A professor sits at rest on a stool that can rotate without friction. The rotational inertia of the professor-stool system is 4.1 kg · m2 . A student tosses a 1.5-kg mass with a speed of 2.7 m/s to the professor, who catches it at a distance of 0.40 m from the axis of rotation. What is the resulting angular speed of the professor and the stool? (Assume that when the professor catches the mass, their arm is extended along a line radially outward from the axis of rotation, and the velocity of the mass is perpendicular to that line.)

Wo small variable-thrust jets are actuated to keep the spacecraft angular velocity about the z-axis constant at ? 0 = 1.16 rad/s as the two telescoping booms are extended from r1 = 1.18 m to r2 = 4.69 m at a constant rate over a period of 124 seconds. the small 19-kg experiment modules at the ends of the booms may be treated as particles, and the mass of the rigid booms is negligible. determine the necessary thrust t for each jet as a function of time where t = 0 is the time when the telescoping action is begun. after you have the general expression for t, answer the questions. show work.