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AI Thread Summary
To achieve "normal" gravity on a rotating space station with a 1000m diameter, the centripetal acceleration must equal 9.8 m/s². The radius is 500m, and the relationship between centripetal acceleration, angular velocity, and radius is crucial. The initial confusion stemmed from incorrectly assuming angular velocity could be set to 9.8 without proper context. By equating centripetal acceleration to gravitational acceleration, the correct angular speed can be calculated. Ultimately, understanding the relationship between these variables leads to determining the necessary rotation period for the desired gravitational effect.
thebigeis
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Suppose a space station is constructed as a 1000m-diameter cylinder that rotates about its axis. What rotation period will provide "normal" gravity?

This is the work I have for this.

angular velocity = 9.8
r = 500m

2pi500/T = 9.8
2pi500/9.8 = T
T = 320.57

What did I do wrong?
 
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thebigeis said:
Suppose a space station is constructed as a 1000m-diameter cylinder that rotates about its axis. What rotation period will provide "normal" gravity?

This is the work I have for this.

angular velocity = 9.8
r = 500m

2pi500/T = 9.8
2pi500/9.8 = T
T = 320.57

What did I do wrong?
Why are you setting the angular velocity at 9.8? What are the units for angular velocity?

What is the centripetal force as a function of rotation speed or angular velocity and radius? Set that force is equal to the force of gravity.

AM
 
Andrew Mason said:
Why are you setting the angular velocity at 9.8? What are the units for angular velocity?

What is the centripetal force as a function of rotation speed or angular velocity and radius? Set that force is equal to the force of gravity.

AM

I'm not given the angular velocity, so I'm assuming it's a number that I should already know. I don't have the mass either. Isn't "normal gravity" mass * acceleration, acceleration equaling 9.8m/s^2. This is why I'm confused. What I wrote above is all I'm given.
 
thebigeis said:
I'm not given the angular velocity, so I'm assuming it's a number that I should already know. I don't have the mass either. Isn't "normal gravity" mass * acceleration, acceleration equaling 9.8m/s^2. This is why I'm confused. What I wrote above is all I'm given.
So what is the centripetal acceleration in terms of rotational speed and radius? Set that equal to the (gravitational) acceleration you are trying to achieve. You are given the radius so you will be able to determine the angular speed needed to produce that centripetal acceleration.

AM
 
Andrew Mason said:
So what is the centripetal acceleration in terms of rotational speed and radius? Set that equal to the (gravitational) acceleration you are trying to achieve. You are given the radius so you will be able to determine the angular speed needed to produce that centripetal acceleration.

AM

a = v^2/r ... I am pretty sure that's what you're asking
and then how can I get the angular speed if i don't have the period it takes for 1 revolution?
 
Oh, wow, I figured out it out. Thanks a bunch, AM. You really helped me out.
 

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