Moments of Inertia with Double Integrals - Vector Calculus Application

Explanation of how to use multivariable calculus (multiple integrals) to calculate the moment of inertia of a solid with varying density.
More informative vector calculus videos: • Valuable Vector Calculus
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Music: C418 - Pr Department

[@dackid2831]

I will be honest, I always thought I=mr^2 was just an arbitrary definition that we build more complex moments of inertial upon. Those first 3 minutes were a pleasure to see. Well done Mu Prime! Edit: I now realize that that wasn't entirely true. I learned a really neat calculus way of thinking about it a while back. I still very much enjoy this algebraic approach though.

[@youssefsultan5838]

wow, how I don't discovery this channel before, ur explanation is amazing, keep it up

[@william.mejiag]

Great explanation and development of the physics concepts and its subsequent application in vector calculus.!

[@nathanisbored]

i hate physics and i always struggled with the physics intuition for things, especially when i took vector calculus. im also pretty sure i never learned about moment of inertia or anything like that. but this video was still really well explained and comfortable for me to watch. also i did a double take when you pulled out smash brothers i thought i was high or something

[@MuPrimeMath]

I couldn't pass up the opportunity to use the Melee disc! lol

[@F1U7R2Y9]

Cool ! Bring these type of new things.

[@kylesegal642]

i love how hes flexing his 200$ GC game. It's so good

[@MichaelChenAdventures]

you explained this extremely well!!!!

[@trigon7015]

I’m confused, are you physics boi or maths boi? I’m maths boi and I have no idea what this is supposed to mean.

[@MuPrimeMath]

This is a physics application of vector calculus!

[@trigon7015]

Yeah but I can’t physics

[@ronaldos3738]

Good explanation

[@drlangattx3dotnet]

Please explain at 7:35 what the Jacobian is and how you used it.

[@MuPrimeMath]

The Jacobian is an expression that occurs during change of variables for double integrals. See my video on the Jacobian: kzbin.info/www/bejne/Y5-raJ-jmpeVr5I

[@theunknownscientist3249]

A great video, thanks, every math book I meet doesn't mention the axis stuff, just gives the formula. But I think you forgot to mention that that density is superficial, mass/area, not mass/volume, the triple integrals use the mass/volume density.

[@MuPrimeMath]

Yes, if we integrate with respect to area, then it only makes sense when the density is area density!

[@LA-cm9uo]

Good, but the first half was a bit too fast, I had to pause many times.

[@LA-cm9uo]

I got 0/5 not pi/5, help please?

[@byronvega8298]