# Homework Help: Angular Velocity; Given Coefficient of Friction and Radius

1. Jun 22, 2009

### Aljazera

1. The problem statement, all variables and given/known data

Consider the carnival ride in which the riders stand against the wall
inside a large cylinder. As the cylinder rotates, the floor of the cylinder
drops and the passengers are pressed against the wall by the centrifugal
force. Assuming that the coefficient of friction between a rider and the
cylinder wall is 0.5 and that the radius of the cylinder is 5m, what is
the minimum angular velocity and the corresponding linear velocity of
the cylinder that will hold the rider firmly against the wall?

2. Relevant equations

theta = 2pie*r/r = 2pie?

angular velocity = w/t

linear velocity = rw

3. The attempt at a solution

I tried to solve for w, being as that is dtheta over delta t; but time was not given so i just assumed one second.

2. Jun 22, 2009

### rock.freak667

In your free body diagram, the Normal force=Centripetal force.

What forces act on the body vertically?

3. Jun 22, 2009

### Aljazera

Gravity

4. Jun 22, 2009

### rock.freak667

Then what should the minimum resultant force between weight and the other force acting?

5. Jun 22, 2009

### Aljazera

With all due respect, what does knowing the resultant force between weight and other forces have to do with it?

1.25 rad/s is the answer to the problem, i just don't know how to arrive to it.

6. Jun 22, 2009

### rock.freak667

Well I don't think you will get 1.25 rad/s but this is how to go about it.

For no motion in the vertical direction (you don't want the people to go flying out of the cylinder)

$$Friction \geq Weight$$

Do you happen to have an expression for Friction?

7. Jun 22, 2009

### Aljazera

Mu and a related equation for Mu ( Vmax = $$\sqrt{}Mu x gravity x Radius$$

8. Jun 22, 2009

### rock.freak667

Well if you went through the reasoning you'd arrive at that equation.

Friction=uN

u= coefficient of friction

N= Normal reaction = Centripetal force in this case.