if there were only 2 atoms connected in a line? If the bonds were infinitely strong, the distance between them would never change. If the distance never changes, then why would the second atom ever exert a force on the first object? If the bond doesn't exert any force, is it there at all?

WOOOHOOOO SUPER HIGH QUALITY EDUCATIONAL VIDEO LET'S GOOOO

Why should the strong third law apply? For instance, it doesn't seem to apply given Maxwell's equations. It's obvious in the case of masses connected by springs, but not clear how it can be generalized. In the absence of that, this seems more like "Torque on rigid bodies cannot be modeled by a collection of point masses connected by infinitely rigid springs"

winnyの金子さんが20年前にこの理論を拡張して物理演算だけの仮想世界を作ってたなぁ。 設定してないのに回転衝突、変形する画期的な技術だった。

Thank you Eugene ✌🏿

only when applied to an object that has mass.

I have a question: What is the difference between the weak & strong form of Newton's third law, and why don't we just use the strong form everywhere, since it includes the weak form (which is the one I've always heard of). My guess is that the difference between them is one is a statement about the conservation of linear momentum, and the other of angular momentum, both of which can be derived from first principles (Noether's theorem).

Can you make longer video to watch at night before sleep?

Yes, this is excellent.

The moose looks really puzzled.

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

Amazing! Thank you!

That's Kira vincent-davis.

Nifty as usual

2:38 : huh? But what about like, the force applied on a particle moving in a magnetic field (with said magnetic field being a result of a number of other moving electric charges) ? Surely this also conserves angular momentum? If I have two electric charges moving around, shouldn’t there be a part of the force between them which isn’t along the line between them?

Where's the music?!

Imagine Patreon was a thing that existed in the 90s/early 00s

Great - no music, thank you

With enough force, everything is a spring

Is there such a thing as a perfectly rigid object there isn't I didn't finish the video before making this comment thank-you for answering I have learned two lessons today.

as a civil engineer, I had ended to the same conclusion when thought of "load bath" throw a structure. that is, without a deformation, we can't imaging how loads on a floor reach columns (transfering of loads from floor to colums).

Thank you!!

hot damn so without deformation, we can't even use a basic lever!

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

_Even for individual electrons, isn't it still a mystery how electro-magnetism (can) exert a force at right angles and do so at a distance?_ - j q t -

The algorithm brought me here

thanks ❤

Double the points agai- NAUR PLEASE NA-

Nice channel👍

Hello, I like your physics video very much, it is very intuitive and deep. I've watched every video over and over. I saw this one, too. Can you use a video to make clear how to put the role of the lever, the force is amplified, this concept is not intuitive!! Counterintuitive!

I think it's the first time I simply don't understand a video from Eugene... 😭

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

Not convinced… i watched all your videos. This one does not adequately explain anything in order to arrive at your conclusion. Pretty sure that even if things were perfectly rigid things would still rotate on a fulcrum I’m pretty sure the rotation is caused by the lack of reactionary moment force within the beam, which as nothing to do with rigidity. I know in I am using torque to describe torque here. But you need the same kind of analysis for structural members. You don’t need an elastic material to have a reactionary force upward when a book sits in a shelf .

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

So… Eugene, are we considering Black Holes and Neutron Stars rigid? We do say BH rotate, but what we mean is that space-time is being dragged by inertia of what has fallen into BH (honestly would be great to dive deep into this topic). For Neutron Stars however we do consider them actually rotational and I guess we can speed them up or slow down by applying torque… Crazy interesting, would love you cover these topics! Thank you both as usual.

Crank until it cracks than half a turn back. That's how dad did it, that's how Mmerica does it 😂

nice!

I only realised recently that the voiceover isn’t AI

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.

I thought you only needed F=ma anyway

I mean ... nothing can exist for perfectly rigid objects ...as they cannot.

All game engines have rigid bodies with torque 🙃

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.

Just op

When dealing with springs, you use diagonals. When dealing with "perfectly rigid bodies", you don't include the diagonals. Add enough diagonals to your perfect rigidity stuff, torque will transmit just fine. Sure, no real thing is perfectly rigid. But the maths of perfect rigidity torque make sense.

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

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

19h

"How can the left part of the body experience an upward force?" Your Video misses a whole point: the fixed axis exerts an upward force, because the net force of the rotating rigid body shown in this video must be zero under the assumption, that the center of mass lies in the fixed axis. Both, the external downward force and the reaction force due to the fixed axis create a force pair generating a torque without an acceleration of the center of mass. Without the fixed axis, the rigid body would experience an angular AND linear acceleration, causing each particle moving downward and to the left/right due rotation and internal forces, but no particle would go upwards.

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.

