Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 5.50 m and, in starting, rotates according to θ = 0.380t², 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

The expression for the acceleration and Θ is given by -

Θ = 1/2*αt^2 ----------------------------------(i)

Given expression is -

Θ = 0.380t^2-------------------------------(ii)

Compare (i) and (ii) -

0.380 = 1/2*α

=> α = 0.76 rad/s^2

(a) Angular velocity, w = α*t = 0.76 x 3.70 = 2.812 rad/s

(b) Linear velocity, v = w*R = 2.812 x 5.50 = 15.47 m/s

(c) Tangential acceleration, a = α*R = 0.76 x 5.50 = 4.18 m/s^2

(d) Radial acceleration, a(r) = w^2 * R = 0.76^2 x 5.5 = 3.18 m/s^2