A planetary space probe is in the shape of a cylinder. To protect it from heat on one side (from the Sun€™s rays), operators on the Earth put it into a €œbarbecue mode,€ that is, they set it rotating about its long axis. To do this, they fire four small rockets mounted tangentially as shown in Fig. 8.51 (the probe is shown coming toward you). The object is to get the probe to rotate completely once every 30 s, starting from no rotation at all. They wish to do this by firing all four rockets for a certain length of time. Each rocket can exert a thrust of 50.0 N. Assume the probe is a uniform solid cylinder with a radius of 2.50 m and a mass of 1000 kg and neglect the mass of each rocket engine. Determine the amount of time the rockets need to be fired.