Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 82

Speed in a loop. In Fig. 11.39, a solid, uniform sphere is released from rest at height \( h = 3R \) and rolls smoothly down a straight track and into a circular loop of radius \( R = 14.0 \text{ cm} \). The release height is sufficiently high that the sphere reaches the top of the loop with some speed \( v \). We repeat the demonstration by gradually increasing \( h \). At what rate \( dv/dh \) does \( v \) increase when \( h \) reaches the value \( 4R \)?