Liquid mirrors take on a parabolic shape due to the balance of gravitational and centrifugal forces during uniform angular motion. Centrifugal force, which increases with the square of the distance from the center, pushes the liquid outward along the x-axis, while gravity pulls it down along the y-axis. This unique interaction results in a surface where every point is equidistant from a focal point and a directrix, defining the parabolic shape. The discussion highlights the significance of these forces in determining the mirror's geometry. Understanding this principle is crucial for applications in optics and astronomy.
