An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11

Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11 m and, in starting, rotates according to ? = 0.30t2, where t is in seconds and ? is in radians. (a) When t = 5.0 s, what is the magnitude of the astronaut's angular velocity? (b) When t = 5.0 s, what is the magnitude of the astronaut's linear speed? (c) When t = 5.0 s, what is the magnitude of the astronaut's tangential acceleration? (d) When t = 5.0 s, what is the magnitude of the astronaut's radial acceleration? Also In the figure below, wheel A of radius rA = 14 cm is coupled by belt B to wheel C of radius rC = 24 cm. The angular speed of wheel A is increased from rest at a constant rate of 1.6 rad/s2. Find the time needed for wheel C to reach an angular speed of 120 rev/min, assuming the belt does not slip. (the figure depicts a small wheel(A) and a large wheel(C). They share a belt labeled B)

Explanation / Answer

a. w = 3 rad s^-1......... b. v = 33m/s....... c. a tan =6.6 m/s^2.............. d. a rad= 99m/s^2.................. e. rA*wA=rC*wC=====> wA = 21.5 rad s^-1.......... time t = wA/ alpha = 21.5/1.6 13.45 sec.........

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