18. Advance Illustration | Rigid Body Dynamics | Moment of Inertia of a Triangular Lamina

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[ishaanagarwal]

When I solved this problem for the first time, we were given this problem as a homework, all my friends were trying different methods of integration, but then i suddenly remebered those 10th standard triangles chapter questions where we used to divide an equilateral triangle into 4 smaller congruent triangles and thought of executing the same and came up with this solution myself. I was elated and thought nobody would ever think of this😁. The next day when i went to class, 4 other ppl had come up with the same.😶That day I realised that the COMPETITION IS REAL.

[adityasaha]

In an Eq Triangle if O is the centroid then AO : OD= 2:1 again AD=Height=√3/2×side
OD=1/3×AD= side/2√3
which is perpendicular dist from centroid to any side. For 2 centroid it is 2×(side/2√3) =side/√3
Here side= L, then finally L/√3

[smpsheep]

Amazing solution, coudn't have thought of this myself.

But I was able to get the same answer usiing parallel axis theorem from base to centroid (as it is also the COM), and then perpendicular axis theorem. Although my method was way less fun, it was actually shorter than this!

[gagandeepnote]

a better and more thinkable solution would be to use perpendicular axis theorem at centre of the base of triangle and then using parallel axis theorem to calculate MOI about centre of mass.

[pulkitbhardwaj]

A Better solution (easy to think)

Apply mh²/6 to find MI for base and axis as median (2×MI of M/2 triangular halfs)

Then apply perpendicular axis theorem to find MI perpendicular to plane of triangle and passing through mid point of edge

Finally use parallel axis theorem to find the MI required, you will get the same answer.

[drujjawalrathore]

Sir in USS the same expression is given as Ml^2/6. Is that wrong?

[Simplesamosa]

Please clarify my one doubt regarding to distance between two centroids L/√3 ;;how .

[ytonly]

Similar que in jee mains 2019 Jan 11th

[ashutoshray]

Sir plz solve this problem with help of integration

[kMEAmartyaPrabhakar]

Respected Sir, why is MI directly proportional to square of dimension of a rigid body?

[abdullabohra-jm]

well i tried with the same method as sir but rather than increasing the triangles i divided it into four equal triangles lol
anyway the variation of this question i am thinking of is finding the moi of tetrahedron that would be crazy any suggestions t solve it??

[jashb]

Why dont we divide triangle into two right angle triangle then apply MH^2/6.
As both will be symmetrical I would be 2(m(l/2)^2/6)=ml^2/12

[kruthikpimpre]

Sir, I used this trick to find out moment of inertia of an Equilateral Triangular Lamina about an axis passing through the altitude of the triangle. Surprisingly, I checked out on the web to find out weather I am correct or not, but I didn’t found out nothing. Please would you help me out?

[puneethgowda]

Sir how do we solve this question using integration method

[namanbiyani]

sir can we make it a rectangular plate and then //axes theorem?

[sonamkaurkhurana]

Sir how to calculate MI of right angled triangle?

[codingwithanonymous]

how to integrate it from where to where bit confused

[Ashishsawadia]

SIR CAN WE ASSUME IT AS A DISK AND WE KNOW ITS MI AND THEN SUBTRACTING IT FROM 3 HALF DISK HAVING DIAMETER
AS THE SIDE OF TRIANGLE .
SIR PLZZ REPLY
PLZZ

[aaryanshukla]

And the same q comes today in jee mains

[kusumajagini]

sir how is the seperation between two centroids is l/root3