What is the method for calculating moment of inertia for basic geometric shapes?

[Eeduh]

Homework Statement

I want to calculate the moment of inertia of a 2d triangle. Let's say we've got a triangle with sides of 20 units. So it has width 20 and height 17,32.
Also, let's say this triangle has a mass of 173.20 mass units (just used the surface). Now I want to calculate the moment of inertia from a given axis of rotation.

Homework Equations

I = M*r^2 for point mass

The Attempt at a Solution

Since the triangle is basically built from an infinite number of point masses, but it has no use to divide the mass by the number of point masses, and calculate the MI for every single point. There must be a more easy way of calculating the moment of inertia for basic geometric shapes, with a given axis of rotation. But I can only find the theory of shapes being built from point masses. Please help

 

[H_man]

This is why you must use integration to solve the problem.

Does this get you started...

 

[Eeduh]

Sorry not really.. I'm not very familiar with integration. Would you be so kind of giving me an example for this problem? For example, with the axis of rotation at 7,2 when the vertexes of the triangle are at 0,0; 17.32,10; 20,0? I understand if this would be too much to ask.

 

[H_man]

Ok, to avoid integration...

In your book you should have what the moment of inertia of a triangle is (about its center of mass).

You can then find the moment of inertia about a general point by adding Mass * Distance to this term. Where Mass is the mass of the whole triangle and distance is the displacement from the center.

So

Moment of Inertia = Moment of Inertia about the center + MR^2

 

[Eeduh]

Allright thanks, I think this will help. btw, I don't have a book :P I want to know this for myself, doing some programming. But I'll have a look on the internet again, and I'll figure it out.