Serway & Jewett — Angular Momentum: Problem 42

Two children are playing on stools at a restaurant counter. Their feet do not reach the footrests, and the tops of the stools are free to rotate without friction on pedestals fixed to the floor. One of the children catches a tossed ball, in a process described by the equation \[(0.730 \text{ kg} \cdot \text{m}^2)(2.40 \hat{j} \text{ rad/s}) + (0.120 \text{ kg})(0.350 \hat{i} \text{ m}) \times (4.30 \hat{k} \text{ m/s}) = [0.730 \text{ kg} \cdot \text{m}^2 + (0.120 \text{ kg})(0.350 \text{ m})^2] \vec{\omega}\] (a) Solve the equation for the unknown \(\vec{\omega}\). (b) Complete the statement of the problem to which this equation applies. Your statement must include the given numerical information and specification of the unknown to be determined. (c) Could the equation equally well describe the other child throwing the ball? Explain your answer.