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Question
Part of riding a bicycle involves leaning at the correct angle when making a turn, as seen in Figure 6.36. To be stable, the force exerted by the ground must be on a line going through the center of gravity. The force on the bicycle wheel can be resolved into two perpendicular components—friction parallel to the road (this must supply the centripetal force), and the vertical normal force (which must equal the system's weight). (a) Show that $\theta$ (as defined in the figure) is related to the speed $v$ and radius of curvature $r$ of the turn in the same way as for an ideally banked roadway—that is, $\theta = \tan^-1{\dfrac{v^2}{rg}}$ (b) Calculate $\theta$ for a 12.0 m/s turn of radius 30.0 m (as in a race).
Question Image
1. see video for derivation
2. $26.1^\circ$
Solution Video