I just discovered your channel, and found it to be amazingly helpful. I study engineering, and your videos are by far better than many lectures I am used to.
You're amazing at explaining; nice microfone, nice speed, pretty handwriting, no caughing or random background noise and overall you get the feeling you truly know and understand the priciples and mathematics you explain. Thank you so much. Cheers!
Eloquently put. Thanks man!!! I shall continue now reading the chapter from my book to then do homework. The diagram and explanation in the book did not help a lot but after watching your video it all makes sense now. You gotta respect people that went through college studying physics and calculus without the internet. The hell with that lol I need my google, youtube and every source I could find :)
Thanks man! That means a lot to me. I agree that UA-cam has become such a powerful education tool! One of my academic heroes, Sal Khan, created the Khan Academy and is using it to change the lives of millions :D
Thanks, mate. I use Microsoft One Note to write on and I now record using a program called Camtasia studio. I've previously used Cam Studio to record my videos but I decided to change because it made my computer lag too much. Hope that helps!
But what if r dash was perfectly vertical? What if the point(element of mass dm) was moved such that r dash is vertical? How would that pan out since you can't take the components of r dash?
Hey mate, imagine dividing this 2D plate into infinitely many rectangular small chunks of mass. So for example, one small chunk of mass could be at the bottom left of the plate and another could be in the middle somewhere to the right etc.. As you can see, in the general case an element of mass will have a vertical (y') and horizontal component (x'). It's true that some chunks of mass which happen to align directly on the y axis will have no horizontal component, but in general this is not true. If we say that the element of mass dm has no horizontal component then we're "telling the equation" that every single chunk of mass is located in a straight vertical line - and this is incorrect. This is a question that really strikes at the heart of calculus, so if you want to learn more I suggest researching 'double riemann sums'. Hope that makes sense :)
your explanation of the integrals of the mixed terms canceling was somewhat misleading I think. those integrals go to zero but not because r' is the distance from the center of mass to the center of mass. they go to zero because you end up with x^2- x^2 when you evaluate the definite integrals.
Icom in your equation contains both x' and y' and they both are zero because you considered origin at centre of mass, then how come the lcom(moment at centre of mass) not zero.
Hey mate! Excellent question! x' and y' are NOT zero! x_bar and y_bar are both 0 for an axis located at the center of mass. From this we can then prove that the integral of x' dm = 0 and the integral of y' dm = 0. Notice that I_com = integral x'^2 + y'^2 dm :)
Matthew James I am sorry buddy, I am still confused about x' and y'. What does they represent in equation, are they components of axis, do they have unit value, please clarify, although I understood why x- and y- are zero (because they are distance of centre of mass from origin).
Hey mate, sorry for not being too clear in my last message. You're absolutely right about x- and y-. :) Let's talk about the _variables_ x' and y'. Look at 1:20 x' is the horizontal distance (units are meters) from the center of mass to an element of mass dm y' is the vertical distance (units are meters) from the center of mass to an element of mass dm Note that IF x' and y' were both zero, then every single bit of mass would be located at the centroid and you wouldn't have an object! You would only have a particle! Hope that makes sense :)
Matthew James Oh buddy, thanks a ton, now I understand the why x- and y- are zero and x'&y' are not. Its all clear now. Thanks again for clearing the doubt. :-) Is there a wat to contact you regarding doubts on other topics like buckling etc.
I just discovered your channel, and found it to be amazingly helpful. I study engineering, and your videos are by far better than many lectures I am used to.
Dion Kllokoqi Hey mate! I'm happy that I could help :D
You're amazing at explaining; nice microfone, nice speed, pretty handwriting, no caughing or random background noise and overall you get the feeling you truly know and understand the priciples and mathematics you explain. Thank you so much.
Cheers!
Its a relief that i found this channel, now finally I ca.n understand dynamics
Simple and elegant thxx man this concept is now crystal clear to me
Eloquently put. Thanks man!!! I shall continue now reading the chapter from my book to then do homework. The diagram and explanation in the book did not help a lot but after watching your video it all makes sense now.
You gotta respect people that went through college studying physics and calculus without the internet. The hell with that lol I need my google, youtube and every source I could find :)
Thanks man! That means a lot to me. I agree that UA-cam has become such a powerful education tool! One of my academic heroes, Sal Khan, created the Khan Academy and is using it to change the lives of millions :D
Really great job. Better than our lecturer. Thanks
Luboš Bešina thank you :)
Amazing explaining !!
