MIT FINAL Exam Physics Problem

[@zhelyo_physics]

What did you think of the problem? I have to say this is one of the most enjoyable problems I have done in a while. Also notice how barely any calculus was needed, I could have called all these accelerations just "a". It's purely algebra! : )

[@krishpandey854]

Another method: Power generated by gravity=rate of change if Kinetic energy if the system. KE of systen can be written as the effctive moment of inertia multiplied by omega squared KE= (1/2 MR^2 + MR^2 + 2MR^2)w^2 =7/2 MR^2 w^2 dK/dt= 7MR^2 w*angular acceleration=Mgwr-mgwrsinalpha Hence, omega is cancelled out and angular acceleration is obtained

[@manansharma9164]

This was quite an easy mechanics problem. Just three equations: Mg - T1 = Ma [Net force on block 1] T2 - 2Mgsintheta - 2 mu Mgcostheta = 2Ma [Net force on block 2] (T1-T2)R = (MR^2/2)(a/R) [Torque on disc] a/R = alpha is the angular acceleration of the disc (in pure rolling a = alpha R)

[@supergamer8030]

Mechanics problems always seem so easy at first, but working it out always is a lot more complicated that initially thought! Thank you for the great, easy explanation!

[@zhelyo_physics]

Completely agree about mechanics problems! Thanks a lot for the comment!

[@BasisthaAnand]

dude rotational is another story

[@tejinderbirsingh1062]

For second (b) part:- Net force = mass*acc. So, Mg - 2Mg*sin(alpha) - u*2Mg*cos(alpha) = M*a +2M*a + moment of inertia of pulley (0.5*M*R*R) * angular acceleration ( a/R) = 3.5Ma

[@tejinderbirsingh1062]

So, a = g( 1- 2sin(alpha) -2u*cos(alpha))/ 3.5

[@blackguardian89]

Great video, as always! It would be very nice if you make some tutorials for the other problems from the exam as well. Thank you and keep up the good work!

[@zhelyo_physics]

Thanks a lot for the comment! Definitely on my filming list : ) and other exams from other universities too.

[@krishpandey854]

Another method: Power generated by gravity=rate of change if Kinetic energy if the system. KE of systen can be written as the effctive moment of inertia multiplied by omega squared KE= (1/2 MR^2 + MR^2 + 2MR^2)w^2 =7/2 MR^2 w^2 dK/dt= 7MR^2 w*angular acceleration=Mgwr-mgwrsinalpha Hence, omega is cancelled out and angular acceleration is obtained

[@zhelyo_physics]

Also for an intro to the moment of inertia - check this out: kzbin.info/www/bejne/n5bRlJiIdtSla5I

[@ANUJ.5]

I have solved because i am jee advance aspirant

[@zhelyo_physics]

Fantastic! Good luck in your preparation, their notes and problems are excellent preparation I think.

[@JayasreeR-st1tj]

Please help how to slove physics problems . I am stuggling

[@BilalKhan-cq6mn]

Same here. The question was of class notes level

[@umutcan450]

This problem is a great calculus combination of mechanical physics. Also I understand, thanks !

[@zhelyo_physics]

Glad to hear, thanks a lot for your comment!

[@Miftahul_786]

6:20 In your formula for angular acceleration you are missing the dot on the θ to the right, sir.

[@zhelyo_physics]

ah yes, thanks fore spotting. It was a test to see if anyone would notice obviously : ) well done!

[@Miftahul_786]

@@zhelyo_physics Hehe of course sir! Glad I could find it :)

[@saarahussain8449]

😦

[@anonymooseuser2150]

im in yr 13, applying for physics at top unis. should i be worried if i cant answer b and c? part a was okay but thats it

[@zhelyo_physics]

You should never be worried if you can't answer a physics problem. That's how we learn. Also this is a problem from a university exam from one of the most elite technical institutions in the world so finding it hard is part of the fun: ) good Luck!

