PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Five small spheres are attached to very light, rigid spokes so that each sphere occupies a vertex of a regular pentagon. Starting at the top vertex and proceeding clockwise, the masses are 0.10kg, 0.15kg, 0.20kg, 0.15kg, and 0.10kg. The pentagon has edge length 0.30m and lies flat in the horizontal plane. A vertical axis passes through the geometric center of the pentagon.
(a) Derive an expression, in terms of the edge length s, for the distance from the center of a regular pentagon to any of its vertices. Show your geometric reasoning.
(b) Using the result from part (a) and the given numerical values, compute the rotational inertia of the five-sphere system about the stated axis.
(c) Suppose the 0.20kg sphere were exchanged with one of the 0.10kg spheres, leaving the mass values unchanged but altering their locations. Without repeating the full calculation, discuss qualitatively and, if possible, quantitatively whether the rotational inertia would increase, decrease, or remain the same. Justify your conclusion.