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Unformatted text preview: Ph-507. Homework 6 (due: Wednesday, March 23).PROBLEM 6-1 (5 pts)Right after a symmetric spinning top (in gravity) has been kicked by a nutty professor, the nutation and precessionrates had values= 0and=, respectively. The orientation of its symmetry axis was given bycos=p,and= 0. Assuming that the spinning is fast, determine the sets of the initial conditions(, p), for which (a)the direction of precession is constant, (b) there is no net precession. Express the results in terms of the followingparameters of the top: frequency of its free oscillations'=pmgl/I, spinning rate'kand "aspect ratio"=Ik/I.PROBLEM 6-2 (3 pts.)A uniform hollow sphere of radiusRcan freely rotate in all directions about certain point on its surface. Thesphere is in the presence of Earth gravityg. While at the equilibrium position, it is set to spinning about its verticalaxis,.with angular velocity'.If you give the sphere a slight kick, the osillations will start and the plane of theseoscillations will be rotating (i.e. precessing). Find the precession rate.PROBLEM 6-3 (4 pts.)Estimate the minimal speed with which you would have to ride a regular bicycle on the Moon (wearing a lightspace suit). The "ride" means a steady motion with no need of active balancing (e.g. by moving your body). Thegravitational acceleration on the Moon isgm1.6m/s2PROBLEM 6-4 (3 pts)Lagrangian of a particle in attractive Coulomb potential, in the presence of a magnetic...
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