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A donut-shaped space station (outer radius R) arranges for
Chapter 9, Problem 9.2(choose chapter or problem)
A donut-shaped space station (outer radius R) arranges for artificial gravity by spinning on the axis of the donut with angular velocity co. Sketch the forces on, and accelerations of, an astronaut standing in the station (a) as seen from an inertial frame outside the station and (b) as seen in the astronaut's personal rest frame (which has a centripetal acceleration A = to2R as seen in the inertial frame). What angular velocity is needed if R = 40 meters and the apparent gravity is to equal the usual value of about 10 m/s2? (c) What is the percentage difference between the perceived g at a six-foot astronaut's feet (R = 40 m) and at his head (R = 38 m)?
Questions & Answers
QUESTION:
A donut-shaped space station (outer radius R) arranges for artificial gravity by spinning on the axis of the donut with angular velocity co. Sketch the forces on, and accelerations of, an astronaut standing in the station (a) as seen from an inertial frame outside the station and (b) as seen in the astronaut's personal rest frame (which has a centripetal acceleration A = to2R as seen in the inertial frame). What angular velocity is needed if R = 40 meters and the apparent gravity is to equal the usual value of about 10 m/s2? (c) What is the percentage difference between the perceived g at a six-foot astronaut's feet (R = 40 m) and at his head (R = 38 m)?
ANSWER:Step 1 of 5
(a)
The free body diagram of the inertial frame can be shown as,
