Angular Velocity and static friction

AI Thread Summary
The discussion focuses on calculating the minimum angular velocity required to prevent a person from slipping down a vertical spinning cylinder in an amusement park ride. The coefficient of static friction is given as 0.61, and the radius of the cylinder is 6.56 meters. Key considerations include identifying the forces acting on the person, specifically the centripetal force and the opposing force due to static friction. The problem emphasizes the need to balance the gravitational force with the frictional force to maintain stability. Understanding these forces is crucial for solving the problem effectively.
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Homework Statement


The coefficient of static friction between the person and the wall is .61. The radius of the cylinder is 6.56 m. An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the loor drops away. What is the minimum angular velocity needed to keep the person from slipping downward?


Homework Equations





The Attempt at a Solution



I don't know how to solve this problem because of the coefficient of static friction. Please help
 
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Well, ask yourself:
1. What force provides the person with her centripetal acceleration?
2. Relative to the wall, is this force a normal force, or a tangential force?
3. What is the force opposing her weight, and that must balance this in order for her not to slip downwards?
 

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Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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