Question

An astronaut is being tested in a centrifuge. The centrifuge has a radius of 10 m and, in starting, rotates according to ? = 0.30t2, where t is in seconds and ? is in radians.Answers must have units!(a) When t = 12.0 s, what is the magnitude of the astronaut's angular velocity?(b) When t = 12.0 s, what is the magnitude of the astronaut's linear speed?(c) When t = 12.0 s, what is the magnitude of the astronaut's tangential acceleration?(d) When t = 12.0 s, what is the magnitude of the astronaut's radial acceleration?

Answer 1

a) ω = 7.2 rad/s

b) V = 72m/s

c)
`a = 6 m/s^2`

d)
`a_c = 518.4m/s^2`

Step-by-step explanation:

Since
`\theta = 0.30*t^2`, we can derive to obtain ω and α:

`\omega=0.60*t[rad/s]`

`\alpha =0.6rad/s^2`

At t=12s:

ω = 7.2rad/s

V = R*ω = 72m/s

`a = \alpha * R = 6 m/s^2`

`a_c = \omega^2 * R = 518.4 m/s^2`