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$4$

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Problem $3$

A top is spun on the floor such that the top precesses around in a circular motion. The top has a mass of $m=0\mathrm{.}1kg$ and it's center of mass is located a distance of $r_{cm}=0\mathrm{.}03m$ above the tip. The top is thrown with an angular velocity of $=250ra\frac{d}{s}.$

a$)$ Calculate the torque felt by the top if it leans an angle $.$

b$)$ Find the direction of the torque felt on the top at the angle shown below.

c$)$ If the top precesses a full revolution in $t=0\mathrm{.}8$ seconds, find the moment of inertia of the top.

$\backslash$table$[[$Variable$,$Type,Data$/$Info$],[$MoI$,$float,$1\mathrm{.}497329730150243$ e$-05],[$g$,$float,$9\mathrm{.}8],[$m$,$float,$0\mathrm{.}1],[$omega$,$in't,$250],[$omegatheta$,$float,$7\mathrm{.}8539815],[$r$,$float,$0\mathrm{.}03]]$