Calculating Centripetal Acceleration for a Spinning Fairgrounds Ride

[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
Then ω=√19.11/8.00= 1.54 rad/s
And this is where I get stuck or confused, or maybe I haven't done it right at all?

 

[haruspex]

= 1.54 rad/s

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: $\frac {v^2}r=\omega^2r$.

 

[Mariesa Yeoman]

That was exactly the problem! Thank you so much!