Question

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

Answer 1

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

$a=\omega^2 r$

where

a is the centripetal acceleration

$\omega$ is the angular speed

r is the radius of the circle

For the person in this problem we have:

$a=9g=88.2 m/s^2$ is the centripetal acceleration

r = 4.64 m is the radius of the trajectory

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

$\omega=\sqrt{\frac{a}{r}}=\sqrt{\frac{88.2}{4.64}}=4.36 rad/s$

b)

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

$v=\omega r$

where

v is the linear  speed

$\omega$ is the angular speed

r is the radius of the circle

For the person in this problem we have:

$\omega=4.36 rad/s$ is the angular speed

r = 4.64 m is the radius of the circle

Therefore, the linear speed is:

$v=(4.36)(4.64)=20.2 m/s$