How do I find moments of inertia for different shapes?

[yazan_l]

Hi, can anyone help me understand how to find the moments of inertia for the following:
1- A triangular lamina (isosceles) of mass M, base 2B and height H. about line of symmetry.
2- A uniform lamina of mass M, bounded by the curve with equation y²=4ax and the line x = 4a about the x-axis.

For (1), I managed to get the answer, but I’m not sure if my way is right: it was finding M.I. of a rectangle base 2B, height H, mass 2M about the line of symmetry through the base, and divide it by 2 (as the triangle is the half of the rectangle!) I just don’t know if this method is right or wrong, or whether there is another method that I should had used. Those questions are from the book, and the book doesn’t explain how to find M.I. for such shapes, it only shows: rod, hoop, and discs. But not a triangle or curves!

Thank you very much,
Help is appreciated

 

[arildno]

You are proceeding along a wrong track here, I'm afraid.
Have you learned that in general, an object's moment of inertia I with respect to an axis is given by the integral:
I=\int_{V}r^{2}dm
where V is the volume of the object (in your 2-D case, an area), r the distance of a mass point within the object to the axis, and dm the (infinitesemal) mass of the mass point?