PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Three identical small spheres, each of mass 0.20kg, are rigidly connected by very light rods so that their centers form an isosceles right triangle of leg length 0.30m. The triangle lies in the xy-plane with its right angle at the origin and the legs along the positive x- and y-axes. Consider a vertical axis that passes through the origin and is perpendicular to the plane of the triangle.
(a) Describe qualitatively how the distance of each sphere from the axis affects its individual contribution to the system’s rotational inertia. Identify which spheres contribute equally and explain why.
(b) Without completing a full numerical calculation, predict whether moving the sphere initially at (0.30m,0) to (0.15m,0) will increase, decrease, or leave unchanged the system’s rotational inertia about the same axis. Provide a clear justification based on the definition of rotational inertia.
(c) State whether the given axis through the origin produces the minimum possible rotational inertia for this three-sphere system. Justify your answer by discussing the relationship between an axis and the system’s center of mass.