Dancing top

A top of mass m=0.5 kgm=0.5~\mbox{kg} rotates with angular speed ω=350 rad/s\omega=350~\mbox{rad/s} around its axis which is tilted by a (constant) angle of θ=45\theta=45^{\circ} as shown in the figure. The moment of inertia with respect to the top's axis is I=2 gm2I=2 ~\mbox{g} \cdot\mbox{m}^{2} and the distance from the tip of the top to the center of mass is l=10 cm.l=10~\mbox{cm}. Determine the force of friction ff in Newtons acting on the tip of the top.

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