A thin uniform cylindrical turntable of radius 2.3 m and mass 22 kg rotates in a horizontal plane with an initial angular speed of 7.3 rad/s. The turntable bearing is frictionless. A clump of clay of mass 8.7 kg is dropped onto the turntable and sticks at a point 1.5 m from the point of rotation. Treat the clay as a point mass. Find the angular speed of the clay and turntable. Answer in units of rad/s.

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?