The Atwood Machine - Equations of Motion using Lagrangian Mechanics
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- Опубликовано: 18 ноя 2024
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Today we are going to derive the equation of motion for the atwood machine! :) Lagrange is the way too go. This experiment is being used to find out the value of g, the gravitational acceleration btw. Enjoy! =D
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![A Rope Sliding Down a Table [Lagrangian Formalism Approach]](/img/1.gif)
A fun variant of this problem is including the moment of inertia of the pulley so you have an angular variable as well.
Now you gotta use quantum field theory to solve an inclined plane problem
String theory*
Well I think you should solve an inclined plane problem in curved space time with torsion
Oof
@@thephysicistcuber175 Good luck with that. String theory can't solve shit.
Anybody: pulls a rope
Mathematician: OMG one side moves at same speed than the other WTF
You should solve a physics problem using both lagrangians and lagrange multipliers
Finally something my tiny engineering brain can understand
Legit using these lagrangian videos to study for my physics exam on Sunday. Thank you Papa Flammy!
One of the few times on this channel that I feel as though this was completely elementary.
Sincerely, a Mechanical Engineering student
Always a pleasure to watch man. Lagrange mechanical work is always great indeed!
@@PapaFlammy69 :D
i have a final tomorrow and Lagrangians are on it! this helped, thanks!
nice video, Andrew Dotson
Very intuitive and fun way of teaching thanks alot
Now we need wave equation!!!
This is the most fabulous channel one would ever get on you tube for fellow mathmatican
You’re an awesome teacher
that was fun. I'm just learning about these in basic mechanics. It's cool to see another way to conceptualize these bloody Atwood machines.
Try a Hamilton-Jacobi boy
So cool man. I'm doing aerospace engineering so this stuff is very interesting.
An inspirational Lagrange method
Eyyyy I could follow at least halfway through so far
Good stuff
:)
Flammy papa you should make a video on solving the easiest problem with Lagrangian mechanics
I love combinations of physics and mathematics
I think the potential energies of the objects are wrong. I think you should write them as mg(h-y) where h is the height of the top of the pulley. But video was very good and Thank you for making such Physics-analysing videos. And I expect to see more videos on your channel like this.
Yes that might be correct but the mgh (when you expand out your expression) acts as a constant potential V_0 being added so it doesn’t impact the solution to the Euler-Lagrange equation. However, I think it’s a better logical explanation of what the potential energy is.
@@arushgarg7303 yeah, I have already realized it. you are right. when you take the derivative mg(h-y) =-mgy. thank you
I want to see an example of a falling body with air resistance.
Lagrangians don’t deal well with energy losses within systems. You’d have to artificially add the air resistance aspect of the formula (like b*v^2) once you’ve obtained the equation
@@GAPIntoTheGame dang it Lagrange
If you go to Pisa, you can be one
@@neilgerace355 I'll try it out, can I borrow a parachute?
@shoop dawhoop This is easier: drop your cellphone.
Eyy papa your physics videos are better than the maths ones
“I’m going to call this length small L”
*proceeds to write capital L*
I love my at_morning_woods machine
It works amazingly well
😏😏
That made sense even to me. I am sure I did this at uni.
Excellent! But why was U of little m negative? If little m is increasing in height, then isn't its potential energy also increasing?
Can you make a weird noise in your next video? Like something so weird form your throat that people who are watching it will think that their headphones are broken but in reality its just you that is broke.
"Now we can construct our Legrangian. We take this piece of shit right here" XD XD
wanted to see all your lectures in physics
I gotta say. Great text on the merch
Yay more physics Papa! Maybe some quantum next time?
Wouldn’t you have to consider the rotational potential energy of the “pulley”(assuming it is rotating)?
Typically you assume massless pulley for Atwood Machine problems
@@chimpluvr5 unless youre in my physics class. It doesnt really make it that hard though if you still assume that the pulley turns frictionlessly.
That's a nice combination of mathics and physematics...
