00:01
In this problem, we're asked to determine the polar area moment of the shaded region that is a square with some half -circular holes cut in it.
00:12
And we want to find their polar area moment about the x and y axes, which are or have an origin down here.
00:20
So in this problem, what we're going to do is we're going to go, well, it's easy to find the polar area moment or the area moment.
00:30
Sorry, of this square about this point.
00:34
So we'll do that.
00:34
And then we'll find the area moments of these two cutouts about this point and subtract those area moments from the area moment here.
00:47
So the area moment of this guy, since it has a width and a height of 4a from at its corner, is one -third, four -a to the fourth power, or 256 over 3a squared.
01:04
And that's the same for x and y.
01:07
Obviously there's symmetry about that axis.
01:12
And we can now get to the more difficult part of finding the area moments of these cutouts about this point.
01:25
So we found in the previous problem we found the area moment of a half circle or a semicircle about its centroid and that was pi over 8.
01:36
Minus 8 over 9 pi times a to the fourth...