Understanding Moments II: Center of Mass, Moment of Inertia, and All That 

Too many options so I went with the one that has 0 creativity 😂

@@AndrewDotsonvideos like a true physicist, "top quark" "bottom quark" "electron neutrino" "tau neutrino" bruh

@@AndrewDotsonvideos me as a high school student yeah i pretend i understand. lol

@@AndrewDotsonvideos reminds me of the Schey text

🥰🥰 momzz

@@fazilnajeeb Fazil!

mrs.dotson andrew NEEDS to do a video where he teaches you physics, that would be fun!!

@@mastershooter64 He does all the time! Most recently was in the video about testicular cancer. I learned about angular momentum! 💕

the virgin vector fan/ the chad tensor enjoyer

I definitely didn’t know it in undergrad. “A thing and then a distance from the thing” feels like what I got

No u

Glad you found it helpful!

Thanks for sticking around!

Thanks a lot!

are you interested in going to physics university?

@@apostolismoschopoulos1876 yup

Really good questions. One way of determining whether and axis of rotation is a principle axis it to apply a force in the direction of the principal axis candidate. If the motion is pure translation instead of rotation then it must have been a principal axis . If the axis is not a principal axis, then the moment isn’t exactly the deviation from the CoM (although they can be related through parallel axis theorem). Instead it describes how far the mass is spread out from that axis. You can also determine the principal axes mathematically by diagonalizing the inertia tensor using its eigenvectors. The eigenvalues of this new diagonal matrix are then the principal moments of inertia.

@@AndrewDotsonvideos Thanks for replying!Was gonna edit my comment a little in order to specify my question a little better(didn't expect you to reply so soon😅).I looked into a book and recalled how you would determine principal axes,which was kind of a side question. The main question is,why does the axis we pick, to calculate the moment of inertia about, have to be the principal axis and not any other axes passing THROUGH THE CENTRE OF MASS in order to describe the variance about the average (or the first moment,or the centre of mass)?Using parallel axis theorem,we would be able to relate moments about axes not passing through the centre of mass,but parallel to the principal axis.At least this is what I understand. Only a high schooler,so I am sorry if my question went way off the point or something, or if I am not able to convey what I am trying to ask 😅.Thanks again! Btw,your videos are really awesome.I am following tensor calculus,and it is really good and fun.One day,even I will be a level 12 tensor boi.Also ,your skits are super funny(I miss Jesse Kyle).😂 If you reply,can you please like the comment,so that I come to know you have ? Actually I have turned off reply notifications.

brilliantly written and presented.

if I understood the moment (in the video, haha) you're talking about, it's because he was doing the "raw" second moment, so with respect to an arbitrary reference.

Good question. The important thing is understanding what directions the deviation spreads into. You can totally define a moment of inertia about the 3-D origin, and it's rotationally invariant which is cool, but I'm not sure what it's used for to be honest. It ends up being related to the trace of the inertia tensor (2I_origin = I^x+I^y+I^z), so that info is contained in the inertia tensor anyway. The principal moments of inertia describe deviations of the mass from a principle axis, which is equivalent to saying how does the mass spread away from the CoM in that plane because all principle axes pass through the CoM. Most instances have rotation about an axis, but the inertia tensor does allow you to talk about instantaneous rotations about a point which sounds like what you're interested in.

@@AndrewDotsonvideos Hey!Not sure if you are still looking into the comments on this video, I understood everything you said in the video (very well explained and motivated) but there's just one thing I am not 100% sure I understand. Does a Moment of Inertia HAVE TO BE about a principal axis in order to represent the variance of the mass distribution about the centre of mass in the plane perpendicular to that axis?Because the property of the principal axis that you seem to be claiming,allows us to deduce this or interpret this,is that it passes through the centre of mass.But then you mentioned that just passing through the centre of mass isn't enough to make an axis a principal axis.What is it then that makes the principal axes unique,or important aside from the fact that the moment of inertia gets minimized along these (mutually perpendicular?) axes?And say,how would one determine which axes are the principal axes out of the infinite passing through the centre of mass?

Zach is a constant reminder that some people are just insanely funnier than me

Yeah, I know the feeling.