Two solid disks, Disk A and Disk B, have the same radius R but different internal mass distributions.
• Disk A is a uniform disk of mass M (all mass spread evenly throughout).
• Disk B has the same total mass M but is constructed so nearly all of the mass is concentrated at the rim; it can be treated as a thin ring.
Both disks are mounted on separate, nearly friction-free axles through their centers. An external device will spin each disk from rest so that both experience the same constant angular acceleration α.
(a) Without performing a numerical calculation, predict which disk requires the larger net torque to achieve the stated angular acceleration. Provide a clear verbal explanation that references the physical characteristics of each disk.
(b) Using the standard expressions for rotational inertia of a uniform disk and of a thin ring, derive an algebraic expression for the ratio τAτB of the torques required for Disk B and Disk A, respectively.
(c) Let M=2.0kg and R=0.15m. Calculate the numerical value of the ratio τAτB. Express your answer to two significant figures.
(d) Explain, in terms of rotational inertia, why two objects with the same mass and radius can nonetheless demand different torques for the same angular acceleration.