Moment of Inertia Tricks | Rigid Body Dynamics for JEE Main & Advanced | Class 11 #PhysicsGalaxyPIM

Moment of Inertia Calculation | Moment of Inertia Calculation tricks | Moment of inertia Problems for JEE Main | Rigid Body Dynamics for JEE Main | Moment of Inertia Problems for JEE Main | Moment of Inertia for JEE Advanced | Moment of Inertia by Ashish Arora | Physics in Minutes by Physics Galaxy | Mechanics #19

There are many tricks used for calculation of moment of inertia in rigid body dynamics. Different types of problems are asked every year based on moment of inertia in JEE Main, JEE Advanced and NEET. In the topic of Rigid Body Dynamics, most of the problems involve calculation of moment of inertia of the object in consideration so questions based on this concepts are essential to be covered in detail. In this video Ashish Arora Sir is explaining calculation tricks of moment of inertia of different objects in rotational motion based on mass distribution property.

For quick coverage of all concepts of Rigid Body Dynamics students can review this topic from Physics Galaxy checklist video of Rigid Body Dynamics available at below given links.

Detailed understanding of all such concept can be covered through the Physics Galaxy Concept videos available through our channel playlist or our website.

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There are 5 Practice Quiz Questions based on concept of vertical circular motion explained in this video. Students are advised to solve below questions and find, out of given questions below which question(s) are given with wrong answer(s) and post your answer in the first comment in comment section. Correct answer with explanation will be shared in after two days.

(1) A thin square plate of mass M, edge length L is rotating about an axis passing through its center of mass, in its plane and at an angle 30° to one of the edge. If half of plate on one side of axis is removed, find moment of inertia of remaining part about this axis of rotation.
[ML²/24]

(2) Find moment of inertia of a Cylinder of mass M, radius R and length L is rotating about an axis of rotation passing through center of one of the circular face of cylinder and perpendicular to central axis of cylinder.
[(1/12)ML²+(1/4)MR²]

(3) A cone of mass M, base radius R and Length L is rotating about its central vertical axis of rotation with its base horizontal. If it is cut in two parts of equal mass M/2 by a horizontal plane parallel to its base and I1 and I2 be the moment of inertial of upper and lower parts of cone then find the ratio I1/I2.
[1/(2^(5/3)-1)]

(4) Find moment of inertia of a hemispherical shell of mass M, inner radius r and outer radius R about an axis of rotation passing through center and perpendicular to its base. (Calculate using the trick explained in above video)
[2M(R⁵ - r⁵)/5(R³-r³)]

(5) A plate of mass m having the shape of a right triangle of edge lengths a,a,a√2 is rotated about a given axis of rotation parallel to one side of length a and passing through the vertex where other side and diagonal intersect. Find moment of inertia of plate about this axis of rotation.

[7Ma²/6]

#physicsinminutes #physicsgalaxy #momentofinertia #physicsgalaxypim

[physicsgalaxyworld]

(1) A thin square plate of mass M, edge length L is rotating about an axis passing through its center of mass, in its plane and at an angle 30° to one of the edge. If half of plate on one side of axis is removed, find moment of inertia of remaining part about this axis of rotation.
[ML²/24]

(2) Find moment of inertia of a Cylinder of mass M, radius R and length L is rotating about an axis of rotation passing through center of one of the circular face of cylinder and perpendicular to central axis of cylinder.
[(1/12)ML²+(1/4)MR²]

(3) A cone of mass M, base radius R and Length L is rotating about its central vertical axis of rotation with its base horizontal. If it is cut in two parts of equal mass M/2 by a horizontal plane parallel to its base and I1 and I2 be the moment of inertial of upper and lower parts of cone then find the ratio I1/I2.
[1/(2^(5/3)-1)]

(4) Find moment of inertia of a hemispherical shell of mass M, inner radius r and outer radius R about an axis of rotation passing through center and perpendicular to its base. (Calculate using the trick explained in above video)
[2M(R⁵ - r⁵)/5(R³-r³)]

(5) A plate of mass m having the shape of a right triangle of edge lengths a, a, a√2 is rotated about a given axis of rotation parallel to one side of length a and passing through the vertex where other side and diagonal intersect. Find moment of inertia of plate about this axis of rotation.
[7Ma²/6]

