Centripetal acceleration formula

AI Thread Summary
Centripetal acceleration for 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 initial attempt incorrectly used the formula ac = v²/r, leading to an inaccurate result of 0.32 m/s². The correct approach involves first calculating linear velocity (v = ωr), resulting in v = 15.47 m/s. Substituting this value into the correct formula gives an acceleration of approximately 26 m/s². Understanding the relationship between angular speed and linear velocity is crucial for accurate calculations.
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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