25.2 Stable and Unstable Equilibrium Points

MIT 8.01 Classical Mechanics, Fall 2016
View the complete course: ocw.mit.edu/8-0...
Instructor: Dr. Peter Dourmashkin
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

[@user-ng4lm1ir2b]

5:17 unstable equilibrium point 6:21 stable equilibrium point

[@hsm2310]

I so loved graphs, using differentiation to plot maxima/minima points and so on. This video reminded me of that love thanks to a random video on unstable equilibrium.

[@ahmeds4]

This instructor is amazing! I wish my school does have someone like him

[@matthewa1729]

How did you get so good at writing backwards?

[@kloo_]

Most likely either the glass layer or the background is overlaid and flipped to get this effect. So not actually writing backwards

[@matthewa1729]

kliu lol I kno

[@Inndjkaawed2922]

Check out their lightboard technology. Its awesome

[@fernandoalvear3739]

The effect is called "lightboard". Its pretty awesome: sites.google.com/site/northwesternlightboard/home

[@ambroseezzat2703]

Ever notice how all these content makers who use the transparent board write with their left-hands? Given the proportion of lefties, this is highly unlikely. They write normally, and then the footage is flipped. Either that, or suddenly everyone of them is ignoring the simple "flip solution" and opting to write with their left hands, backwards, and wearing their wedding rings on their right hand too. In that case, I'd like to joint hat club. Sounds like they're pretty fun people if that's the case.

[@tamaghnachaudhuri9675]

Rather than just giving differential inequalities it's teaches the intuitive way of understanding.... Nice and thank you!!

[@VanJake-pu2us]

Great 👌 your works are so accurate 🤩🤩 thanks so much for your helping

[@tougue]

It's just incredible how many of those clever people are left handed...

[@the_sophile]

Are you joking? Because this is flipped and he is actually writing with his right hand

[@tougue]

@@the_sophile yup, humour it was ;)

[@rafaelschwertner5353]

I couldn't understand it very well. Apllying the theorem of stability of equilibria the point x=2 is stable. The analysis of this graph, interpreting the slope, would make sense if the potential function was plotted.

[@1light4love]

YOU'RE AMAZING!!! Very insightful without becoming overwhelming! 🙏 Thank you so much (for this and the followup video 🤓) This is the last section before our exam in 2 days... and I feel solid on this stuff before even entering the eCovid Classroom today😅👍🙏 ✨Watcha me shine, ya'll☀️

[@varunkharayat4251]

Great explanation sir

[@vijaymahla2709]

how you are writing backward please explain i think you have used software

[@mitocw]

Yes, software was used. See lightboard.info/ to see how this was done.

[@_tasneem7378]

Wow, super clear!

[@刘津茜]

Thank you

[@eshnaroy779]

This video is so awesome!!! Thank you!!

[@jonathansum9084]

Why my professors did not say F =-slop, and she or he told me local max is slowing down? Because of my professors lazy?

[@matthewheck4933]

I know its filmed through a mirror, but watching him "write backwards" is very distracting

[@GabrielKelly98]

Incredible!

[@ashishkumar-qz1bb]

at x =4/3 potential should be zero??

[@accumulator4825]

Though so as well for a second, but that's where the force is equal to zero.

[@sarthakchavhan]

No bro

[@chaosend3815]

At x=0 and at x=2 the potential is 0. At x=0 and at x=4/3 the derivative of the potential (the force) is 0. Those are called critical points, basically where the slope is 0. Note: The point x=0 is shared by both.

[@andyroo4720]

Peter makes a big mistake at 5:30-6:00. First of all, his description of stable and unstable equilibrium points is not rigorous, but moreso an intuitive explanation of some way of classifying equilibrium points, which is fine. But, the mistake he makes is when describing unstable (and stable) equilibrium points, he says, "And so if a particle is displaced a little bit from the 0 point, it moves off to the right, and it will continue to feel a force in this direction, and so it will move away from the 0 point of the force" (vice versa for the other side). Since there is no net force acting on the particle at the equilibrium point, he assumes that the particle starts off a bit past it (in the +x direction), but what he concludes is just false. Feeling a force in the positive x-direction does not mean that the object will actually move in that direction, it just means that there is an instantaneous acceleration in that direction, not necessarily motion in that actual direction. This is one of the most common misconceptions physics learners have when starting off, equating the direction of the force with the direction of the motion, and its a shame he mixes the two. While the overall quality of the course content is high, and I do ignore mistakes of Peter's here and there, like when he treats differentials like fractions or confusingly differentiates between coordinate systems and reference frames when they are the same thing, this is just egregious.

[@jscexaminer4005]

"Since there is no net force acting on the particle at the equilibrium point, he assumes that the particle starts off a bit past it (in the +x direction), but what he concludes is just false. Feeling a force in the positive x-direction does not mean that the object will actually move in that direction, it just means that there is an instantaneous acceleration in that direction, not necessarily motion in that actual direction" If a net force is acting on something, could you please explain how there can be no motion?

[@andyroo4720]

⁠@@jscexaminer4005Yes, obviously a net force in the +x direction means a net acceleration in that direction by F=ma, but the object could already be moving in the -x direction in the first place with some initial velocity, and the acceleration may not be “large” enough to overcome this velocity and actually move the object in the +x direction. It may be a bit of a nitpick, but he mentions nothing about the kinetic energy of the particle or kinetic energy at all (just that Wnc=0 which is unrelated). Thus even if a particle is located in the +x direction from the second equilibrium point, its motion may not be as he described.

[@LT-mf9uf]

why Fx = -du/dx ,why there is a mius sign?

[@huzaifaabedeen7119]

Chinese 🦠😷

[@adityayadavx447]

Because force is the -ve of the slope or potential. F(x)= -du(x)/dx.

[@YourAashique]

Subscribed on 6th Muharram 1445 Hijri, 24th July, 2023 at 8:08 pm (Indian Standard Time).

[@brendawilliams8062]

Thankyou

[@ConquerTheCurve]

I have more examples like this on my channel if anyone wants more practice!

[@eduoliveiraAtUTube]

Are these values for a and b arbitrary? If not, how to calculate them? Thanks in advance.

[@itkeeks]

is this man writing backwardsssss

[@huzaifaabedeen7119]

yes dear

[@daniellelafferty142]

Incredible!

[@ConquerTheCurve]

I have more examples like this on my channel if you want more practice!