An astronaut is being tested in a centrifuge The centrifuge

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11.5 m and, in starting, rotates according to = 0.17t², where t is in seconds and is in radians. When t = 5.0 s, ... what is the magnitude of the astronaut\'s angular velocity?

... and what is the magnitude of the astronaut\'s linear velocity?

... and what is the magnitude of the astronaut\'s tangential acceleration?
... and what is the magnitude of the astronaut\'s radial acceleration?

Solution

theta = 0.17 t²

a) w = dtheta / dt = 0.34 t

w(5) = 0.34 * 5 = 1.7 rad/s

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b) v = r w = 11.5 * 1.7

v = 19.55 m/s

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c) alpha = dw / dt = 0.34 rad/s²

a_tang = r * alpha = 11.5 * 0.34

a_tang = 3.91 m/s²

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d) a_cent = r w² = 11.5 * 1.7²

a_cent = 33.25 m/s²