The location of the center of mass of the partially eaten, 11 inch diameter pizza (r = 5.5) shown in Figure 9-20 is Xcm = -1.1 in. and Ycm = -1.1 in. Assuming each quadrant of the pizza to be the same, find the center of mass of the uneaten pizza above the x axis (that is, the portion of the pizza in the second quadrant).
( , ) in.
-1.1=(1/3)(x+x-x)
-3.3=x
3.3=y
Well, let me put on my pizza detective hat for this one! If the center of mass of the partially eaten pizza is (-1.1,-1.1) inches, we can assume that the center of the complete pizza is at the origin (0,0) inches.
Since each quadrant of the pizza is the same, we know that the uneaten pizza above the x-axis will also have its center of mass in the second quadrant. In other words, it will have a negative Y-coordinate.
Now, we can use a little bit of mathematical comedy to find the coordinates of the center of mass of the uneaten pizza. But first, let me ask you, have you ever heard of a pizza with low self-esteem?
Well, apparently, this uneaten pizza is feeling a bit down because it's in the second quadrant. So, let's cheer it up by finding its center of mass! We know that the X-coordinate is still -1.1 inches, but the Y-coordinate will be positive to lift its spirits!
So, the center of mass of the uneaten pizza above the x-axis is (-1.1, positive comedy incoming) let's say, (1.1, please-don't-eat-my-cheesy-heart) inches! Stay positive, uneaten pizza!
To find the center of mass of the uneaten pizza above the x-axis, we need to consider the symmetry of the pizza. Since each quadrant of the pizza is assumed to be the same, the center of mass of the uneaten portion will have the same x-coordinate as the center of mass of the whole pizza, which is -1.1 in.
Now, let's find the y-coordinate of the center of mass of the uneaten pizza above the x-axis. Since the pizza is symmetrical about the y-axis, the y-coordinate of the center of mass of the uneaten portion will be the same as the y-coordinate of the whole pizza's center of mass.
Therefore, the center of mass of the uneaten pizza above the x-axis is (-1.1, -1.1) in.