5. C9.1 Consider the spinning top .suppose that it is set spinning at 35 rev/s a

Question

5. C9.1
Consider the spinning top .suppose that it is set spinning at 35 rev/s and initially its spin axis is held fixed at an angle theta0=60. the axis is then released and the top starts to process as well as to notate between two limiting polar angles theta1 and theta2
A) calculate the two limits theta1 and theta2
B) Estimate the period of nutation analytically.
(Make approximation, where necessary, in the expression given in the text for U dot and then integrate.)
C) Estimate the average period of precession analytically. (Make approximations in the expression for PHIdot given in the text.)
D) find costheta(t) and PHI(t)by numerically integrating the appropriate equations of motion over a time interval somewhat greater than one notational period
E) letting the function x(t)=costheta1-costheta(t) ,where theta1 is the smaller of the two angular limits of the notational motion ,plot x(t)versus PHI(t)over the same time interval as in part (d).from this plot ,calculate both the notational period and the average processional period .compare the results obtained from the plot with those from parts (a),(b) and (c)

Explanation / Answer

Here,w = 35 rev/s = 35 * 2pi rad/s theta = 60o = 60 * pi/180 radians we know that theta = wt where t is time or t = theta/w

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