[parkhigoyal]

Dear sir, You are the only teacher I have seen till date who is also teaching in an offline institute but still helping students with a noble heart❤️
Loads of love nd respect to you sir 🙏
A true definition of teacher😊🙏
Multimillion folds thank you to the entire *physics* * Galaxy * *team* and *Ashish* *sir*
❤️❤️😊

[VikashKumar-kemq]

10:15 Moi about axis perpendicular to plane (I)= M( L^2 + L^2)/12 = M(L^2)/6

by perpendicular axis theorem,

I = I1 + I2 (where I1 and I2 are MOI about diagonal axis on the plane of rectangular plate)

=> I1 = I2 = I/2 = M(L^2)/12 (since rectangular plate is symmetrical I1 and I2 are same)

Now we cut the plate about a diagonal axis into two parts and that part again into 2 parts, and now we have the triangular laminar plate given in the ques... since these parts are symmetrical about the axis, the MOI wont change...

So MOI of the triangular laminar plate
I = M(L^2)/12
I = M(a^2)/6

Note: I lost all my braincells trying to figure out why you substituted the mass plate as 4M first which makes the mass of triangular plate in ur assumption as M and then you substituted the mass of triangular plate again as (M/4), which did not sit right with me... so i present to u my solution

[ShyamKumar-neqw]

Sir, this theorem is called "Theorem of Symmetrical Expansion".
My teacher also have taught this, but this theorem is not present in books generally ..

[jeswanthgrandhi]

Sir, If I become at least half as talented, energetic and knowledgeable as you are, I will consider myself as a most successful physics teacher. 🙏🙏🙏🙏

[manaspatil]

Some days you click fastest to open a video, some days to Set the Reminder. But I hope everyday we get to see you and get the benefit of your knowledge, Sir.

[anmolmangaraj]

Sir i just completed this 😎😎😎.i hope sir will definitely bring a mindblowing video

[mihirjha]

Sir please one request!!,
please make full strategy video containing time table, how to follow PG books, time for practice, tests, other material to follow that purely focusses on JEE Advanced 2021..
please sir make a video, please don't wait for more same type of requests
this would be very very helpful for the viewers.
I am saying this to to because you are one of the best and ideal teacher for me.
please make it's very humble request.

[NishantKumar-gxco]

Sir cuboid wale case me mass Ko M/2 Kiya ... Fir length Ko L/2 kyu nhi kiya

[priyasharma]

3:45 I was thinking of the same thing.😇😇✌️

[aksingh]

361K subscribers, amazing sir, I think at the end of 2020, you will hit 500K

[satinathghosh]

Sir when will the NCERT notes be coming?
And my request is that to make an another playlist for NCERT notes, which will be very much helpful for us.

[prakharsingh]

Sir, if I am preparing for jee mains only, should I do the advanced illustrations on your channel?

[AT-lyud]

Sir your all video are helpful.
Every video there is always something new which I have learned for the first time 🙏🙏 thank you for your hard work🙇💯😀

[SumanSharma-dxfn]

Sir please make one vedio for some study strategies for class 11 students for better preparation.🙇🙇

[siddhesh]

Sir in yesterday's video you said that jee advanced is a different ball game . Can you please make video on explanation of this ball game . Please sir make one video on jee advanced....

[vidhanpatni]

6:23 The sphere looks like the same thing Bahubali 😎used in the final battle....
Jokes apart,
very helpful video sir!

[Getsetrelax-qe]

Sir using the animation and explanation which smart board people can't

[userismad]

Sir i just wanted to thank you from the bottom of my heart.. I've been following your channel and concept videos ...those 8-9 years old videos are amazingly relevant till this day and have helped me thoroughly learn the chapters in my preparation for BOARDS and NEET... I'm appearing for class 12 boards exam and NEET in 2021 and I'm confident that your videos will definitely help me achieve a higher score..

[najabajajajara]

sir as in sphere case in 8:41 IA+IB=2/5MR^2 HOW COULD IB greater than 2/5mr^2. If IB> 2/5mr^2 then IA should be negative. how moment of inertia is negative sir.