As their booster rockets separate, Space Shuttle astronauts typically feel accel

Question

As their booster rockets separate, Space Shuttle astronauts typically feel accelerations up to 3g, where g = 9.80 m/s^2. In their training, astronauts ride in a device where they experience such an acceleration as a centripetal acceleration. Specifically, the astronaut is fastened securely at the end of a mechanical arm, which then turns at constant speed in a horizontal circle. Determine the rotation rate, in revolutions per second, required to give an astronaut a centripetal acceleration of 3.15g while in circular motion with radius 9.17 m.

Explanation / Answer

ac = 3.15 g, g = 9.8 m/s^2 ,r = 9.17 m

ac = rw^2

3.15*9.8 = 9.17*w^2

w = 1.835 rad/s

w = 1.835/(2*3.14)

w = 0.292 rev/s

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