Probably the most clearly explained derivation anywhere on the internet! You did a great job!

@MichelvanBiezen

10 жыл бұрын

Sassan, Thanks for this positive feedback. Much appreciated.

@RiaziMohandesi

5 жыл бұрын

سلام ساسان. واقعا تدریسش فوق العادست.

@DARK__G

Жыл бұрын

PW laughing in the corner

You are a good teacher. You do calculations thoroughly, you take your time to make us understand it and your drawings are very good. You have got an A+ from a physics student.

Yes, there are some derivations in other topics. Gravity. Electrical potential, equations of motion, etc. After I cover all the physics topics, I will go back and include additional examples of how to derive many other physics concepts.

Sharon, Look in the playlist PHYSICS 33 FLUID STATICS There are a number of videos on surface tension.

That was an amazing lecture!!! I thought this would be more difficult yet you explained it so well that I could understand after only taking 1 semester of calculus.

Your writing is so clear, and the explanation is as well. Thank you for this, a late night refresher that I will surely need in the coming days.

With classes going online and it being difficult to get help at the moment, these videos have been so helpful. Thank you so much Michel!

@MichelvanBiezen

Жыл бұрын

You are welcome. Glad the videos were helpful. 🙂

this has taken me such a long time to understand but you explained it quite eloquently sir and I thank you!

Thank you so much, amazingly clear and easy to follow. The diagram with the flat strip of a cylinder helped a lot.

great job! I love this video.

Thank you! Crystal clear.

This is, by far, the best explanation. However I seem to have an issue when it comes to relating mass with volume, area or length. I would really appreciate it if you could mention an example for each.

Awesome, thank you very much for this incredible material!

you are an amazing man thank you for all the hard work and effort you put into making your videos they are very very much appreciated. this is a wonderful thing you are doing

@MichelvanBiezen

6 жыл бұрын

Behind all this is an amazing woman (my wife) who directs, films, edits, and produces these videos and makes all the thumbnails. These wouldn't exist without her.

@michaeljagdharry

6 жыл бұрын

Michel van Biezen kudos to both of you, you are blessed to have such a supportive partner and amazing wife

great video professor your the man!!

amazing teacher

This was great! Can we do the same thing but using polar co-ordinates instead? I guess though that that would be a double integral.

Amazing Thank you so much!

a ring will have different inner and outer radius. the radius keeps increasing. when stretched like a plane it will have different dimensions at bottom and top. my point is area of ring should be calculated by subtracting the empty area inside from the whole area. but you have used the formula for a cylindrical tin

Great!!! do you have more videos on derivation for other topics like Newton's law of gravitation, coulomb's law etc?

Excellent!

hady, Look at the comments further down, I gave a response to a similar question.

great job..............can u explain aboutsurface tensions

U SAVED MY LIFE

would it be possible to write the integral as a function of dh rather than dV, considering the whole volume as a set of thin circular slice ? In this way, the moment of inertia would be written as integral of r^2 * rho(density) * pi * R ^ 2 * dh ( between 0 and H) ?

@MichelvanBiezen

6 жыл бұрын

You can, but then you would have to figure out the moment of inertia of the small disk first (assuming you want to start from the fundamental principle of moment of inertia).

This makes integration much more interesting

This guy makes khan academy seem like his pupil!

Sir you are The icon of PHYSICS FUNDAMENTALS Teller.🤘🤘🤘

@MichelvanBiezen

Жыл бұрын

Wow, thanks

great explanation on the topic, thank you for that , what if the cylinder is tensioned and has two fix supports? I want to find the bending stiffness of a wire (16 mm diameter) I need to find the flexural rigidity EI in order to multiply it to the coefficient of my stiffness matrix .

@MichelvanBiezen

6 жыл бұрын

For that you will have to look at our mechanical engineering videos.

@mersedehmaksabi3287

6 жыл бұрын

any exact video?

Thank you very much sir.

Good one!

Goat, much respect sir.

@MichelvanBiezen

Жыл бұрын

Thank you. Glad you found our videos! 🙂

Mr. Michael, is it possible to say dI = double integral of dmx(sq) dl. And it comes in handy if the radius keeps changing along L. Thank you so much?

@MichelvanBiezen

5 жыл бұрын

That my not require a double integral. You may be able to express the single integral to take into account the changing radius. We have some examples of that.

thank you sir and btw for moment of inertia of any symmetrical body,can't we just do the integral for half the part ,for eg for cylinder(ofc not for the axis given in this example but say the axis was from top of the board to bottom,from middle of cylinder(z axis), integrate half way round and multiply by 2?ANd next question-for rigid bodies,like MOE of rod in x axis about origin,why can't we take center of mass of rod and multiply it's square by the mass of rod??Thanks again

@MichelvanBiezen

2 жыл бұрын

That is indeed a calculus trick we use all the time when it makes the calculation easier, but not necessary in other situations.

