Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness.

(a)If a human centrifuge has a radius of 4.64 m, what angular speed (in rad/s) results in a centripetal acceleration of 9g?

rad/s
(b)What linear speed (in m/s) would a person in the centrifuge have at this acceleration?

m/s

a) 4.36 rad/s

b) 20.2 m/s

Explanation:

a)

For an object in uniform circular motion, the centripetal acceleration is related to the angular speed by the equation

where

a is the centripetal acceleration

is the angular speed

r is the radius of the circle

For the person in this problem we have:

is the centripetal acceleration

r = 4.64 m is the radius of the trajectory

Solving for , we find the required angular speed to produce this centripetal acceleration:

b)

For a uniform circular motion, the relationship between angular speed and linear speed is

where

v is the linear  speed

is the angular speed

r is the radius of the circle

For the person in this problem we have:

is the angular speed

r = 4.64 m is the radius of the circle

Therefore, the linear speed is:

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