An Astronaut in a centrifuge - solution

 An astronaut is rotated in a horizontal centrifuge at a radius of 6.0m. What is his speed if the centripetal acceleration is 5g. What is the frequency of this rotation?

Given:

R = 6.0m – radius of rotation

a = 5g – centripetal acceleration

We are looking for:

v = ? – speed of the astronaut

f = ? – frequency of rotation

Solution:

We write two formulas from the uniform circular motion theory,

a = v²/R            (1)

v = 2πRf           (2)

Substituting 5g for a and solving the first formula with respect to v, we get

    (3)

From solution (3) and formula (1) we get

After substituting numbers given in the problem

v=17.16m/s

f=0.455 s^-1

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