Unformatted text preview: ted on an airplane is
very important since it affects the stability of the plane.
In order to find this balancing point we need to first find the First Moments: the moment with respect to the xaxis and
the moment with respect to the yaxis. (remember moments are used to solve problems of balance and rotation)
Again, we have already approached this problem in 101B with the 1D case: First Moment =
where x1 is the distance from the origin and m1 is the point mass. In 2D, we have two moments since we have the
distance the mass is from the xaxis and the distance the mass is from the yaxis. Our goal is to find the balancing point
in two directions – making sure it doesn’t rotate around the xaxis nor the yaxis. We will let My represent the moment
with respect to the yaxis and Mx represent the moment with respect to the xaxis.
For My we need to find out how far our mass (
Thus ) is from the yaxis which is given by the xcoordinate. The same logic holds for the moment with the xaxis: These moments are a measure of the distribution of the mass of the lamina with respect to the x and yaxis. We can
now use this informati...
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 Spring '08
 Loukianoff,V
 Calculus, Integrals, Jacobian, coordinates

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