Dancing top

A top of mass \(m=0.5~\mbox{kg}\) rotates with angular speed \(\omega=350~\mbox{rad/s}\) around its axis which is tilted by a (constant) angle of \(\theta=45^{\circ}\) as shown in the figure. The moment of inertia with respect to the top's axis is \(I=2 ~\mbox{g} \cdot\mbox{m}^{2}\) and the distance from the tip of the top to the center of mass is \(l=10~\mbox{cm}.\) Determine the force of friction \(f\) in Newtons acting on the tip of the top.

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