On a popular amusement park ride, the riders stand along the inside wall of a large cylinder with a diameter of 8.27 m. the cylinder rotates and when it reaches a rotational frequency of 0.66 revolutions per second the floor drops out. what is the minimum coefficient of static friction needed between a rider and the cylinder wall to prevent the rider from moving down?

Explanation:

D = 8.27 m   ⇒  R = D / 2 = 8.27 m / 2 = 4.135 m

ω = 0.66 rev/sec = (0.66 rev/sec)*(2π rad/1 rev) = 4.1469 rad/s

We can apply the equation

Ff = W  ⇒  μ*N = m*g   (I)

then we have

N = Fc = m*ac = m*(ω²*R)

Returning to the equation I

μ*N = m*g    ⇒    μ*m*ω²*R = m*g   ⇒ μ = g / (ω²*R)

Finally

μ = (9.81 m/s²) / ((4.1469 rad/s)²*4.135 m) = 0.1379

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.