Calculating Angular Velocity in a Centrifuge: Astronaut Test Problem

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To calculate the astronaut's angular velocity in the centrifuge, the equation for angular displacement is given as θ(t) = 0.21t². The correct angular velocity is derived from the derivative of this equation, resulting in ω(t) = 0.42t. At t = 5.0 seconds, substituting into the equation yields an angular velocity of 2.1 radians per second. The radius of the centrifuge is mentioned but is not necessary for calculating angular velocity in this context. Understanding the relationship between angular displacement and angular velocity is crucial for solving similar problems.
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An astronaut is being tested in a centrifuge. The centrifuge has a radius of 8.5 m and in starting, rotates according to theta= .21t^2, where t in seconds give theta in radians. When t=5.0 s, what are the astronaut's angular velocity?

I did .21(5.0)^2 / 5, to get angular velocity, but it was wrong. Can someone steer me in the right direction?
 
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I have no idea what equation that is that your using.

\theta(t) = .21t^2

\omega(t) = .42t

by the relationship \omega(t) = d\theta(t)/dt
 
Last edited:
Why do they give the radius,if they don't ask for the tangential speed...?:bugeye:

Daniel.
 
Probably needs help on just one part of the problem.
 
Ok I see what I was doing. Thanks so much
 

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