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?

a) ω = 7.2 rad/s

b) V = 72m/s

c)

d)

Explanation:

Since , we can derive to obtain ω and α:

At t=12s:

ω = 7.2rad/s

V = R*ω = 72m/s

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.