Moments of Inertia of Rigid Objects with Shape

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  • Опубликовано: 28 ноя 2024

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  • @aadrath1236
    @aadrath1236 3 года назад +39

    If you were in India a temple would have been built in your name XD. Can't believe how underrated this channel is. One of the best for CONCEPT CLARITY 💯

  • @mangoface7914
    @mangoface7914 3 года назад +13

    Even though I used calculus to derive these equations on my own, I still could not intuitively conceive these formulae. Your video was so incredibly helpful! It also helps that you insinuate a classroom setting where each student comes to the answer on their own, so it makes it even more memorable. Thank you for putting these out on the internet!!

  • @freddibiri
    @freddibiri 4 года назад +27

    i love how the guy in the middle is always high.

  • @quahntasy
    @quahntasy 6 лет назад +27

    Another one of the great video!

  • @crazyfacts2600
    @crazyfacts2600 3 года назад +5

    Beautifully explained
    And for the first time I enjoyed and learnt seriously
    Good luck mate

  • @sanjaySingh-ck6kd
    @sanjaySingh-ck6kd 3 года назад +1

    I salute the best Physics teacher.

  • @_BhagavadGita
    @_BhagavadGita 6 лет назад +5

    You are the best, Mr P.

  • @eranshukumari7591
    @eranshukumari7591 Год назад

    In my life, first tine I understood rotational physics.🥰🥰🥰🥰

  • @vivektodakar3426
    @vivektodakar3426 3 года назад +1

    I like the way of teaching.

  • @KaviBarwari-o6y
    @KaviBarwari-o6y Год назад

    thank you your the best teacher

  • @Raage.
    @Raage. 4 года назад +4

    Thanks For your Contribution to our understanding of physics.

  • @tinimunson1242
    @tinimunson1242 Год назад

    Thank you so much for this video! It really helped me understand Rotational Inertia very well! But I have a question: Why does the thin hoop have a larger rotational inertia than the hollow sphere? I keep getting confused by it.

  • @anishkumarsingh1019
    @anishkumarsingh1019 3 года назад

    You are an amazing teacher!!!

  • @sajaldeb329
    @sajaldeb329 5 лет назад +1

    Nice explanation sir

  • @anarmehraliyev1286
    @anarmehraliyev1286 2 года назад +1

    That's very informative, thanks!

  • @scamsituation3982
    @scamsituation3982 6 лет назад +2

    I can certainly relate with that Beau.

  • @phenomenalphysics3548
    @phenomenalphysics3548 4 года назад +3

    0:59 will you please post calculus based explanation for calculation I

    • @FlippingPhysics
      @FlippingPhysics  4 года назад +1

      My in-class lectures about this are here :ruclips.net/video/X36BAPvxWQs/видео.html

    • @phenomenalphysics3548
      @phenomenalphysics3548 4 года назад +1

      @@FlippingPhysics thank you

  • @ajaykrishnanr6468
    @ajaykrishnanr6468 4 года назад

    Really worth watching...great effort

  • @Cutelobya
    @Cutelobya 6 лет назад

    THIS VIDEO SAVED MY LIFE THANKYOU!!!!!!!

  • @AstroBananna
    @AstroBananna Год назад

    Very good

  • @I-used-to-be-orcaz
    @I-used-to-be-orcaz 6 месяцев назад

    I know this is 5 years late but I rlly like ur shirt

  • @jonvassella1076
    @jonvassella1076 3 года назад

    very cool approach indeed - thank you very much

  • @reemazam3225
    @reemazam3225 2 года назад

    Thank you so much sir..

  • @KnightBlaze55
    @KnightBlaze55 5 лет назад +1

    Very nice 😀 explanation sir

  • @alondrarivera6153
    @alondrarivera6153 4 года назад

    Thank you so much! My final is around the corner

  • @AyalaMrC
    @AyalaMrC 6 лет назад +2

    Seams like there was a conceptual leap from the solid cylinder's fraction to the solid sphere's; I would have paused and looked at the differences in the shapes, or how the sphere tucks more of the mass in close. Other than that, great video!

    • @FlippingPhysics
      @FlippingPhysics  6 лет назад +1

      The video was already way too long and I decided not to dwell on that particular issue, though I agree it is the least obvious of the comparisons.

    • @itsjoeeeeee
      @itsjoeeeeee 3 года назад

      @@FlippingPhysics Where could I find an explanation for how the shape of sphere and cylinder affects its moment of inertia?