[@ikshu0769]

its okish do it this way its kinda long so what we can do is use Work energy theorum and within one equation we get our acceleration and other things as well one more, ohh waitt i have another method just calculate angular momentum of system and differentiate so that u equate to net torque again the ans comes in one equation this was considered a very easy problem in our class of rotational mechanics anyways love from india ❤

[@Kraoty]

THIS QUESTION IS A JOKE FOR A SERIOUS IIT JEE ASPIRANT

[@ejgames8484]

This was a fun one. Question: when I tried it I used ay = R(alpha) = ax = a (Using theta as the angle and x and y are subscripts for acceleration). Is there a reason why you didnt use a universal variable for acceleration? And would you recommend straying away from that method? Edit: Nevermind I ended needing to specify which one was which anyways

[@zhelyo_physics]

For sure! I only realized after that you can call these derivatives just "a", but since this exam is calculus based I guess you never know if you might integrate at some point. Turns out this problem is basically algebra though if you have done angular acceleration.

[@ejgames8484]

@@zhelyo_physics that makes sense, thanks!

[@avishkapeiris3098]

The question would be more interesting if we give the right angled block a mass and if it’s allowed to freely move 😍

[@JanSlejkoLjub]

You can solve these problems much faster if you just add up all of the equations instead of expressing and subbing T1 and T2. In the case of adding up, T1 and T2 always cancel out.

[@zhelyo_physics]

thanks for the comment, this did take me a crazy amount of time and checking over the answers! haha

[@JanSlejkoLjub]

@@zhelyo_physics Forgot to mention, nice videos! :)

[@zhelyo_physics]

thanks a lot! much appreciated!

[@B21_raider]

We are supposed to do problems like this in under 3 min in jee advanced 😅 ( ps this was an easy one)

[@gokudegrees]

Why didn't we simply substitute T1 and T2 from Equations 1 and 3 into equation 2 and solve for y ddot?

[@gokudegrees]

You can arrive at the answer a bit faster haha

[@zhelyo_physics]

Excellent point, I guess it was the first solution that I arrived at. Thanks for the comment!

[@gokudegrees]

@@zhelyo_physics No problem, do you have any other interesting problems?

[@zhelyo_physics]

definitely! Pick your favourite from this playlist: kzbin.info/aero/PLSygKZqfTjPCKus_q7vWTaRClR2hi6XFe

[@ashwinprabhu1231]

Why do we assume that the direction of T_2 is parallel to the incline?

[@zhelyo_physics]

the diagram. Also if something slides across it in balance, you'd generally expect it.

[@harrychen3316]

Nice explain, is this the problem the most simple problem for MITs lol

[@zhelyo_physics]

Thanks for the comment! Have a browse through the exam: ocw.mit.edu/courses/8-012-physics-i-classical-mechanics-fall-2008/15cdb14e63ed07c47115ce18c73917bf_final.pdf I thought the rocket question (Problem 3) was a lot simpler, but it's pretty similar to this derivation I filmed not too long ago: kzbin.info/www/bejne/oYaYgq1soZade5o

[@adityavsx]

in a is the pulley massless?

[@zhelyo_physics]

Nope, it has a mass and hence a moment of inertia

[@adityavsx]

@@zhelyo_physics then why don't we take its moment of inherits into account when writing eqs for block going up and down?

[@zhelyo_physics]

@@adityavsx such an excellent question, we are not really looking directly at the pulley but we are comparing 4 forces with the fact that the pulley has a mass tells us that T1 and T2 are different and cause an angular acceleration as shown in the second part. To get the angle we just compare really the first and last force, in which there is no rotation but just regular motion. Hope this helps!

[@adityavsx]

@@zhelyo_physics great thanks actually 🥰

[@Rajbanerjee518]

Thank you so much

[@zhelyo_physics]

anytime, thank you for the comment!

[@dakerbal]

why is T1 not equal to T2? I thought tension in a string is constant?

[@zhelyo_physics]

excellent question. In a massless pulley yes, however this one hear has mass so we need to consider differences in tension. If a pulley has a mass, then we need to consider its moment of inertia like in the question. Hope this helps!

[@ikshu0769]

​@@zhelyo_physicssir actually not to offend really i respect u a lot and i know it very well ur far superior than me whos in jus high school but tensions will actually be different because there is no slipping it means there's a tangential force so tensions just cant be equal and sir i wanted to ask whther i should learn langrangian methods for my high school or i'd say jee advanced if it helps me solve mechanics faster and with more ease sir pls assist me on this one i have been in a delema to read david morin or any other material or even do lagrangian in the first place

[@indianbeast644]

Good question

[@zhelyo_physics]

Glad you enjoyed it!

[@KrishKumar-so1ct]

Easy one. noobs get scared just because of diagram and variables.