astronauts train for high accelerations they experience during launch by using a

Question

astronauts train for high accelerations they experience during launch by using a centrifuge that consists of a little room suspended at the end of a long boom that is rotated in a horizontal plane. if the total apparent effective gravitational field strength in the room is supposed to have a magnitude of 5g, and the distance between the room's center and the center of rotation is 10 m, about how long should it take the boom to rotate once? I got an answer of 2.8 seconds, but not the surest. Thank you

Explanation / Answer

r = 10m

we know that,
ay = g ( always )
and ax = v2 / r ( due to the rotation of the room )
and mag of the acceleration observed = 5g m/s2

therefore,
ax = sqrt ( (5g)2 - g2 )
ax = 4.89g m/s2

equating ay,
4.89g = v2 / r {g = 9.8 m/s2 }
48 * 10 = v2
v = 21.9 m/s

for 1 rotation,
t = (2 * pi * r) / v

t = 2.87 s

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