Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 12 m and, in starting, rotates according to θ = 0.24t2, where t is in seconds and θ is in radians. When t = 2.9 s, what are the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration?

Answer 1

The radius of the centrifuge R = 12 m

the equation of moion

θ = 0.24t^2

The angular velocity is

w = dθ/dt = 0.48*t

a) When t = 2.9 s, what is the magnitude of the astronaut's angular velocity is

w = 0.48*2.9 = 1.39 rad/s

b) When t = 2.9 s, what is the magnitude of the astronaut's linear speed is

v = Rw

v = 12 m * 1.39 rad/s

v = 16.7 m/s

c)

When t = 2.9 s, what is the magnitude of the astronaut's tangential acceleration is

a = v²/R

a = 16.7^2/12 = 23.24 m/s²

d)

When t = 2.9 s, what is the magnitude of the astronaut's radial acceleration

a = Rw^2

a = 23.18 m/s^2