# Calculating Centripetal Acceleration for a Spinning Fairgrounds Ride

• Mariesa Yeoman
In summary, the problem involves a fairgrounds ride with a spinning motion and a circular path of radius 8.00 m. The goal is to find the number of revolutions per minute at which the riders will experience a centripetal acceleration of 1.95 times that of gravity. Using the equation α=ω^2r, the angular velocity ω is found to be 1.54 rad/s. This value can then be converted to rpm to obtain the final answer.
Mariesa Yeoman

## Homework Statement

A fairgrounds ride spins its occupants inside a flying-saucer-shaped container. If the horizontal circular path the riders follow has a 8.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration 1.95 times that of gravity?

## Homework Equations

α= 1.95*9.8m/s^2= 19.11
ω=ν/r

## The Attempt at a Solution

So, I attempted this by solving for α =19.11m/s^2
And this is where I get stuck or confused, or maybe I haven't done it right at all?

Mariesa Yeoman said:
I get slightly nearer to 1.55rad/s.
It remains to convert to rpm. I would use a rad/sec value with some more digits for that, rounding afterwards.

Edit: it is not clear to me how you arrived at your answer, and you seem to be unsure yourself.
It is useful to remember a second form of the expression for centripetal acceleration: ##\frac {v^2}r=\omega^2r##.

That was exactly the problem! Thank you so much!

berkeman

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