    • @carultch
      @carultch 3 года назад +1

      ​@@itsjoeeeeeeYou ultimately need calculus to determine why these moments of inertia are what they are. The thin cylinder and thin ring are two trivial examples that don't need calculus, since it is immediately obvious that all of the mass is concentrated at the full radius. You can use this as a shortcut, so that your differential mass unit is a series of thin cylinders, that approximate the solid cylinder or solid sphere. You then set up a sum of the corresponding moments of inertia of these differential mass units, which becomes an integral when there are infinitely many of them.
      Here's the solution for the solid cylinder:
      Given a cylinder of radius R, length L, and density rho, set up the differential mass element as a thin cylindrical shell at position r and thickness dr. It will also have length L and density rho like the solid cylinder.
      This differential mass element can unwrap like the label of a can, and will have thickness dr, length L, and width 2*pi*r, consistent with the circumference. Its mass dm is therefore dm=2*pi*rho*L*r*dr.
      We know the moment of inertia of a thin cylinder is m*R^2, so the differential moment of inertia (di) of our differential mass element cylinder of mass dm and radius r:
      dI = dm*r^2
      Substitute dm:
      dI = 2*pi*rho*L*r*r^2*dr
      Simplify:
      dI = 2*pi*rho*L*r^3*dr
      We can treat 2*pi*rho*L as a constant. Pull it out in front as we integrate:
      integral dI = 2*pi*rho*L* integral r^3*dr
      I = 2*pi*rho*L * integral r^3 dr
      integral r^3 dr = 1/4*r^4 + C
      Evaluate the difference from r=R to r=0, noting that the arbitrary constants C cancel:
      1/4*R^4
      Reconstruct:
      I = 1/2*pi*rho*L*R^4
      Recall that rho is mass/volume, and that the volume of a cylinder is pi*R^2*L:
      I = 1/2*pi*M/V*L*R^4
      Substitute V = pi*R^2*L
      I = 1/2*pi*M*L*R^4 / (pi*R^2*L)
      Cancel pi, L, and 2 of the R's. Simplify and we get our solution:
      I = 1/2*M*R^2

  • @nasirkhalid6770
    @nasirkhalid6770 6 лет назад +2

    Thanks you are the best.

  • @tannazheidari7857
    @tannazheidari7857 3 года назад

    It was excellent.thank u so much 👍👌

  • @amarj9909
    @amarj9909 5 лет назад +1

    Why it is r2 in moment of inertia ....instead of r from axis of rotation ...I feel one r is enough to make rotation ...then why r square...pls help to understand .... I hope you will explain .... thanks

    • @FlippingPhysics
      @FlippingPhysics  5 лет назад

      I explain it in this video. ruclips.net/video/gdUkXvBWdcs/видео.html

  • @Harshitabha
    @Harshitabha 2 года назад

    Just wondering how did you get (1/12)mL^2 for the moment of inertia of a thin rod rotating about its center of mass? Is that something that just needs to be memorized or something we can derive?

    • @FlippingPhysics
      @FlippingPhysics  2 года назад +1

      I derive that equation in this video:
      www.flippingphysics.com/thin-rod-rotational-inertia.html
      Please do not memorize moments of inertia. You need to understand how mass distribution affects rotational inertia and to be able to compare their relative magnitudes like we do in this video, however, you do not need to have the equations memorized.

    • @Harshitabha
      @Harshitabha 2 года назад

      @@FlippingPhysics thank you!

  • @ashishpant7146
    @ashishpant7146 6 лет назад +2

    Thanks sir

  • @ליהיימליך
    @ליהיימליך 6 лет назад +1

    wow, that's a great video!

  • @abhisheaksharma3765
    @abhisheaksharma3765 5 лет назад +1

    Bo is my favourite.

  • @أساطيركرةالقدم-ه1ح
    @أساطيركرةالقدم-ه1ح 3 года назад

    you are cool my friend

  • @sayantan5663
    @sayantan5663 3 года назад

    Thank u sir❤️

  • @freddibiri
    @freddibiri 4 года назад

    flipping useful.

  • @stimulantdaimamld2099
    @stimulantdaimamld2099 Год назад

    great

  • @TheSeriousShowURL
    @TheSeriousShowURL 4 года назад

    super fun :))))

  • @Mdsalmankhan8674
    @Mdsalmankhan8674 4 года назад

    I think aarti Sangwan from india and are you from flipins

  • @vestafarhan7580
    @vestafarhan7580 4 года назад

    Pls help me
    How you make difference between point mass
    And extended object

    • @carultch
      @carultch 2 года назад

      A point mass has all of the mass concentrated in a volume of space that is negligible. In other words, you can treat the object as if all of its mass is at the same point, and still get the same result as if you considered its distribution. A point mass is usually an approximation to keep the math simple, and not necessarily something that exists in reality.
      An extended object has a distribution of mass that is important to the problem in question, and we need to consider the location and distribution of mass to get the correct answer.
      As an example, consider a 100 gram (m) apple hanging on a string of negligible mass with its center 1 meter (L) below the top of the string, with a radius of 3 cm (r). In other words, a simple pendulum. Assume 3 significant digits. If we treat the apple as a point mass, the moment of inertia about the top of the string would be 0.1 kg-m^2, calculated via m*L^2. If we account for the apple's size, and treat it as a uniform solid sphere, we will calculate moment of inertia about the top of the string through 2/5*m*r^2 + m*L^2, and get the moment of inertia to be 0.100036 kg-m^2, which rounds to the same answer we had before. The apple might as well be treated as a point mass, since its size is insignificant compared to the 1 meter string length.
      Now, let's shorten the string to so that the center of the apple is 10 cm below the top of the string. Treating the apple as a point mass, gets us a moment of inertia of 0.001 kg-m^2. Treating the apple as an extended object, accounting for its shape as a uniform solid sphere, we will instead get 0.001036 kg-m^2, which we'd need to round to 0.00104 kg-m^2 for 3 significant figures. You now see that the 3 cm radius of the apple makes a difference, compared to what it would be if treated it as a point mass.

  • @giuseppemeola397
    @giuseppemeola397 3 года назад

    Mr clutch

  • @ilovepersephonie
    @ilovepersephonie 4 года назад

    i hate physics that is all

  • @mukulbelwal
    @mukulbelwal 5 лет назад

    Thanks sir