# Find Moment of Inertia

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1. Mar 24, 2016

### LoveBoy

1. The problem statement, all variables and given/known data
http://i.imgur.com/7ZRsVj5.png

2. Relevant equations
I can't apply correct method !

3. The attempt at a solution
In bigger figure, i cut into 8 equal parts.So , total moment of inertia=8 I
But it's wrong !
I know it's wrong because i can't able to find angle between any two sides when i cut into 8 equal parts.
So,just as a guessing approach , i supposed each part is equal to I . Therefore,corresponding to total 8 I.

2. Mar 24, 2016

### SteamKing

Staff Emeritus
You don't have to cut anything, but you should think how the inertia of the sample triangle changes when the dimensions 'a' are multiplied by the same scale factor.

3. Mar 24, 2016

### jbriggs444

You cut the square into eight parts because the area of [a triangular half of] the square is eight times the area of the triangle? How did you manage this feat? Where do you make the cuts to get eight 1x1 triangular half-squares out of a triangular half square that is $2\sqrt{2}$ on a side?

Consider, as SteamKing hints, cutting the square into four pieces, each of which is an isoceles right triangle and each of which has a side other than the hypotenuse on the axis of rotation.

4. Mar 24, 2016

### LoveBoy

As per your given hint, if i double the sides of isosceles triangle , then i would get hypotenuse equals the side of square .
But i'm confused in the thing that if we double the sides , is moment of inertia becomes 4 times ?

5. Mar 25, 2016

### Nathanael

The moment of inertia typically looks like kML2, right?
For uniform density distributions, similar geometries turn out to have the same coefficient k.

Start with a triangle of side length a and mass m with moment of inertia I1 = km1a2.
Now scale it up to side length 2a; the moment of inertia becomes I2 = km2(2a)2.

If m2 = m1 then I2 = 4I1. Is the "if" part true though?

6. Mar 25, 2016

### LoveBoy

I don't think so because if we double the length, mass also differs.

7. Mar 25, 2016

### LoveBoy

8. Mar 25, 2016

### Nathanael

Right, because the problem statement said that the triangles are of the same density and thickness. More area with the same density means more mass. What is the exact relationship though? If you double the legs what happens to the mass?
(Then, what is the total effect on the moment of inertia?)

9. Mar 25, 2016

### LoveBoy

If we double the legs keeping density and thickness same,then mass becomes 4 times.
And if mass becomes 4 times ,then leg becomes 2 times, then moment of inertia becomes 16 times.
So, total moment of inertia=4*16 I = 64I

Therefore, 64 I is our answer !

10. Mar 25, 2016