Chapter 10, Problem 80P

(I) A rolling hall slows down because the normal force does not pass exactly through the CM of the ball, but passes in front of the CM. Using Fig. 10–41, show that the torque resulting from the normal force ( ${\tau }_{\text{N}}=\mathcal{l}{F}_{\text{N}}$ in Fig. 10–41) is $\frac{7}{5}$ of that due to the frictional force, ${\tau }_{\text{fr}}=r_{0}F$ where r₀ is the ball’s radius; that is, show that ${\tau }_N=\frac{7}{5}{\tau }_{\text{fr}}$.