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21_gyroscope

21_gyroscope - INDIANA UNIVERSITY DEPARTMENT OF PHYSICS...

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INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY Laboratory #21: Gyroscope Goal: Study rotation of a symmetrical, rigid body. Investigate moments of inertia, and the phenomena of precession and nutation. Equipment: Ealing (#13-220) 4" ball air bearing gyroscope, motorized driver, frequency- calibrated stroboscobe, stop watch. (A) Introduction A detailed discussion of the equations of motion of a rigid body is given in [GOL80]. The most concise treatment of a force-free spinning top I have found is [LAN59]. Here we give only the most important definitions and results. The top in our case is a steel sphere with a shaft. The sphere sits in a low-friction air bearing, such that the center of the sphere (FP in fig 2) is stationary. The symmetry axis is along the shaft (direction 3 in fig.3). The moment of inertia around that axis is I 3 , and I 1 around an axis through FP and perpendicular to the symmetry axis. Since the shaft has less mass than the steel bore in which it is located, the center of gravity (CG in fig.2) is displaced with respect to FP. By adding a compensation mass m 1 to the shaft, the center of gravity can be made to coincide with FP: the gyroscope then is "force-free".
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