An astronaut is being tested in a centrifuge. The centrifuge has a radius of 12

Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 12 m and, in starting, rotates according to = 0.30t2, where t is in seconds and is in radians.

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 12 m and, in starting, rotates according to 0 0.30t2, where t is in seconds and 0 is in radians. (a) when t 4.0 s, what is the magnitude of the astronaut's angular velocity? rad/s (b) When t 4.0 s, what is the magnitude of the astronaut's linear speed? m/s (c) When t 4.0 s, what is the magnitude of the astronaut's tangential acceleration? m/s (d) When t 4.0 s, what is the magnitude of the astronaut's radial acceleration? m/s

Explanation / Answer

angular velocity = rate of change in displacement

w = 2*0.3*t = 0.6*t

(a)

t = 4

angular velocity w = 0.6*4 = 2.4 rad/s <<<<<-------answer

(b)

linear speed v = r*w = 12*2.4 = 28.8 m/s   <<<<<-------answer

(c)

angular acceleration alpha = dw/dt = 0.6 rad/s^2

tangential acceleration a = r*alpha = 12*0.6 = 7.2 m/s^2 <<<<-----answer

(d)

radial acceleration a = v^2/r = 28.8^2/12 = 69.12 m/s^2 <<<<<<-------answer

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