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. hint (a) if a human centrifuge has a radius of 5.15 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)

The relationship beween centripetal acceleration and angular speed is

where

is the angular speed

r is the radius of the circular path

Here we gave

is the centripetal acceleration

r = 5.15 m is the radius

Solving for , we find:

(b) 21.3 m/s

The relationship between the linear speed and the angular speed is

where

v is the linear speed

is the angular speed

r is the radius of the circular path

In this problem we have

r = 5.15 m

Solving the equation for v, we find

Explanation:

(a) Centripetal acceleration,

Radius, r = 5.15 m

Let is the angular speed. The relation between the angular speed and angular acceleration is given by :

(b) Let v is the linear speed of the person in the centrifuge have at this acceleration. It is given by :

v = 21.26 m/s

Hence, this is the required solution.

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