Halliday, Resnick & Walker — Rotation: Problem Problem_90

Ballet en pointe. When a ballerina stands en pointe, her weight is supported by only the tips of her toes in a rigid toe box in her shoes (Fig. 10.38a). Her center of mass must be directly above the toes, but that positioning is difficult to maintain. To see how her height affects the balancing, treat her as a uniform rod of length \(L\) that is balanced vertically on one end (Fig. 10.38b). (a) What is the angular acceleration \(\alpha\) around that end if the rod leans by a small angle \(\theta\) from the vertical? (b) For a given angle, is \(\alpha\) larger or smaller for a taller ballerina? (Does a taller ballerina have less time or more time to correct an imbalance?)