An astronaut is being tested in a centrifuge. The centrifuge has a radius of 10

Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 10 m and, in starting, rotates according to ? = 0.30t2, where t is in seconds and ? is in radians. (a) When t = 15.0 s, what is the magnitude of the astronaut's angular velocity? (b) When t = 15.0 s, what is the magnitude of the astronaut's linear speed? (c) When t = 15.0 s, what is the magnitude of the astronaut's tangential acceleration?(d) When t = 15.0 s, what is the magnitude of the astronaut's radial acceleration?

Explanation / Answer

angular velocity=d?/dt=2*0.30t=0.6t at t=15 sec angular velocity=0.6*15=9 rad/sec linear speed=2*9*10=180 m/sec radial acceleration=d^2?/dt^2 =0.6 rad/sec^2

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