Originally Posted by CanAutM3
Read my post again, I am referring to axle weight distribution, in response to the post I was replying to. Not overall weight distribution.
Using the centre of gravity as the referential, polar moment and axle weight distribution are not related. Polar moment depends on how weight is distributed around the centre of gravity (how much and how far). Axle weight distribution depends on the position of the centre of gravity relative to the axles.
Now under dynamic conditions, it gets more complicated, as a car does not necessarily rotate around the centre of gravity.
I don't want to get too technical here, but for those interested, there is a very good book published by the Society of Automotive Engineers called Fundamentals of Vehicle Dynamics by T. D. Gillespie that explain these principles very well (with plenty of equations
Still disagree. Getting way OT but...
Consider two equal masses m, a distance d apart, say equal to a wheelbase. This is an idealized two point mass "car". This results in 50:50 weight distribution and the polar moment I(about cg) = m d^2/2. Alter the weight distribution radically so 100% is on one axle. Weight distribution = 100:0, total weight unchanged. Now here I(about cg) = 0. For the more general case you can solve for the generalized I about the cg for any value of m1 and m2.
I = (m1 m2 d^2)/(m1+m2)
Again even though m1+m2 is fixed change their ratio
and you can compute exactly how I changes.
Through this simple example you should be able to see that axle weight distribution and polar moment are intricately linked. You can extrapolate to the case of a continuous variation in mass along the length rather than two point masses. In both cases though change one and you change the other. In the simple cases there will be an analytical solution, in the general case certainly not.
Good book by the way!