Problem $5$: A girl sits snugly inside a large tire such that both the girl and tire have a total weight of $185$ lb $,$ a center of mass at $G,$ and a radius of gyration $k_G=1\mathrm{.}65$ ft about $G.$ If the tire rolls freely down the incline, determine the normal and frictional forces it exerts on the ground when it is in the position shown and has an angular velocity of $6ra\frac{d}{s}.$ Assume that the tire does not slip as it rolls.