Physics 68 Lagrangian Mechanics (9 of 25) Example: The Atwood Machine (with Mass)

In this video I will find the equation of kinematics of an atwood machine (where the pulley has mass M) using the Lagrangian equation.

Next video in this series can be seen at:

[jacobrose]

Most underrated channel on YouTube. This will help me on my physics GRE for sure

[bhoopendragupta]

Great explanation, never thought lagrangian could be this easy.

[madspihl]

Oh the clarity of this. Fantastic, thanks!

[astyutechick]

4:04
I think you forgot to copy the minus sign.
Love your videos btw. They've been very helpful!!
Edit: Never mind, you correct it right away at 4:58

[anshgupta]

Why you haven't consider P.E. of "Pulley" since it is hanging ?

[luisjanuario]

It´s L=(1/2m1+1/2m2+1/4M)Ẋ^2-(-m1gX-m2gl+m2gX), you forgot one minus on m1gX

Forget it, he corrects it at 4:58.

[hfgjjhkjjbvkkb]

Hi. Dont you have to add the potential energy of the pulley when calculating PE ?
I already know it wont add any important modification because partial derivatives
will take it to zero; Just wondering, and just that. By the way, thanks for your videos !

[biswajitghosh]

Thank you so much sir . I learned a lot from you ❤❤.

[manishmks]

Why don't you consider mass of pulley in calculation of potential energy..

Dear sir you have mistakenly taken the PE=0, for the roof it should be a line passing through centre of pulley

[roopjeetbpatro]

Hello there, have you considered the pulley to be at negligible distance from the ceiling, due to which there is no term of the potential energy of the pulley ?

[Steven_Salah-Eddine]

Hi,

I believe you forgot to negate the 1/2*m2*(v2)^2 term in your Kinetic Energy equation. Therefore KE for the second mass is 1/2*m2*(v2)^2 = 1/2*m2*(-xdot)^2, since v2 = -xdot

[anesmerazi]

sir, shouldn't be the velocity of the mass m2 : X dot 2 rather than X dot ?

[animalslife]

I want to know the traditional way of solving atwood's machine which includes the mass of the pulley. I haven't tried it yet. Thanks.

[mohdshariquealam]

Can you please explain how you got P. E for m2 =(l-x).... I'm kind of stuck here🤔

[happyhedgehog]

You're a life saver thanks a lot!!!

[burakoner]

does not PULLEY has potential energy ?

[tkftns]

why is the inertia of the fixed disk = 1/2 M(R^2).. shouldnt it be M(R^2) ?
Thank you so much for everything you do sir, i really benefit alot!

[emeraldeyegaming]

why didn't we took PE of the pulley?

[GamerTheTurtle]

this feels like cheating compared to using newtonian from high school. Or maybe I'm just a lot better at physics problems then I was back then...

[Ayayron_e]

how come you didn't change signs in the parenthesis at 4:10 and you mention to be careful with the signs? shoudn't it "-(m1gx+...-...)" since the negative is on the outside.