Thanks a lot ORZ~~
Good job mate! It was helpful.
Amazing job what software did you use to make this video?
Thanks, mate. I use Microsoft One Note to write on and I now record using a program called Camtasia studio. I've previously used Cam Studio to record my videos but I decided to change because it made my computer lag too much.
Hope that helps!
Thank you for your effort, can you please give me the link of explaining. y dash dm =0 and x dash as well
But what if r dash was perfectly vertical? What if the point(element of mass dm) was moved such that r dash is vertical? How would that pan out since you can't take the components of r dash?
Hey mate, imagine dividing this 2D plate into infinitely many rectangular small chunks of mass. So for example, one small chunk of mass could be at the bottom left of the plate and another could be in the middle somewhere to the right etc.. As you can see, in the general case an element of mass will have a vertical (y') and horizontal component (x').
It's true that some chunks of mass which happen to align directly on the y axis will have no horizontal component, but in general this is not true. If we say that the element of mass dm has no horizontal component then we're "telling the equation" that every single chunk of mass is located in a straight vertical line - and this is incorrect.
This is a question that really strikes at the heart of calculus, so if you want to learn more I suggest researching 'double riemann sums'.
Hope that makes sense :)
Very good explanation, thank you.
its good sir thanks for nice video .....................
Thanks mate :)
Awesome video!!!!
Thank you so much for telling me the math and principle behind this thm:)
Thank you! Great job! It helped me a lot!
no worries!
Superb work.
Thanks!
Man you are the BEST!
Very Very good explanation thanks
Well done
This is a good video!!!
very useful!!thanks a lot!
your explanation of the integrals of the mixed terms canceling was somewhat misleading I think. those integrals go to zero but not because r' is the distance from the center of mass to the center of mass. they go to zero because you end up with x^2- x^2 when you evaluate the definite integrals.
Icom in your equation contains both x' and y' and they both are zero because you considered origin at centre of mass, then how come the lcom(moment at centre of mass) not zero.
Hey mate! Excellent question! x' and y' are NOT zero! x_bar and y_bar are both 0 for an axis located at the center of mass.
From this we can then prove that the integral of x' dm = 0 and the integral of y' dm = 0.
Notice that I_com = integral x'^2 + y'^2 dm :)
Matthew James I am sorry buddy, I am still confused about x' and y'. What does they represent in equation, are they components of axis, do they have unit value, please clarify, although I understood why x- and y- are zero (because they are distance of centre of mass from origin).
Hey mate, sorry for not being too clear in my last message.
You're absolutely right about x- and y-. :)
Let's talk about the _variables_ x' and y'. Look at 1:20
x' is the horizontal distance (units are meters) from the center of mass to an element of mass dm
y' is the vertical distance (units are meters) from the center of mass to an element of mass dm
Note that IF x' and y' were both zero, then every single bit of mass would be located at the centroid and you wouldn't have an object! You would only have a particle!
Hope that makes sense :)
Matthew James Oh buddy, thanks a ton, now I understand the why x- and y- are zero and x'&y' are not. Its all clear now. Thanks again for clearing the doubt. :-) Is there a wat to contact you regarding doubts on other topics like buckling etc.
Hey mate! No problem. Happy to help :)
Sure! Feel free to message me on my channel or email me. I'll help out where I can :)
great video sir, thank you very much!
Wohoo! Glad you enjoyed it.
You are the best bro
thanks, dude :D
Great explaining
Eivind Hagen glad you found it helpful!
Great video Thanks
great work man
Thanks :D
great video, thanks man
Glad you liked it !
Thanks, mate :)
Thank you so much
Thanks!
乾我咕狗平行軸定理咕了半天沒一個證明是看的懂的，只有這個！！！末兩項=０那個解釋的超棒，還是啊都仔比較厲害-3-
Tanks for your distinct explanation of the yucky theory.
good one
Helped alot. thanks
Thank you :D
No worries, all good
You should really invest in a pop filter. Otherwise great video.
I love u the video is amazing
Thank you :D
bless you sir. bless you.
haha cheers :D
your awesome
No, you're awesome :P Thanks mate.
Tooo complicated because the constant to and fro !
lol, spoiler alert in a physics video.
good one