Calculating Artificial Gravity Rotation Frequency in RPM

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Homework Help Overview

The discussion revolves around calculating the rotational frequency required to generate artificial gravity in a rotating space station, specifically focusing on a wheel with a diameter of 333m that aims to create an acceleration of 9m/s² at its outer rim.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between linear velocity and angular velocity, questioning how to correctly apply the equations of motion to find the rotational frequency. There are attempts to equate forces and derive relationships between variables.

Discussion Status

Some participants have provided clarifications regarding the distinction between linear and angular velocity, and there is an ongoing exploration of the relationships between the variables involved. The original poster has expressed confusion about their calculations, and others are guiding them towards a clearer understanding of the concepts.

Contextual Notes

Participants emphasize the importance of unit consistency and the correct application of formulas in their calculations. There is a recognition of the need to relate linear and angular velocities appropriately to solve the problem effectively.

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"Artificial Gravity"

Homework Statement



A space station in the form of a large wheel, 333m in diameter, rotates to provide an "artificial gravity" of 9m/s^2 for people located on the outer rim. Find the rotational frequency of the wheel that will produce this effect. Answer in units of rpm [revolutions per minute]

Homework Equations



w = 2pi/T , Frequency = 1/T

The Attempt at a Solution



I first equated the normal force with the centripetal force, which is mg = mv^2/r. Cancelling out the m, I got gr = v^2. After I solved for V, I plugged it into the w = 2pi/T equation to find T, then 1/T. To convert the answer to rpm, I multiplied what I got for F by 60 and divided by 2pi. However I kept getting the wrong answer. Can someone please help? Thank you!
 
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After I solved for V, I plugged it into the w = 2pi/T equation to find T
How did you relate v to w when finding T in this step?

Be sure to keep track of the units to make sure things make sense.

What answer did you get?
 
I got 3.487429162 rpm
 
I also know that w = 2 x pi x frequency
 
Yes, but remember that v is linear velocity, and w is angular velocity. They are not interchangeable. Do you know the relation between those two quantities?
 
I know that w = v/r
 
So what do you get if you make use of that? You found what v is, and ultimately what you want to find is w (in rev/min).

You're initial approach is OK, it's just the long way around. But you still need to use v=rw.
 
oh! I got it now! Thank you so much!
 
You're welcome. :smile:
 

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