Why do the bounds of the integral change from x=0, x=R to x=0, x=L? Thanks

@MichelvanBiezen

7 жыл бұрын

In this example the limits of integration are from x = 0 to x = R

very nice, you draw good

I understand how that formula is derived. πr^2 will cancel out and dr^2 is very small and equal to zero. thanks for Ur reply I have another question, how to find moment of inertia of rectangular frame with thickness and axis of rotation through transverse axis and not through longitudinal. please help me to.

@MichelvanBiezen

7 жыл бұрын

Did you look at the other videos in the playlists?

this would be amazing if it wasnt for the audio only being in one ear

@MichelvanBiezen

Жыл бұрын

Yes, our older videos were recorded in mono sound (not stereo) before we figured out what we were doing.

You explain so beautifully 🤗

@MichelvanBiezen

2 жыл бұрын

Thanks a lot 😊

Hey Michael, if the cylinder was not solid but had a fairly thick shell, would it be correct to say that you just change the lower limit :/

@MichelvanBiezen

6 жыл бұрын

Yes, changing the lower limit would be correct.

@AwesomeAngryBiker

6 жыл бұрын

Michel van Biezen cool thanks Michael, appreciate the reply and keep up the awesome videos 🙋👌👍🙌

Great vid thnx!

F-A-N-T-A-S-T-IC............ Muy bueno. Awesome.

@MichelvanBiezen

10 жыл бұрын

Thank you for your comment.

U r my hero woohoo thank u so much!

Sir when you divide the cylinder into n number of shells then the shell closets to the outer layer of the cylinder still has the same distance x from the neutral axis ?

@MichelvanBiezen

5 жыл бұрын

Yes, since the shell is infinitely thin.

@aliwaqas2396

5 жыл бұрын

thanks

Why cant we find the area moment of inertia of a circle using single integration?? Why do we have to use double integration

As mass is infinitesimal, the length x is also infinitesimal. So rather than derivative to mass, can we do derivative to x length? So, it is like ∫(m*dx^2)

@MichelvanBiezen

Жыл бұрын

No, that will not work. (Because we need to use the defintion of the moment of inertia, even for an infinitesimal small piece, is: dI = dm R^2

beautiful

what a legend!!!!

@MichelvanBiezen

Жыл бұрын

Thank you. Glad you liked the video 🙂

thank you very much

@MichelvanBiezen

Жыл бұрын

You are welcome 🙂

Thank you... Thank you so much

@MichelvanBiezen

Жыл бұрын

You are welcome.

Can we instead take an elementary disc, and then integrate the moment of inertia of the disc.I tried it, but I don't know how to get the expression for the elementary mass.

@MichelvanBiezen

9 ай бұрын

That would require another integration. In the end, it doesn't matter how long the cylinder is. You will always obtain the same answer.

Aweeeeeesome!!!!!

U said radius affect the moment of inertia. So why there r videos showing 2 cylinders having different radius sliding over an inclined surface and they reach bottom at the same time? Isnt it supposed that the smaller radius arrive first because it has smaller MOI??

@MichelvanBiezen

7 жыл бұрын

When you attach an object to a string and swing it around, the moment of inertia will increase as you increase the length of the string, (that is the basic definition of moment of inertia). A cylinder with a bigger radius will have a bigger moment of inertia for the same reason. The acceleration down an incline is only in part affected by the moment of inertia. It is like asking: "why doesn't a bigger rock fall faster to the Earth?", since it weighs more.

@theextremist4829

7 жыл бұрын

I believe that although the cylinder with the greater radius has a greater moment, the one with the lesser radius has to rotate at a faster rate. I would assume that these two factors cancel each other out.

Where did X^2 at the beginning come from? why not only X?

@MichelvanBiezen

Жыл бұрын

Are you referring to the x^2 used in the moment of inertia calculation? Assuming yes, the definition of the moment of inertia (I) is: I = mR^2 (the mass multiplied with the distance from the center of rotation to the position of the mass squared.)

Nice!!!

what would be if the density is not constant, if the density is proportional to radius?

@MichelvanBiezen

11 ай бұрын

Then replace the density in the integral with the density as a function of the radius: D = Do r where Do is a constant.

Can you please explain why the distance from the center is x²☺️

@MichelvanBiezen

Жыл бұрын

Are you referring to the x^2 used in the moment of inertia calculation? Assuming yes, the definition of the moment of inertia (I) is: I = mR^2 (the mass multiplied with the distance from the center of rotation to the position of the mass squared.)

thaks sir

what if the axis of rotation is parallel to the radius? i mean like a hollow rod spinning

@MichelvanBiezen

Жыл бұрын

If it is a hollow rod, the moment of inertia would be I = mR^2

@harithfawwaz

Жыл бұрын

@@MichelvanBiezen how do I explain this, imagine a ring, spinning; but the axis is not the same as this. The rotational axis is the aligned to the radius.

@MichelvanBiezen

Жыл бұрын

Ah, I think I understand now. You have the axis of rotation going through opposite ends of the ring. That can only be done via calculus. That is too complex to explain via a comment, but we'll make a not of it and plan to make a video on that.

