Weightlessness on a Ferris Wheel

AI Thread Summary
To determine the revolutions per minute for a 15.1 m diameter Ferris wheel to achieve weightlessness at the top, one must analyze vertical circular motion and centripetal acceleration. The key equation is centripetal acceleration = (velocity)^2/radius, where at the top, the centripetal force equals gravitational force. By setting the gravitational force equal to the centripetal force, the velocity can be calculated. The conversion from velocity to revolutions per minute involves using the circumference of the wheel. The problem was ultimately solved with assistance from others in the discussion.
Sumbhajee
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Homework Statement


How many revolutions per minute would a 15.1 m diameter Ferris wheel need to make for the passengers to feel "weightless" at the topmost point of the trip?


Homework Equations





The Attempt at a Solution


I assume this problem has something to do with finding acceleration and converting from there. I have been having a lot of trouble with this problem.
 
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What are the things you know about vertical circular motion?
 
I know that Centripetal acceleration = (velocity)^2/radius
 
If you're weightless at the top, what does that mean? Draw your free body diagram, then figure out which forces are acting where.
 
Sumbhajee said:
I know that Centripetal acceleration = (velocity)^2/radius

Can write this in terms of angular velocity?
What happens at the top of the wheel?
 
If you are weightless at the top you should have mass * gravity acting down and a centripetal force equal to gravity acting up. But how does this information help to discover revolutions per minute?
 
To set up the equation would I use the following:

9.80=V^2/7.55 and solve for velocity? But how do you convert velocity to revolutions per minute?
 
I found the answer! Thank you for all the help.
 
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