Question

As their booster rockets separate, Space Shuttle astronauts typically feel accelerations up to 3g, where g = 9.80 m/s². 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 2.97g while in circular motion with radius 9.55 m.
revolutions per second

Answer 1

Answer 2

29.4 m/s/s=v^2*9.74 m

29.4/9.74=v^2

w^2= 3.01848 radians/sec

w= 1.7374

because there is 2*pi radians per revolution, then it comes out to;

1.7374 radians/sec* 1 rev/(2*pi rad)= 0.2765 rev/sec

Answer 3

2.97g = 29.13 m/s^2

so centripetal accn. of 2.97g = 29.13 m/s^2 = $\omega^2R$
$\Rightarrow \omega = \sqrt{\frac{2.97g}{R}} = \sqrt{\frac{29.13}{9.55}} = 1.74 \ rad/s$

so, rotation rate in rev/sec = 0.2769 rad/s