2d center of 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 center in red (intersection of opposite side bisectors called the medians!), center of mass in blue shifted up and to the right due to linear mass density distribution increasing to the right with contours shown in the triangle.Stewart 8e 15.4. example 2Find the center of mass of the triangle below (vertices 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 so bounded on the top right by the hypotenuse 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) with density function 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 where the density contours are straight lines giving the most weight to the lower right vertex of the triangle compared to the geometric center of the triangle at the intersection of the 3 angle bisectors.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 like a small shift compared to the density plot over this triangle.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visualizing the center of mass, centroidIf we don't compare these numbers with the actual figure and our intuition, we are failing to take this seriously.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The centroid, for comparison is: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The centroid coordinates are the averages of the vertex coordinates, or the intersection of the three "medians" which are the line segments from each vertex to the midpoint of the opposite side. 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geometric center (centroid) is at the intersection of the 3 angle bisectors (where else could it be?), where the red dot is.Because the density grows in the direction of the increasing contours, the center of mass is shifted upward and to the right from the centroid (green) . My wild guess would have been that the shift would have been perpendicular to the contours and then down slightly, but clearly the situation is more complicated than that guess. The center of mass is in fact above the normal line instead of below it. You can see better by zooming into the location of the two points.You can safely ignore the remaining interesting examples.Stewart 8e 15.4.5 more interesting triangleStewart 8e 15.5.5 density function 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 over this triangle with vertices 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 (so with lower boundary 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 and upper boundary 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) where the density contours are straight lines parallel to the farthest side of the triangle from the origin. This gives more weight to that edge of the triangle compared to the geometric center of the triangle at the intersection of the 3 angle bisectors, so it should push the center of gravity up and towards the upper right side of the triangle, up and to the right from the centroid.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 the center of mass, centroidIf we don't compare these numbers with the actual figure and our intuition, we are failing to take this seriously.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The centroid, for comparison is: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 geometric center (centroid) is at the intersection of the 3 angle bisectors (where else could it be?), where the green dot is.Because the density grows in the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn direction, the center of mass is shifted upward and to the right from the centroid (green) as we guessed it might.Stewart 8e 15.4.11 quarter circle with density proportional to distance from x axisHere is the centroid. The center of mass with a density proportional to the distance from the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn axis (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) would be shifted up, and slightly sideways, but which way is not clear in advance.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From a hand calculation the centroid has this value for both coordinates: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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Seems to make sense, there is more mass in the upper left corner of the pie slice, so the blue dot is shifted up and to the left with respect to the geometric center.Stewart 6e 15.4.7 exponential boundary regionFind the center of mass of this region if the density function is 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. This will shift the centroid up and to the right because the upper right corner is weighted more.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 does this compare to the centroid?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quarter disk with density proportional to distance from originHere is the centroid. The center of mass with a density proportional to the distance from the 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) would be shifted out along the bisector of the quadrant, because of the symmetry about that line for both the region and the density function.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Seems to make sense, there is more mass in the upper left corner of the pie slice, so the blue dot is shifted up and to the left with respect to the geometric center.semicircle disk with density proportional to distance from originHere is the centroid. The center of mass with a density proportional to the distance from the 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) would be shifted out along the bisector of the quadrant.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 to make sense, there is more mass in the upper part of the disk, so the blue dot is shifted up with respect to the geometric center.
If we wanted to plot the density function over the circle, we would do this. But to show the difference of these two plots I insert a 2. In the first setup it plots r versus z, in the second z versus r. We will get to this when we study cylindrical coordinates.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NjczMzU1Nzk2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjIiIhLCQqJCUjUGlHISIiIyIiJSIiJEYlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzQyMjUyWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCQqJCUjUGlHISIiIyIiJSIiJEYnRiU=TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzQzMjA0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIrOT04V1UhIzVGJ0YlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzQzNzQ4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjIyIiJCIiKSwkJSNQaUcjRigiIztGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzQ0ODM2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIrKysrXVAhIzUkIitFaVshKmVGKUYlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzQ1MTA4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjKiYsJiMhIiIiIiUiIiItSSRleHBHNiQlKnByb3RlY3RlZEclKF9zeXNsaWJHNiMiIiMjRixGK0YqLCYjRiwiIilGLEYtRjZGLComRihGKiwmI0YqIiIqRiwtRi42IyIiJCNGLEY7RixGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzM5MzgwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIrQ2s8bGwhIzUkIit4WmxGOCEiKkYlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzQwMTk2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjKiQsJiEiIiIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkRyUoX3N5c2xpYkc2I0YqRipGKSomRihGKSwmI0YpIiIlRiotRiw2IyIiIyNGKkY0RipGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzQxMjg0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIrcXF3PmUhIzUkIit2WHEmSCpGKUYlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzMzOTI0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCQqJCUjUGlHISIiIyIiJSIiJEYnRiU=TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzM0NzQwWColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIrOT04V1UhIzVGJ0YlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzM1Mjg0WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjLCQqJCUjUGlHISIiIyIiJCIiI0YnRiU=TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzM2NTA4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIrI0hbWXglISM1RidGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzI5MTQ4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIiIUYoJCIrOT04V1UhIzVGJQ==TTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzI5ODI4WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjIiIhLCQqJCUjUGlHISIiIyIiJCIiI0YlTTdSMApJQVJUQUJMRV9TQVZFLzM2ODkzNDg5Nzk3NzAzNzMwMjM2WColKWFueXRoaW5nRzYiNiJbZ2whIyUhISEiIyIjJCIiIUYoJCIrI0hbWXglISM1RiU=