PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
Five identical point masses, each of mass m, are attached rigidly to a very light frame that forms a square of side L. Four masses occupy the corners of the square, and the fifth mass is fixed at the geometric center of the square. Consider rotation axes that are all perpendicular to the plane of the square.
Answer parts (a)–(d).
(a) Express the rotational inertia of the system about an axis that passes through the center of the square.
(b) Express the rotational inertia about an axis that passes through the midpoint of one of the edges of the square.
(c) Express the rotational inertia about an axis that passes through one corner of the square.
(d) Rank the three axes of parts (a)–(c) in order of increasing rotational inertia and provide a clear justification for your ranking using quantitative comparisons.