Centripetal Acceleration and period of rotation

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Homework Help Overview

The problem involves calculating the period of rotation required to achieve specific magnitudes of centripetal acceleration for a volunteer in a horizontal circular motion. The context is centered around concepts of centripetal acceleration and rotational dynamics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between centripetal acceleration and period of rotation, questioning the correctness of the initial approach and the derived equations. There is an exploration of how to relate velocity to the period of rotation.

Discussion Status

Some participants have provided guidance on deriving the necessary equations and clarifying the relationships between variables. The discussion is ongoing, with multiple interpretations of the equations being explored.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is a focus on ensuring the correct application of formulas related to centripetal acceleration.

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Homework Statement



In a test of a “g -suit,” a volunteer is rotated in a horizontal circle of radius 7.7m.

What must the period of rotation be so that the centripetal acceleration has a magnitude of 3.7g ?

What must the period of rotation be so that the centripetal acceleration has a magnitude of 10g?



Homework Equations


F=ma
w=ma
4pi^2r/T

The Attempt at a Solution



Ok I started by converting 3.7g, by doing this 9.8*3.7 = 36.26

4pi^2(7.7)/ 36.26

but it is wrong, how would I solve this?
 
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4pi^2r/T

This isn't right, check the units. It's supposed to be acceleration, right? Did you derive it yourself?
 
I've been told it has something to do with the equation, although I don't think I am using properly.

what would you do in the following situation?
 
Well, start with the equation for centripetal acceleration, a = v^2/r. You need to relate it to the period. You can do that by the velocity term. What's a way to express the velocity of an object moving in a circle?
 
velocity would be distance/time.

Circumference = 2*pi*Radius

v=2pir/t ?
 
That's right. Now put that together with the a=v^2/r and you should come up with the equation you need.
 
a = 4pi^2r / t^2

?
 
Yes. So solve that for t and use it to find the period.
 
ok got it. thank you
 

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