Rotating a space station can simulate gravity for its occupants. A ring-shaped structure with a radius about the length a football field could be spun a few times a minute to achieve a sensation of normal gravity, comfortable for human habitation. Consider a ring space station, rotating counter-clockwise at 0.3141 rad/s (the figure says 0.6282 rad/s - please ignore that value! It takes too much time to fiddle with all these figures). O Fig. 1-a spinning space station. -0.6282 rad/s a. What is that angular velocity, 0.3141 rad/s, in revolutions per minute? Show your work, don't just punch this into google. b. If the centripetal acceleration at the rim of the station is 9.81m/s², what is the radius of the structure? c. What is the linear, tangential velocity v of a chunk of stuff on the rim of the station, at the radius you found in (b)?

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2. Rotating a space station can simulate gravity for its occupants. A ring-shaped structure
with a radius about the length a football field could be spun a few times a minute to
achieve a sensation of normal gravity, comfortable for human habitation.
Consider a ring space station, rotating counter-clockwise at 0.3141 rad/s (the figure says
0.6282 rad/s - please ignore that value! It takes too much time to fiddle with all these
figures).
O
Fig. 1-a spinning space station.
-0.6282 rad/s
a. What is that angular velocity, 0.3141 rad/s, in revolutions per minute? Show your
work, don't just punch this into google.
b.
If the centripetal acceleration at the rim of the station is 9.81m/s², what is the
radius of the structure?
c. What is the linear, tangential velocity v of a chunk of stuff on the rim of the
station, at the radius you found in (b)?
Transcribed Image Text:2. Rotating a space station can simulate gravity for its occupants. A ring-shaped structure with a radius about the length a football field could be spun a few times a minute to achieve a sensation of normal gravity, comfortable for human habitation. Consider a ring space station, rotating counter-clockwise at 0.3141 rad/s (the figure says 0.6282 rad/s - please ignore that value! It takes too much time to fiddle with all these figures). O Fig. 1-a spinning space station. -0.6282 rad/s a. What is that angular velocity, 0.3141 rad/s, in revolutions per minute? Show your work, don't just punch this into google. b. If the centripetal acceleration at the rim of the station is 9.81m/s², what is the radius of the structure? c. What is the linear, tangential velocity v of a chunk of stuff on the rim of the station, at the radius you found in (b)?
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