W A I T
Papa Lagrange would be proud
Funny thing, even though I am not into Physics or Mechanics, this stuff, when taught in elementary algebra (not all of it), is not satisfactory enough as popping some Calculus love in the mix.
What do the voices say at the beginning of the video? "Pappay Flammy's -----" I can't understand it
I love the jacket so cute cute. Maybe I will get a copy 😁😁😉
So.. the Langrangian L is a different L from the length of the rope.. and..
when differentiating with respect to y' do you treat y as a constant?
yes
Wait in the potential ener gu byiu forgpt to add the tension term of the rope pulling up on the rest of the rooe..in addition to gravity?
Great video as usual papa x
I was wondering why the potential energies for both M and m were negative? As their displacements in the y direction are in opposite directions
ist die Gleichung nur für die Masse m1? Also ganz am Ende hast du vergessen die y(t) als y1(t) zu bezeichnen. Wenn ja, dann löst man nach y2(t) auf indem man y1(t) in die Länge Gleichung L = y1+y2+piR einsetzt oder?
I just finished all of my finals, what math concepts should I try to learn over break?
Flammable Maths Thanks papa flammy
Unrelated but video request.
You can define the second derivative as an infinite matrix if you define all functions to be a matrix of Taylor coefficients. Solve the equation of a spring oscillator by finding the eigan vectors on the second derivative matrix
And our lagrangian is this peace of s... Right here 😂
Good one.
Thanks, now I wonder if I should attempt to use these instead of the good old Newtonian equations for my upcoming 101 midterm exam tomorrow...
@@PapaFlammy69 I drove my grader nuts by using topology to do my assignments in my first real analysis course. Fun days!
i know you're german from your accent 😅 keep going bro good luck
beautiful!
0:00 Animals have an end. Usually in my gut
After a trip to a hot grill.
umu
@@Gameboygenius I like grills
@@neilgerace355 Sounds like you're a heat-erosexual then.
Use F=ma to solve double pendulum
You should have solved it with hamilton-jacobi.
Nice!
What about Atwood machine whit a pulley whit mass?
When u did the potentials. Why are both negative?
Arman Braca , both y coordinates are smaller then zero every time. Just look at the picture
@@yourdad9885 thx
We want more examples on the same topic
Lagrange and Hamilton redeemed classical physics in the eyes of mathematicians.
Not sure about that... Classical Physics was obnoxiously geometric before that, but that domain was still within mathematics.
@@manueljesusarredondoruiz2444 you mean the Newtonian herezy? Even Leibniz hated it when he was still alive.
*rope*
This video made me COOOOOOOOOOMMMMMMM!!!
Please create more physics videos..
that height is a bit :thinking:
add the mass of the rope and see what happens
It goes from a physics to an engineering problem!!!
And then you can approximate all your variables and constants to 1 and it gets really easy :)
Double dot ✌
Papa Newton is a proud boi.
Based
Small nice lagrangian problem. Quite sad you decided not to assume the rotation energy of block. Тем не менее, отличное дерьмо!
Papà flammy uses Lagrangian mechanics
Newton mechanics: am I a joke to you?
Hallo einflussreicher Mathematiker. Ich habe dir gesagt, dass du Physik magst.
Einer Prophezeiung zufolge wird sich Mr. Flammy (Genie) bald treffen.
I know my newtonian mechanics well but this shit looks like it's from a higher dimension
I was like, why the fuck the lagrangian is y1+y1+pi r?
then I noticed it was the laplace transform and not the lagrangian xd
A resolução entendi, queria mesmo era compreender as explicações, más infelizmente não entendo inglês
SEXY FLAMMABLE
the starting part is a kind of humor? don't understand
Early
@@PapaFlammy69 (个_个) notice me senpai moment right here
sorry... i love math but i really hate physics....
........ I'm really bad at physics. :(
same
Physics lovers: *triggered*
@@shambosaha9727 XD XD