An astronaut is being tested in a centrifuge. The centrifuge has a radius of 9 m

Question

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 = 6.0 s, what is the magnitude of the astronaut's angular velocity? (rad/s)

(b) When t = 6.0 s, what is the magnitude of the astronaut's linear speed? (m/s)

(c) When t = 6.0 s, what is the magnitude of the astronaut's tangential acceleration? (m/s2)

(d) When t = 6.0 s, what is the magnitude of the astronaut's radial acceleration? (m/s2)

Please show all work, and steps - I can't figure this one out. Thank you so much!

Explanation / Answer

the equation for the acceleration and is
= 1/2*t^2 , so 0.32 is 1/2* -->
= 0.64 rad/s^2
-----
a) angular velocity w is
w = *t = 0.64*6.0 = 3.84 rad/s

b) w = v/R --> v = w*R
v = 3.84*9 = 34.56 m/s

c) = a/R --> a = *R
a = 0.64*9 =5.76 m/s^2

d) a(r) = w^2R = 0.64^2*9 = 3.686 m/s^2

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