HRWP8p297

Problem 8 contains the relation, r << R, which means "r is much less than R" (see page A-9 for meanings of symbols). That means that you can approximate the smaller object as a point mass in relation to the larger object. In problem 8, this means that you can assume that the ball's center-of-mass rises 2R from the bottom of the loop to the top. In reality, the center-of-mass only rises 2R-2r because the CM is at r at the bottom of the loop and is r below the top of the loop when it is at the top.