Centriptial Accleration

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A centrifuge is used for training astronauts to withstand large accelerations. It consists of a chamber (in which the astronaut sits) that is fixed to the end of a long horizontal and rigid pole. The arrangement is rotated about an axis perpendicular to the pole’s free end. Such a centrifuge starts from rest and has an angular acceleration of 0.25 rad/s2. The chamber is 3.0 m from the axis of rotation. Through what angle has the device rotated when the centripetal acceleration experienced by an astronaut in the chamber is four times the acceleration due to the earth’s gravity?


i know that the angle= tan^-1 (a/w) to calculate a is a=(ac^2+at^2)^(1/2) but from this point i don't know what to do .
 

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jamesrc
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I may be over-simplifying here, but doesn't the problem only ask you to consider the centripetal acceleration? If so, I think the tangential acceleration is irrelevant; simply set rω^2 = 4g and then find the angle this occurs at due to the constant acceleration, α of the centrifuge (Δ(ω^2;) = 2*α*Δθ).
 

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