Question

A disk-shaped space station 125 m in diameter spins at a constant angular velocity. If the acceleration of a point on the rim of the disk is to be equal to "g", how long does it take for the station to make one revolution?

Answer 1

Answer:

  t = 22.44 s

Explanation:

The acceleration of the station is centripetal which has the formula

         a = v² / r

linear and angular velocity are related

         v = w² r

as they indicate that the acceleration is equal to the acceleration of gravity

         g = w² r

         w = $\sqrt{ \frac{g}{r} }$

         

let's calculate

         w = $\sqrt{ \frac{9.8}{ 125} }$

         w = 0.28 rad / s

to calculate the time use us

          w = θ / t

in a complete revolution θ = 2pi

          t = θ / w

let's calculate

          t = 2π / 0, 28

          t = 22.44 s