Serway & Jewett — Oscillatory Motion: Problem 29

You have scored a part-time job at a company that makes small probes to be released from satellites to study the very thin atmosphere at the location of satellite orbits. In order to keep the probes in a proper orientation in space, they will be spun about their axis before being released. It is important to know the moment of inertia of the odd-shaped probe. Your boss asks you to measure its moment of inertia. You set up a system such as that in Figure 15.18, modifying it by adding a very light frame (Fig. P15.29) into which you can place objects, centering them on the disk. The frame is attached at the edges of the disk. The support wire is rigidly connected to the top of the frame so that it does not interfere with the objects you wish to place on the disk. The disk is of mass \(M = 5.25\text{ kg}\) and has a radius of \(R = 25.8\text{ cm}\). You rotate the empty disk from its equilibrium position and let it operate as a torsional pendulum. You carefully measure its period of oscillation to be \(T_{\text{empty}} = 10.8\text{ s}\). You then place the probe on the disk and adjust its position until the disk hangs exactly horizontal, so you know that the center of mass of the probe is directly over the center of the disk. You rotate the loaded disk from its equilibrium position and let it operate as a torsional pendulum. (a) You carefully measure its period of oscillation to be \(T_{\text{loaded}} = 18.7\text{ s}\), and from this result you determine the moment of inertia of the probe about its center of mass. (b) When you present your results to your supervisor, she asks you about the moment of inertia of the frame you built. You go back to your desk and think about it. When you consider that the frame has some moment of inertia, is the value calculated in part (a) too high or too low?