Problem 1.1: A disk of mass 2 kg and radius .5 m is hung from a wire, then rotated a small angle such that it engages in torsional oscillation. The period of oscillation is measured at 2 seconds. Given that the moment of inertia of a disk is given by I =

, find the torsional constant, κ, of the wire. [Solution]

Problem 1.2: The disk from problem 1 is replaced with an object of unknown mass and shape, and rotated such that it engages in torsional oscillation. The period of oscillation is observed to be 4 seconds. Find the moment of inertia of the object. [Solution]

Problem 1.3: A pendulum of length L is displaced an angle θ, and is observed to have a period of 4 seconds. The string is then cut in half, and displaced to the same angle θ. How does this effect the period of oscillation? [Solution]

Problem 1.4: A pendulum is commonly used to calculate the acceleration due to gravity at various points around the earth. Often areas with low acceleration indicate a cavity in the earth in the area, many times filled with petroleum. An oil prospector uses a pendulum of length 1 meter, and observes it to oscillate with a period of 2 seconds. What is the acceleration due to gravity at this point? [Solution]

Problem 1.5: What is the angular velocity of a particle moving in uniform circular motion that has the same period as a mass of 2 kg on a spring with constant 8 N/m? [Solution]