A thin metal disk of mass m = 2 x 10^-3 kg and radius R = 2.20 cm is attached at its center to a long fiber. When the disk is turned from the relaxed state through a small angle theta, the torque exerted by the fiber on the disk is proportional to theta:
T= -k*theta The constant of proportionality k is called the "torsional constant" and is a property of the fiber.
a). Find an expression for the torsional constant k in terms of the moment of inertia I of the disk and the angular frequency omega of small, free oscillations. Express your answer in terms of some or all of the variables I and omega.
b). The disk, when twisted and released, oscillates with a period T of 1.00 s. Find the torsional constant k of the fiber.
Step by step solution provided.