Moment of Inertia

Hi,

I'm trying to teach myself some physics (dynamics in this case) and there's something I don't really get. It's how to calculate the moment of inertia.
I know the standard formula is I = m*r^2 for point masses, and I = (1/3)*m*r^2 for rigid bodies with equally divided mass, which is the case I'm interested in (I'm working on some 2d game, thats why).

Now can someone tell me what the 'r' is really refering to? Some lectures speak of the radius of the body, but I think that would be silly because then it would be the same for every point of rotation.

Is it then the distance from the point of rotation to the center of mass? This seems kind of logical, because the further away the point of rotation is from the center of mass, the more torque it'll require to rotate the object. But this would also mean that when the point of rotation is the same as the center of mass (which will be the case in many situations), moment of inertia would be 0 for r = 0, which would mean the object is infinitely easy to rotate. Makes no sense either.

Then what is r refering to? I hope someone can give me the answer.

 

Allright thanks, that's at least one step in the right direction. But the distance from the axis of rotation to what? CM? Because there's a problem with that which I've allready described in my first post..

 

Hmm I still don't really get it.. perhaps I should read some more on the subject. Thanks anyway.

 

Yeah I get it now but there remains a problem. For a rigid body, you theoretically have to sum up all the point moments of inertia. But how am I going to approach this then? For a 2d rigid body in a game, this would mean dividing the mass by the amount of pixels the object is built from, calculation the point moment of inertia for each pixel and summing it up again? There must be a better and more accurate way. please help?