Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 64

64 A ballerina begins a tour jeté (Fig. 11-19a) with angular speed \(\omega_i\) and a rotational inertia consisting of two parts: \(I_{\text{leg}} = 1.36 \text{ kg} \cdot \text{m}^2\) for her leg extended outward at angle \(\theta = 90.0^\circ\) to her body and \(I_{\text{trunk}} = 0.620 \text{ kg} \cdot \text{m}^2\) for the rest of her body (primarily her trunk). Near her maximum height she holds both legs at angle \(\theta = 30.0^\circ\) to her body and has angular speed \(\omega_f\) (Fig. 11-19b). Assuming that \(I_{\text{trunk}}\) has not changed, what is the ratio \(\omega_f / \omega_i\)?