As their booster rockets separate, Space Shuttle astronautstypically feel accele

Question

As their booster rockets separate, Space Shuttle astronautstypically feel accelerations up to 3g, where g =9.80 m/s2. In their training, astronauts ride in adevice where they experience such an acceleration as a centripetalacceleration. Specifically, the astronaut is fastened securely atthe end of a mechanical arm, which then turns at constant speed ina horizontal circle. Determine the rotation rate, in revolutionsper second, required to give an astronaut a centripetalacceleration of 2.89g whilein circular motion with radius 9.77m.
1 revolutions persecond

Explanation / Answer

F = m a = m v2/r = m 2r So a = 2r So, 2.89 * g =2.89 * 9.8 m/s^2 = 2 *9.77 Solve for omega and you're done

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