(Solved): please solve  both parts within 30-60 min  The figure shows an overhead view of a rectangu ...

The figure shows an overhead view of a rectangular slab that can spin like a merry-go-round about its center at \( O \). Also shown are seven paths along which wads of bubble gum can be thrown (all with the same speed and mass) to stick onto the stationary slab. (a) Rank the paths according to the angular speed that the slab (and gum) will have after the gum sticks, greatest first. \[ \begin{array}{l} 4>7>1>2<3=5>6 \\ 4=6>7>1>2=3=5 \\ 4>6>7>1>2=3=5 \\ 6>2=3=5>4>7>1 \end{array} \] (b) For which paths will the angular momentum of the slab (and gum) about \( \mathrm{O} \) be negative from the view of the figure? 1 2 3 4 5 6