A space station is designed in the shape of a large, hollow donut that is uniformly rotating. The outer radius of the station is 350 m. With what period must the station rotate so that a person sitting on the outer wall experiences "artificial gravity," i.e. an acceleration of 9.8 m/s²? A)230 s B)170 s C)110 s D)76 s E)38 s

Question

Quizplus · Accepted Answer

The centripetal acceleration required for artificial gravity is given by a = ω²r, where ω is the angular velocity and r is the radius. Solving for ω gives ω = sqrt(a/r). The period T is related to ω by T = 2π/ω. Substituting the values, T = 2π/sqrt(9.8/350) ≈ 38 s.

A Space Station Is Designed in the Shape of a Large