Angular Velocity and static friction

[kitty9035]

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

 

[arildno]

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?

 

[m2003]

I would suggest using the equation for angular velocity, which is ω= v/r, where v is linear velocity and r is the radius. In this case, the linear velocity can be calculated using the coefficient of static friction and the acceleration due to gravity (9.8 m/s^2). The minimum angular velocity needed to keep the person from slipping downward can then be calculated by setting the linear velocity equal to the velocity at which the person would slip downward, which can be found using the coefficient of static friction and the weight of the person. It is also important to consider the direction of the angular velocity in relation to the direction of the person's weight.