PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Three identical point masses, each of mass m, are rigidly connected by very light rods to form an isosceles triangle whose equal sides each have length a and whose base has length b<2a. Label the apex mass at the top of the triangle as point P and the two base masses as points Q and R. Consider the following two rotation axes, each perpendicular to the plane of the triangle:
Axis 1: passes through point P.
Axis 2: passes through the center of mass of the three-mass system.
Answer all parts symbolically in terms of m, a, and b, showing each logical step.
(a) Derive an algebraic expression for the rotational inertia of the system about Axis 1.
(b) Derive an algebraic expression for the rotational inertia of the system about Axis 2.
(c) Compare the two results and state which axis yields the smaller rotational inertia, explaining the physical significance of your finding.
(d) Suppose the triangle is "stretched" so that the apex mass P is moved directly upward, increasing the equal side length a while b remains fixed. Qualitatively describe how this change affects the rotational inertia about each axis and justify your reasoning.