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 x-axis and
the moment with respect to the y-axis. (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 x-axis and the distance the mass is from the y-axis. Our goal is to find the balancing point
in two directions – making sure it doesn’t rotate around the x-axis nor the y-axis. We will let My represent the moment
with respect to the y-axis and Mx represent the moment with respect to the x-axis.
For My we need to find out how far our mass (
Thus ) is from the y-axis which is given by the x-coordinate. The same logic holds for the moment with the x-axis: These moments are a measure of the distribution of the mass of the lamina with respect to the x and y-axis. We can
now use this informati...
View Full Document