Centripetal acceleration formula

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SUMMARY

The centripetal acceleration experienced by riders in a carnival ride with a radius of 9.1 meters and an angular speed of 1.7 rad/s is calculated using the formula ac = rω². The correct centripetal acceleration is 26 m/s², derived from first calculating the linear velocity (v = ωr) and then applying the formula ac = v²/r. The initial misunderstanding involved incorrectly using the formula ac = v²/r without converting angular speed to linear velocity.

PREREQUISITES
  • Understanding of angular speed and its relation to linear velocity
  • Familiarity with the formula for centripetal acceleration
  • Basic knowledge of circular motion dynamics
  • Ability to perform algebraic manipulations of equations
NEXT STEPS
  • Study the derivation of the centripetal acceleration formula ac = rω²
  • Learn how to convert between angular speed and linear velocity
  • Explore examples of centripetal acceleration in real-world applications
  • Investigate the effects of varying radius and angular speed on centripetal acceleration
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Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators seeking to clarify concepts related to centripetal acceleration.

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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