A space station of mass 4.5 × 104-kg is to be constructed in the shape of a thin annular cylinder (or ring). The inner radius of the annular cylinder is 100-m, and the outer radius (and location of the floor) is 105-m. Artificial gravity equivalent to free-fall acceleration, g, will be implemented by rotating the hoop through its central axis. Once the space station is constructed, two small rockets attached tangentially to opposite points on the hoop will be fired to set the space station into rotation. If each of the rockets produces a thrust of 105-N, for what time interval, in minutes, must they be fired to achieve the desired rotation? Assume the mass of the space station will be distributed uniformly within the annular ring.
t = ( ) minutes