Angular Velocity and static friction

In summary, the minimum angular velocity needed to keep the person from slipping downward on the amusement park ride can be determined by considering the centripetal acceleration and the forces at play, including the normal force and the opposing force of the person's weight. The coefficient of static friction between the person and the wall is also a factor in this calculation.
  • #1
kitty9035
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0

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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  • #2
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?
 
  • #3


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.
 

What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates around a fixed axis. It is typically represented in units of radians per second (rad/s) or degrees per second (deg/s).

How is angular velocity calculated?

Angular velocity can be calculated by dividing the change in angular displacement by the change in time. It can also be calculated by multiplying the radius of rotation by the linear velocity of the object.

What is static friction?

Static friction is a type of friction that occurs between two surfaces in contact with each other, where one object is not moving. It is a force that resists the motion of the object and acts in the opposite direction of the applied force.

How does static friction affect angular velocity?

Static friction can affect angular velocity by decreasing the speed at which an object rotates. This is because static friction acts as a resistance force, making it more difficult for an object to rotate at a higher angular velocity.

How can static friction be overcome?

Static friction can be overcome by applying a greater force to the object or by decreasing the coefficient of static friction between the two surfaces. This can be done by using lubricants or by increasing the smoothness of the surfaces in contact.

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