Try polar coordinates.Manwe Sulimo said:
I haven't worked in those for a while (I'm not sure I remember how to use them); but I'm fairly certain my teacher wants me to stick with x-y coordinates.SammyS said:
You've already tried trig substitutions. Think of polar coordinates as a form of trig substitution.Manwe Sulimo said:
You swapped ##M_x## and ##M_y##.Manwe Sulimo said:
Try starting like this:
A centroid is the geometric center of a two-dimensional shape or the center of mass of a three-dimensional object. It is often used to represent the average location of all points in a shape.
The centroid of a shape can be calculated by finding the mean of all the x-coordinates and the mean of all the y-coordinates of the points that make up the shape. This can be done using a formula or by graphically finding the intersection point of the medians of the shape.
Finding the centroid of a shape is important in many fields, including mathematics, physics, and engineering. It can help determine the center of mass and balance point of an object, as well as aid in the calculation of important values such as moment of inertia and center of pressure.
The number of points in a shape does not affect the calculation of the centroid. As long as the x and y coordinates of all the points are known, the centroid can be calculated regardless of the number of points in the shape.
Yes, the centroid can be outside of the shape. This can happen if the shape is irregular or has a concave section. In such cases, the centroid will still be the point of intersection of the medians, but it may fall outside of the shape.