An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11
ID: 1969529 • Letter: A
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 = 13.0 s, what is the magnitude of the astronaut's angular velocity?
rad/s
(b) When t = 13.0 s, what is the magnitude of the astronaut's linear speed?
m/s
(c) When t = 13.0 s, what is the magnitude of the astronaut's tangential acceleration?
m/s2
(d) When t = 13.0 s, what is the magnitude of the astronaut's radial acceleration?
m/s2
Explanation / Answer
Given The radius of the centrifuge R = 11 m The angular displacement is = 0.30t2 The angular velocity is = d/dt = 0.6t a) When t = 13.0 s, The magnitude of the astronaut's angular velocity is = (0.60)t = (0.60)(13.0 s) = 7.8 rad/s ---------------------------------------------------------------------------------- b) When t = 13.0 s, The magnitude of the astronaut's linear speed is v = R =(11 m)( 7.8 rad/s) = 85.8 m/s ---------------------------------------------------------------------------------------- c) When t = 13.0 s, The magnitude of the astronaut's tangential acceleration is at = R The angular acceleration is = d/dt = 0.60 rad/s2 at = ( 0.60 rad/s2)(11.0 m) at = ( 0.60 rad/s2)(11.0 m) =6.6 m/s2 ----------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------- d) When t = 13.0 s, The magnitude of the astronaut's radial acceleration a = R2 = (11.0 m)(7.8 rad/s)2 = 669.24 = 669.24Related Questions
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