Calc 2, Lec 16C: How to Find the Center of Mass (Centroid) of a Lamina with Constant Density

A semi-circular lamina (thin plate) has constant density δ (mass per unit area). How can we find its center of mass using calculus? Since the density is constant, this is the same as the centroid of the semicircle. First, we can use symmetry to say that, if the lamina is centered on the y-axis, the x-coordinate of the center of mass is x̄=0. The y-coordinate of the center of mass is M/m, where m is the mass m=∫dm= ∫δL(y)dy (L(y)dy is the cross sectional area element) and M is the moment about the x-axis M=∫ydm= ∫δyL(y)dy. We need to use the formula for a circle to find L(y).

Links and resources
===============================

AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.