Barrel of Fun Carnival Ride, and the relationship between Friction and ω

[bac2789]

"Barrel of Fun" Carnival Ride, and the relationship between Friction and ω

Homework Statement

A ”Barrel of Fun” consists of a large vertical cylinder that spins about its axis fast enough so that any person inside will be held against the wall.

Assume: At an angular speed ω₁, an upward frictional force F₁ holds a person against the wall without slipping.

What is the friction force F₂, if the angular speed is doubled;i.e., ω₂ = 2ω₁.

Homework Equations

This is what has me stumped. I have no idea which equations I should bee looking at!

F=ma
F_F= μF_N

But all of these are accounting for linear motion, not circular. The rider will be suspended by a static Frictional Force that must counteract the pull of gravity. I have no idea what the relationship is between Force of Friction and Angular Speed.

The Attempt at a Solution

 

[PhanthomJay]

The person is accelerating centripetally (inward toward the center of the barrel, in the horizontal direction), but, as you noted, the person is not accelerating in the vertical direction, so the frictional force is just equal to the person's weight. Remember that this static friction force (static since there is no slipping) is less than or equal to uN. With this information, what is the static friction force when the angular speed is doubled?