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Old Sep 13th 2010, 07:55 PM   #1
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Particle in Uniform Circular Motion

A 20-g centrifuge is horizontal tube 58 ft long. Assume an astronaut in training sits in a seat at one end, facing the axis of rotation 29.0 ft away. Determine the rotation rate, in revolutions per second, required to give the astronaut a centripetal acceleration of 20.0g

i start the problem like this a_c={v^2}{R}
when i plug in the values i get 20.0g(29.0ft)=v^{2}
that gives me 24.08gft but the book says the answer is .749rev/s
i dont know how to convert my answer to that or if it is even right
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Old Sep 13th 2010, 11:44 PM   #2
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Originally Posted by vinson24 View Post
A 20-g centrifuge is horizontal tube 58 ft long. Assume an astronaut in training sits in a seat at one end, facing the axis of rotation 29.0 ft away. Determine the rotation rate, in revolutions per second, required to give the astronaut a centripetal acceleration of 20.0g

i start the problem like this a_c={v^2}{R}
when i plug in the values i get 20.0g(29.0ft)=v^{2}
that gives me 24.08gft but the book says the answer is .749rev/s
i dont know how to convert my answer to that or if it is even right
Acceleration a_c = ω^2*R

20*32/29 ft = ω^2

Find ω = 2*pi*f, where f is the frequency of rotation.
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Old Sep 14th 2010, 06:44 AM   #3
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Why did you multiply 32*20?
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Old Sep 14th 2010, 06:54 AM   #4
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Originally Posted by vinson24 View Post
Why did you multiply 32*20?
a_c = 20*g and g = 32 ft/s^2
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Old Sep 14th 2010, 11:38 AM   #5
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Originally Posted by vinson24 View Post
when i plug in the values i get 20.0g(29.0ft)=v^{2}
that gives me 24.08gft but the book says the answer is .749rev/s
First you are using the wrong formula for acceleration, as sa-ri-ga-ma pointed out. The correct equation is v^2 = ω^2/R. And second, you are mixing up units. You have R = 20 ft, and the acceleratoin is 20 g = 20 x 32 ft/s^2 = 640 ft/s^2. So::
ω^2 = (640 ft/s^2) /29ft) = 22.07 /s^2.
ω = sqrt (22.07/s^2) = 4.7 radians/s.
Rev/Sec = Rzdians/sec /(2 pi), so:
Rotatoinal speed in revs per second = 4.7 radians/s /(2 pi)
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