i started watching your videos when i was still deciding to study physics. one year later, when i was starting my undergrad first year i came back to your channel (and this video) and i thought "wow one day i'm gonna understand what you're doing". i remember reading the word "tensor" and not having idea what it meant. now, 3 years later, i'm taking my second course of classical mechanics and i finally came to this video hoping it'll help me undertstand the subject for my exam. i get the physics you're talking about now. it's such a good feeling!! keep it up guys, we're all gonna make it someday.

First year undergrad here, I was just thinking "wow, I'll be able to understand this, isn't this nice" and then some epsilons and deltas came in

Staring at Goldstein for hours and Andrew comes along and clarifies everything in 10 minutes! Bless up

As someone taking some graduate level courses in my last year of undergrad studies, I have really appreciated these types of videos. Keep them up Andrew, I'm loving them!

I don't understand anything he's talking about, I just find his voice and the sound of the marker relaxing. I'm not even a physics student, I just just find his videos interesting.

The best way of learning is by explaining the material. Awesome video, helped a lot!

Your integral is very revealing of how to derive the inertia tensor directly by identifying from r²ω-r(r•ω) the r²δ and the dyadic/cross product

My classical mechanics textbook skipped the part where you evaluated the double cross products so this definitely helped. Thank you

I am a physics grad student and I appreciate your videos very much! Keep up the good work!

That was super informative and just helped me with what I am working on. Thanks!

I dare to say, you just saved my theoretical mechanics test tomorrow. gj

It's worth mentioning, that on 2:08 the first r_i doesn't necessarily have to be equal to the second r_i. That is because linear velocity desribed by cross product includes radius of rotation, while the first r_i is simply a radius vector, which in the most general case (like when there are several points of a rigid body lying on the rotation axis), again, may be different from the radius (the second r_i)

really good teaching style, thanks!

this was very helpful, thank you!!

In the exterior calculus formalism, the angular momentum is actually not a vector, but a bivector, whose components are represented by a tensor of order 2. Similarly, the angular velocity W is a tensor of order 2, such that v = Wr, where v and r are the velocity and position vectors. Under this formalism, the inertia tensor is sometimes defined as a tensor of order 4, with four indices. For instance, if L and W are contraviant, then I is mixed. If W is contraviant and L covariant, then I is contravariant. In each case, it is suggested that W doubly contracts with I, which leaves a tensor of order 2, and this is L. The relationship L = IW is maintained as in your video, but each quantity has doubled in indeces. Can you make a video deriving this? I know it would be a pain, but I would love to see it.

man...as a bsc physics student i have to say that you saved me now

Great video.

i wish i had a teacher like you

Best video on the topic!

I remember when my dynamics teacher did this, we were so confused

Excellent. Thanks.

Very good video. Thanks.

Andrew, does this count as one of the Tensor Calc. series video? If not, how's that going?

One question! You made it seem like the inertia tensor is defined for a point particle, and that for a rigid body you would only need to sum for every particle in the body. So is it correct to say that a point particle needs this tensor as well, when rotating about an arbitrary axis? Because I've never seen the tensor being used for a point mass. Maybe because it was always rotating on a plane normal to the axis it was rotating around and a bunch of terms drop to 0, but I'm just asking for completeness!

omlll I love the title!

what a nice video to watch

Thanks for you

Yeah... I got a D in calculus, this is a no from me chief. still watched the video though

@Andrew Some people from Jlab are going to be presenting preliminary results from their 12 GeV upgrade at this APS regional conference I'll be attending in TN, so I'll def (maybe) attend these talks. (I'm more of a condensed matter guy so we'll see if I can make them...though there is an increasing overlap between CM and high energy physics because of all the quasiparticles we've been finding in CM, so that's pretty dope). Also, sorry this has nothing to do with this video...but twas a great video.

Video is enjoyed

My algebra teacher told us a tensor is a map of (V x V x V ...) onto R ( V being a vector of a vector field E). Nevertheless, the inertia tensor prensented here just looks like a matrix that maps a vector of E to another vector of E. Someone please explain, Im confused.

gah im confused. how can we say v = w x r if v can have components parallel to r? (edit - maybe it doesn't matter anyway because you cross v with r after)

Papa Andrew has uploaded for us peasants

A random question, is this collage or school level in the US?

🤯

Don't you already have a video on the inertia tensor?

I'm confused, I didn't think there was supposed to be a negative sign in the product of inertia terms

Should be tittled moment of inertia Tensor.

It would be cool if you used this linear algebra/tensor approach to solve a simple University physics problem. Something like a ball rolling on a plane

un grande este weon jjjajaj

can you prove the levi-cevita symbol expansion identity you are using,

time for another physics meme review before my meme sinks to the bottom

the tensor notation for the cross product gave me cancer. Your video 'cross products using levi civita' was useful though.

You often erase stuff a little too much for those of us learning it for the first time

Just showed up in my freshman mechanics class and I'm so confused

Just a few pedantic notes; Einstein summation notation only applies when the index appears exactly twice. If the index appears three times you should explicitly write the sum. At 1:00 you left off the subscript for p_i making it look like the sum of all momenta At 6:40 you equated a scalar with a vector; you should have put (...)_i around it.

Can you redo this video for beginner who just got a grasp of what angular momentum is😂

13:53 How did you know?? Ha ha

First one🎈🎈

Why does it have that hashtag..... Honestly I am kinda dissapointed :(

Are you sure deriving Inertia tensor is just girly things LMAO>

Indian fans hit like.

Last

what the fuck

Ew you're using index notation. Excuse whilst I throw up in my mouth