Session 11:Center of Mass, Centroid, Moment of Inertia & Radius of Gyration using Double integration

[@AT-ud3yk]

Just love the way you teach sir. My concepts are getting better

[@DrMathaholic]

Very glad to hear that..😊 good luck

[@muwongeevanspaul9166]

Thank u so much. I love the time saved coz surely u are discussing to some guys who know maths. Thank u indeed. Am so greatiful. But ,try to tell your audience that the limits for x are obtained by calculation ,solving simultaneously otherwise man can get lost asking where did -1 and +1 come from. Otherwise it's a great video. So precise and concise 👍👍👍👍👍👍 love u man....u have made my day.

[@DrMathaholic]

Suggestion noted..thank you😊😊

[@DrMathaholic]

Multiple Integration.: kzbin.info/aero/PLwaXU7G6Urbc0Yctvj9GKR9MwS5lpp_r8

[@shreeniketfatangare668]

1] Centroid = (0, 3/5) 2] RoG abt x axis = (10/21)^0.5 RoG abt y axis = (3/14)^0.5

[@DrMathaholic]

🙌🙌

[@sanjaygheji1925]

RoG about y axis is root 1/5 &. About x axis root 3/7 , Verify plz.

[@shreenikam032]

Centroid = (0,4/5)

[@adeshchoudhar9558]

Sir, but in the question ρ(x, y)=y+1, if density was dependent on x, we cannot say x̄ = 0, even though it is symmetric about Y-axis.

[@DrMathaholic]

Try with density Equal to x or x^2. Check n let me know what answer u got

[@adeshchoudhar9558]

I tried with ρ = x for the same example, then I got a non-zero value as the last integration contained all even functions and for ρ = x^2 we get 0, as all were odd functions in the last integration.

[@swaranjalighutake4879]

1) mass -(0, 9/14) 2) radius of gyration -(√3/14 ) here ,Iy=16/35 , M=32/15

[@DrMathaholic]

Thanks for posting the answer 😀

[@aniruddhguranna6920]

Sir , I just wanted to make some corrections : 1)Mass : (x,y)-(0,9/14) 2)Iy=16/35 3)Ry=(3/14)^(0.5)

[@DrMathaholic]

Great..so u could find radius of gyration.. good.

[@atharvakannal9720]

Iy =3/10

[@DrMathaholic]

@@atharvakannal9720 you did not get 16/35?

[@VIVEKKUMAR-xs9zp]

Sir how to find MI of Trapezoid

[@DrMathaholic]

1. You should know the density. If it is not given then take as 1. 2. When u do double integration, you integrate in the order dxdy. 3. To find limit of x, draw a line parallel to x axis and see from where it enters and leaves the trapezoid. It enters n leaves from a line. Once a trapezoid is given, you find the equations of line and this will give you limit for x. 4. Now from the trapezoid given, find the extreme points of y and that will b limit of y

[@atharvakannal9720]

Sir for radius of gyration what is the M.I taken

[@DrMathaholic]

You check:)... See in the question, axis is mentioned...

[@aniruddhguranna6920]

1)Mass : (x,y) - (0,9/14) 2)Centroid :(x,y)-(0,3/5) 3)Radius of gyration - I m not able to solve

[@DrMathaholic]

Oh. Why,? You got Ix and Iy?

[@aniruddhguranna6920]

@@DrMathaholic no sir not able to

[@DrMathaholic]

@@aniruddhguranna6920 ok, i will solve n get back to u

[@swaranjalighutake4879]

@@DrMathaholic sir in symmetry of parabola, u have given in problem so can we consider Ix?? Because our x bar = 0 also Ry?

[@shainajindal1804]

Ix da answer 16 /15 aaa rhea a