Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 12 m and, in starting, rotates according to θ= 0.25t², where t is in seconds and θ is in radians. When t = 1.5 s, what are the magnitudes of the astronaut's (a)angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration?

Answer 1

Given

   radius of centrifuse is r = 12 m

   equation is θ= 0.25t2,

at t = 1.5 s

a) angulara velocity is w = dθ/dt = 2*0.25*t
               = 2*0.25*1.5 rad/s

               = 0.75 rad/s

b) linear velocity v = r*w = 12*0.75 m/s = 9 m/s

c) tangential acceleration a = r*alpha = 12*0.5 = 6 m/s2

d) radial acceleration is a = v^2/r = 9^2/12 = 81/12 m/s2 = 6.75 m/s2