Barrel of Fun - Circular Motion

[thaixicedxtea]

Homework Statement

Given: The coefficient of static friction between the person and the wall is 0.66, the mass of the person is 73 kg, the radius of the cylinder is 7 m, and g = 9.8 m/s.
A barrel of fun consists of a large vertical cylinder that spins about the vertical axis. When it spins fast enough, any person inside will be held up against the wall.
Find ώc, the critical angular speed below which a person will slide down the wall of the cylinder. Answer in units of rad/s.

Homework Equations

Ac = V^2.r or ώ^2=Ac
µ = ώ^2r/g

The Attempt at a Solution

So I used µ = ώ^2r/g and solved for ώ but it was wrong...
That's basically it.
What did I do wrong?

 

[thaixicedxtea]

nvm... got it...

 

[thomate1]

I would like to first clarify that the given information and equations are not sufficient to solve for the critical angular speed below which a person will slide down the wall of the cylinder. We need to know the height of the cylinder in addition to the given parameters to fully understand the system and solve for ώc.

However, assuming that the height of the cylinder is not relevant to the problem, I can provide a general response to help guide your approach.

To solve for the critical angular speed, we need to consider the forces acting on the person inside the cylinder. The normal force from the wall will be equal and opposite to the weight of the person, and the maximum frictional force will be equal to the coefficient of static friction multiplied by the normal force. This frictional force will act in the opposite direction of the person's motion.

Using these forces, we can set up an equation of motion for the person in the tangential direction and solve for the critical angular speed. This equation will involve the radius of the cylinder, the mass of the person, the coefficient of static friction, and the acceleration due to gravity.

It is also important to note that the critical angular speed will depend on the direction of rotation of the cylinder. If the cylinder is rotating clockwise, the critical angular speed will be different than if it is rotating counterclockwise. This is because the direction of the frictional force will change depending on the direction of rotation.

In summary, to solve for the critical angular speed, we need to consider the forces acting on the person and set up an equation of motion. More information about the system, such as the height of the cylinder, may be needed to fully solve the problem.