An astronaut is being tested in a centrifuge. the centrifuge has a radius of 9 m and, in starting, rotates according to ? = 0.30t2, where t is in seconds and ? is in radians.

(a) when t = 9.0 s, what is the magnitude of the astronaut's angular velocity?

(b) when t = 9.0 s, what is the magnitude of the astronaut's linear speed?

(c) when t = 9.0 s, what is the magnitude of the astronaut's tangential acceleration?

(d) when t = 9.0 s, what is the magnitude of the astronaut's radial acceleration?

5.4 rad/s

48.6 m/s

5.4 m/s²

262.44 m/s²

Explanation:

r = Radius of centrifuge = 9 m

Differentiating with respect to time

At t = 9 s

Angular velocity is 5.4 rad/s

Linear speed

The linear speed of the astronaut is 48.6 m/s

Differentiating with respect to time

Tangential acceleration is given by

Tangential acceleration of the astronaut is 5.4 m/s²

Radial acceleration is given by

The radial acceleration of the astronaut is 262.44 m/s²

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