This problem requires that you have a toy gyroscope available. The purpose of this problem is to make as concrete as
possible the unusual motions of a gyroscope and their analysis in terms of fundamental principles. In all of the following
studies, the effects are most dramatic if you give the gyroscope as large a spin angular speed as possible.
(a) If you knew the spin angular speed of your gyroscope, you could predict the precession rate. Invent an appropriate
experimental technique and determine the spin angular speed approximately. Explain your experimental method and
your calculations. Then predict the corresponding precession rate, and compare with your measurement of the
precession rate. You will have to measure and estimate some properties of the gyroscope and how it is constructed.
(b) Make a quick measurement of the precession rate with the spin axis horizontal, then make another quick
measurement of the precession rate with the spin axis nearly vertical. (If you make quick measurements, friction on
the spin axis doesn't have much time to change the spin angular speed.) Repeat, this time with the spin axis initially
nearly vertical, then horizontal. Making all four of these measurements gives you some indication of how much the
spin unavoidably changes due to friction while you are quickly changing the angle. What do you conclude about the
dependence of the precession rate on the angle, assuming the same spin rate at these different angles? What is the
theoretical prediction for the dependence of the precession rate on angle (for the same spin rate)?