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Homework Help Overview

The discussion revolves around calculating the rotation period of a cylindrical space station designed to simulate "normal" gravity through rotation. The problem involves concepts from rotational motion and centripetal acceleration.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between angular velocity, centripetal force, and gravitational acceleration. Questions arise regarding the assumptions made about angular velocity and the need for mass in the calculations. There is also a discussion on how to express centripetal acceleration in terms of rotational speed and radius.

Discussion Status

The discussion is active, with participants questioning the initial assumptions and exploring the necessary relationships to find the angular speed needed for the desired centripetal acceleration. Some guidance has been provided regarding setting centripetal acceleration equal to gravitational acceleration.

Contextual Notes

Participants note the lack of information on angular velocity and mass, which adds to the complexity of the problem. The focus remains on deriving the necessary relationships without resolving the calculations fully.

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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