(Solved): 5) ( 20 points) The figure is an overhead view of a thin uniform rod of length 0.5m and mass M ro ...

5) ( 20 points) The figure is an overhead view of a thin uniform rod of length $$0.5\mathrm{m}$$ and mass $$M$$ rotating horizontally on a frictionless surface at angular speed $$20\mathrm{rad}/\mathrm{s}$$ about an axis through its center. A particle of mass $$M/3$$ initially attached to one end separates from the rod and travels along a path that is perpendicular to the rod at the instant of separation. If the particle's speed $$v_p$$ is $$2\mathrm{m}/\mathrm{s}$$ greater than the speed of rod's end just after separation, what is the value of $$v_p$$ ? (For a uniform thin rod $$I_{CM}=\frac{1}{12}M{L}^2$$ )