An astronaut is being tested in a centrifuge. The centrifuge has a radius of 9 m

Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 9 m and, in starting, rotates according to ? = 0.30t2, where t is in seconds and ? is in radians.


(a) When t = 9.0 s, what is the magnitude of the astronaut's angular velocity?

(b) When t = 9.0 s, what is the magnitude of the astronaut's linear speed?

(c) When t = 9.0 s, what is the magnitude of the astronaut's tangential acceleration?

(d) When t = 9.0 s, what is the magnitude of the astronaut's radial acceleration?

Explanation / Answer

the equation for the acceleration and T is T = 1/2*at^2 , so 0.37 is 1/2*a --> a = 0.74 rad/s^2 ----- a) angular velocity w is w = a*t = 0.74*3.2 = 2.368 rad/s b) w = v/R --> v = w*R v = 2.368*5.9 = 13.97 m/s c) a = a/R --> a = a*R a = 0.74*5.9 = 4.366 m/s^2 d) a(r) = w^2R = 0.74^2*5.9 = 3.230 m/s^2

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