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 6 = 0.30t2, where t is in seconds and 9 is in radians. When t = 12.0 s, what is the magnitude of the astronaut's angular velocity? rad/s When t = 12.0 s, what is the magnitude of the astronaut's linear speed? m/s When t = 12.0 s, what is the magnitude of the astronaut's tangential acceleration? m/s^2 When t = 12.0 s, what is the magnitude of the astronaut's radial acceleration? m/s^2 the Linear and Angular Variables

Explanation / Answer

here,

radius of cntrifuge, r = 10 m

theta = 0.30t^2

Part A:
Angular velocity, w = d(theta)/dt = 0.30*2 *t = 0.60*t

at time, t = 12 s, w = 0.60 * 12 = 7.2 rad/s

Part B:
Since linear speed, v = w*r = 7.2 * 10 = 72 m/s

Part C:
Since, tangential Acceleration, aplha = dw/dt = 0.60 rad/s^2

Part D:
Radial acceleration, a = alpha * r = 0.60 * 10 = 6 m/s^2

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