Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11.0 m and, in starting, rotates according to θ = 0.390t2, where t is in seconds and θ is in radians. When t = 3.70 s, what are the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration?

Answer 1

ω = 2.9 rad/s, v = 31.7 m/s, α = 0.78 rad/s², a = 91,6 m/s²

Step-by-step explanation:

I will assume the given equation reads as Ф = 0.39t².

The angular velocity ω is the time derivative of Ф.

ω = 0.78t

The linear velocity v is given by ωr, where r is the radius of the centrifuge.

v = 0.78t r

The tangential acceleration α is the time derivative of ω.

α = 0.78

The radial acceleration a is given by: a = ω²r

a = (0.78t)²r