A spaceship in outer space has a gyroscope within it used for rotation and stabilization. The moment of inertia of the gyroscope isIg = 24.5 kg · m2about the axis of the gyroscope, and the moment of inertia of the rest of the spaceship isIs = 5.00 ✕ 105 kg · m2about the same axis. Initially both the spaceship and gyroscope are not rotating. The gyroscope is then switched on and it nearly instantly starts rotating at an angular speed of 120 rad/s. How long (in s) should the gyroscope operate at this speed in order to change the spaceship's orientation by 40.0°?

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?