Two rigid assemblies are constructed from identical
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
Two rigid assemblies are constructed from identical, slender metal rods of uniform density and identical total mass. In Assembly S, all the rods are joined end-to-end in a single straight line of length 2L. In Assembly L, the same rods are joined to form an L-shape consisting of two perpendicular line segments, each of length L, that meet at their ends.
For each assembly, the rotation axis is perpendicular to the plane of the rods and passes through the assembly’s own center of mass.
(1) Part 1: (a) Without numerical calculation, determine which assembly has the greater rotational inertia about its stated axis.
(2) Part 2: (b) Provide a qualitative argument that supports your conclusion in part (a), explicitly addressing how the average distance of mass from the axis differs between the two assemblies.
(3) Part 3: (c) Explain how symmetry (or lack thereof) in each assembly influences the way mass is distributed relative to the axis and, consequently, the rotational inertia.