A circular space station of radius 100 m rotates twice each minute. a. Find the acceleration of an astronaut standing at the outer edge of the space

station. How many g's does she feel? (1g=9.8ms2)

b. What must the period of rotation of the space station be in order for astronauts

at the outer edge to experience the same acceleration as on earth?

The space station completes 2 revolutions each minute, so that it traverses a distance of 2π (100 m) = 200π m each minute, giving it a linear/tangential speed of

v = (200π m) / (60 s) ≈ 10.472 m/s

(a) The astronaut would experience an acceleration of

a = v ² / (100 m) ≈ 1.09662 m/s² ≈ 0.1119g ≈ 0.11g

(b) Now you want to find the period T such that a = g. This would mean the astronaut has a tangential speed of

v = (200π m) / T

so that her centripetal/radial acceleration would match g :

a = g = ((200π m) / T )² / (100 m)

Solve for T :

(100 m) g = (400π ² m²) / T ²

T ² = (400π ² m²) / ((100 m) g) = (4π ² m)/g

T = √((4π ² m) / (9.8 m/s²)) ≈ 2π √(0.102 s²) ≈ 2.007 s ≈ 2.0 s

mistakes are ok

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