Physics Explanation

This simulation demonstrates the center of gravity (centroid) of a uniform disk with a circular hole cut out.

Problem Statement: From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The center of the hole is at a distance d = R/2 from the center of the original disk.

Solution: The center of gravity is located at R/6 from the original center, opposite to the center of the cut portion.

Mathematical Derivation:

Mass of original disk: M = σπR²

Mass of removed hole: m = σπ(R/2)² = M/4

Center of mass (x-coordinate): x_cm = (M×0 - m×d)/(M - m) = -(M/4 × R/2)/(3M/4) = -R/6