- #1

Nexus99

- 103

- 9

- Homework Statement
- Find the moment of inertia of an isosceles triangle of mass M = 1.0 kg, height h = 0.4 m and base angles equal to ## \alpha = \frac{ \pi}{6} ##, with respect to an axis passing through its vertex

- Relevant Equations
- moment of inertia

I did in this way:

## I = \int dm \rho^2 ##

Dividing the triangle in small rectangles with ##dA = dy x(y) ## where ##x(y) = 2 ctg( \alpha ) (h - y) ##

we have : ## dm = \sigma 2 ctg( \alpha ) (h - y) ##

Now i have ## \rho^2 = x^2 + (h-y)^2 ##

Now I don't know what I can do because it would be an integral in 2 variables that I don't know how to do