Not meaningful. Moment equilibrium can be obtained using newton laws and vector calculus. No other one is required. There is an enginnering concept, machine theory, to analyze the motion of 'rigit' bodies. Also in finite element analysis, there are many rigit element types to transfer the moment

Liquidity infinity to illusionary solidity of liquidity infinity. External heat energy is within mass as internal magnetic fields grounding currents into itself and surrounding mass through its nucleus or core. Heat has to ground or burn as decaying internal magnetic fields. External magnetic fields don't ground energy and circulation around the sphere of absolute zero heat energy within its core or nucleus as a monopole of complete repulsion to heat propulsion energy from surrounding space and mass disolving its internal magnetic fields grounding currents by disrupted normal space filled with dark heat energy outside of entanglement of mass as potential renewable heat energy when entanglement with mass occurs. Space is a weak external magnetic field filled with dark heat energy outside of entanglement. Distance is always equal to force. Hydrogen has the strongest internal magnetic field of force. Hydrogen under extreme pressure expands into helium. Helium occupies more occupational space within mass, and more occupational space itself has more force of pressure from repulsion within mass and distance traveling cycling circulation patterns of internal magnetic field increases in equalization to force of pressure decreases. As mass moves away from the core of earth's internal magnetic field grounding currents through its nucleus or core where force is stronger and distance traveling is minimal, it increases in distance traveling and decreases in force of pressure currents grounding through all masses in its path. Currents are the force of pressure known as weight. As mass moves away from the central point of earth's internal magnetic field, grounding currents weaken as distance traveling increases and force of pressure from current grounding decreases. Equalization to force of pressure and distance traveling cycling circulation patterns as mass. The more currents grounding as weight, the more repulsion to the mass and distance traveling cycling circulation decreases. Force of pressure is always equalization to distance traveling, and weight is currents grounding through mass as weight. Table of elements proves hypothesis. Hydrogen has more force of pressure currents grounding than helium. And has the least distance traveling cycling circulation patterns. As mass expands, its internal magnetic field grounding currents weaken. Equalization without gravity. Magnetism. Theoretically factual probability that works with quantum physics without gravity. Friction causes sparks of striking resistance of mass as potential renewable heat energy passing through all masses in its path until resistance is overcome by open space itself and returns to dark heat energy outside of entanglement of mass as potential renewable heat energy when entanglement with mass occurs again. Liquidity infinity to illusionary solidity of liquidity infinity. Alpha and Omega. Cold repulsion of space to heat energy singularities. Cold and heat coexist as space itself as a weak external magnetic field. External heat energy within mass in quantum internal magnetic fields grounding currents through all masses in its path. Space has a weak external heat energy field as maximum distance traveling through space and least amount of heat energy force of pressure to and from cold repulsion of space itself as perpetual motion. Force is when the accumulation of heat energy singularities is unified of unidirectional flow repulsion back onto itself as internal magnetic fields grounding heat currents as force fields of pressure holding mass together as the weakest point of repulsion back onto itself as internal magnetic fields grounding currents into the weakest point of repulsion. Mass neutralizes repulsion as outward pressure exerted within mass and without mass equalization. Mass is always the weakest point of repulsion. In a greater internal magnetic field, grounding currents synchronization as directional force of pressure grounding currents as weight. Outside of a greater internal magnetic field, grounding currents into itself is weightless. Outward pressure is weightless without a greater internal magnetic field directional pressure of force. Magnets show the bonding force of pressure known as weight when you try to pull them apart. No negative force of flow. Unification of unidirectional flow. One flow redirected trajectories by repulsion of cold space. Alpha and Omega. Clockwise and counterclockwise. Same flow cycling circulation patterns of magnetism grounding currents as force of pressure known as weight. Quantum Internal magnetic fields grounding currents. Hydrogen and oxygen sharing currents are grounding as water. Cold repulsion unification of hydrogen and oxygen. Ice in a glass of liquid condensate oxygen and hydrogen sharing internal magnetism grounding currents as water. Atmospheres grounding currents as water molecules sharing internal magnetism grounding currents into each other as friction. Heat exchanging singularities point to point chain reactions through all masses in its path. Equalization is lightning strikes burning through atmospheres, gasses releasing heat singularities as friction of spark lighting up atmospheres. Sparks (electrons) light up atmospheres. Grinding friction causes sparks lighting up. Heat transference lighting up atmospheres as daylight magnetism exchanging singularities point to point chain reactions through all masses in its path. Heat waves traveling through space and atmospheres piggyback light as heat waves, magnifying light throughout space and atmospheres. Light is only present in resistance. Lightning proves hypothesis. Fire is the decay of internal magnetic fields releasing heat singularities outside of entanglement of mass as potential renewable energy absorbed by surrounding masses. Liquidity infinity to illusionary solidity of liquidity infinity. Heat is always present in exchanging singularities point to point chain reactions through all masses. It's not the waste product. Electricity is rapid heat exchanging through mass. Heat has to ground or mass burns. Lightning burns through atmospheres. Electricity is sparks of electrons lighting up as friction. Heat currents grounding themselves through all masses or mass burns or decay of internal magnetic fields. Engines ground heat energy to anti freeze and radiators ground to atmospheres and atmospheres grounding currents into surrounding atmospheres or earth's internal magnetic field. Grounding currents of heat is equalization of internal magnetic fields temperature control. If internal magnetic fields grounding currents fails it decays as heat releasing e external energy flow as fire or molten masses. Refrigerators and air conditioning remove heat and leave behind cold repulsion of space. As usual, water is found condensate. Unification of internal magnetic fields grounding currents into surrounding mass sharing heat energy. Magnetism is a force of pressure known as space itself filled with dark heat energy outside of entanglement of mass. Mass is the expansion of space. Monopoles of pure fabric of cold space repulsion are external magnetic fields that don't ground energy. Galaxies and planets prove the hypothesis of cold repulsion within entanglement of mass and without mass. Theoretically factual probability that works with quantum physics without gravity.

I am not sure this conclusion is correct. For example, there is torque applied in Euler equations for rigid body rotation of a spinning rigid top.

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