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

1. Nov 29, 2011

### bac2789

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

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

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.

2. Relevant equations

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

F=ma
FF= μFN

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.

3. The attempt at a solution

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Last edited: Nov 29, 2011
2. Nov 29, 2011

### PhanthomJay

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

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?