There we go, why does the book not say why it's 2pir and not pir^2. Thanks

@MichelvanBiezen

7 жыл бұрын

What is the word "it" represent in your question?

@MrKaloszer

7 жыл бұрын

Michel van Biezen circle "volume". I thought of slices as flat planes and not 3d space

@MichelvanBiezen

7 жыл бұрын

Aha, now I understand. Finding the volume of an object through integration requires the summation of an infinite number of infinitesimally small dV (volume segments). Thus the cylindrical slice cut open and laying flat has a length (L) a width (2 pi r) AND a thickness dr, thus it has a small amount of volume. L * 2 pi r * dr

Sir what is the difference between area moment of inertia and mass moment of inertia? When do these both come into account.....How to calculate inertia for a linear moving bodies...??

@MichelvanBiezen

9 жыл бұрын

Jitendra, Moment of inertia technically is only to be used for mass. But when you have a flat object and the mass isn't given you can assume that the mass is proportional to the area, and you can therefore use the area instead of the mass. (Off course you don't get the correct units and the answer isn't truly the moment of inertia unless you know the mass per unit area.)

@Mech.Masters

9 жыл бұрын

How to calculate inertia for linear moving bodies? Sir, why cant we calculate the area moment of inertia of a circle taking a single circular strip and then using single integration.. I tried using single integration but i got half the value to that obtained by double integration... Why so sir please help?

@Mech.Masters

9 жыл бұрын

And how do we calculate Polar moment of inertia???

@MichelvanBiezen

9 жыл бұрын

Jitendra malviya I just worked out the moment of inertia of a circular object (rotating about its axis) and the moment of inertia is: I = (1/2) m R^2 And this was done using a single integral using a circular strip as the dm

@Mech.Masters

9 жыл бұрын

Yes sir,i got it....actually i was trying to calculate area moment of circle about an axis passing through C.G and perpendicular to its plane and this gives me the polar moment of inertia of a circle.......

0:42 DID HE JUST DRAW WHAT LOOKS LIKE A PERFECT CIRCLE WITHOUT A PROBLEM

@rakhipal2610

7 жыл бұрын

Odyssa Alcantara yeaahh

@rakhipal2610

7 жыл бұрын

Odyssa Alcantara yeaahh.....that was amazing

@Barnicalsify

5 жыл бұрын

Take #523...

area of cross section taken as 2πxdxL is wrong... it should be π(x+dx)^2 - πx^2

@MichelvanBiezen

7 жыл бұрын

2 pi x dx L = dV and it is correct.

OMG I just noticed that cute little eagle

@MichelvanBiezen

6 ай бұрын

Yes, lurking in the corner. 🙂

why do we integrate along R

@MichelvanBiezen

3 жыл бұрын

Because we are adding the moment of inertia of each infinitesimal thin layer of thickness dr. (That is the principle of integration).

Circumference was taken in dx while area was taken in whole circle why??

@MichelvanBiezen

4 жыл бұрын

dx is the thickness of the volume element.

Can the I be like I=0.5M(R1^2+R2^2)

@MichelvanBiezen

5 жыл бұрын

No, that is not correct. (that would make it larger than I = 0.5 M R^2)

@mdasikkhan1610

5 жыл бұрын

@@MichelvanBiezen but in my book it says I=0.5M(R1^2+R2^2)

@MichelvanBiezen

5 жыл бұрын

Are you referring to a hollow cylinder or a solid cylinder.

These are a bit much for me. I am only up to absolute and relative max/min points on the derivative calculus section on the Khan Academy. Haven't touched on Integrals much. I have a deep desire to study Moment of Inertia and Torque so I can get a grasp of how gyroscopic precession works, gyroscopes amaze me. Bah, need to spend more time focused on the math.

@MichelvanBiezen

10 жыл бұрын

Everything in its time. You'll catch on as you learn more of the mathematics.

@Peter_1986

8 жыл бұрын

Integrals are kind of like the opposite of derivatives - you find a function that has a certain given derivative. For example, the integral of 2 is 2x + C (where C is any constant). Integrals are cool for many reasons - one application is that they allow you to find the area under a graph.

@phynos8936

8 жыл бұрын

Yeah, that post was quite a long time ago. I am now in my second year of my Physics degree! I'm fairly familiar with integration. At the time of the original post I was in upgrading school, or just finishing it.

incomplete, as you just found the MOI w.r.t. one axis i.e., the polar axis. What about the other two axes????

@MichelvanBiezen

6 жыл бұрын

It depends on the purpose of this video, which is to show a technique to find the moment of inertia along its central axis of rotation. There are dozens of other videos in the physics and mechanical engineering videos that show all the other techniques of finding the moment of inertia as well.

why x square ??

@MichelvanBiezen

9 жыл бұрын

Naveen Arenas By definition, moment of inertia = m * x^2

@naveenarenas

9 жыл бұрын

Michel van Biezen ohh alright i still couldnt get it straight anyways thanks!

Excellent Sir thank you

@MichelvanBiezen

3 жыл бұрын

Most welcome