Centripetal acceleration formula

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Homework Help Overview

The problem involves calculating the centripetal acceleration experienced by riders in a spinning circular room, with given parameters such as radius and angular speed. The subject area pertains to circular motion and dynamics.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between angular speed and linear velocity, questioning the application of the centripetal acceleration formula. Some participants attempt to clarify the correct formula to use, while others express confusion about the initial calculations.

Discussion Status

The discussion is active, with participants exploring different methods to derive the centripetal acceleration. Some guidance on the appropriate formulas has been provided, and there is an acknowledgment of the initial misunderstanding regarding the relationship between angular speed and linear velocity.

Contextual Notes

There is a noted discrepancy between the initial calculation of centripetal acceleration and the expected result, prompting further exploration of the formulas involved. Participants are working within the constraints of the problem as presented, without additional context or information.

BensonCa
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Homework Statement


In a certain carnival ride, visitors enter a circular room with radius r=9.1m. The room then begins spinning around its center, reaching an angular speed of 1.7rad/s. What centripetal acceleration do the riders experience?

Homework Equations


ac= v^2/r

The Attempt at a Solution


I believed that ac= v^2/r which would equal .3175824176 or .32 m/s^2

but the answer is 26 m/s^2 and the explanation is Centripetal acceleration is given by ac=rω2. WHY?
 
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You're given angular speed, and you're trying to plug it into a formula with velocity.
 
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Good effort though! You have omega, the formula you want to be using is a = w^2 r substituting w = v/r into the original formula you have.
 
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Oh, I see what I did, thank you
 
I would rather go with:
v= wr
v =1.7 x 9.1 = 15.47

to find the acceleration:
a = v^2/r
a = (15.47)^2/9.1
a = 231.32/9.1
a = 26.299 ( and can be rounded to 26)
 

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