The carnival ride has a 2.0m radius and rotates 1.1 times persecond.
a. find the speed of a rider.
b. find the centripetal acceleration of a rider.
c. what produces this acceleration?
d. when the floor drops down riders are held up byfriction. what coefficient of friction is needed to keep theriders from slipping?

a) v = 13.8 m / s , b) a = 95.49 m / s² , c) a force that goes to the center of the carnival ride  and d)   μ = 0.10

Explanation:

For this exercise we will use the angular kinematics relationships and the equation that relate this to the linear kinematics

a) reduce the magnitudes to the SI system

     w = 1.1 rev / s (2pi rad / 1rev) = 6.91 rad / s

The equation that relates linear and angular velocity is

     v = w r

     v = 6.91  2

     v = 13.8 m / s

b) centripetal acceleration is given by

     a = v² / r = w² r

     a = 6.91² 2

     a = 95.49 m / s²

c) this acceleration is produced by a force that goes to the center of the carnival ride

d) Here we use Newton's second law

     fr -W = 0

     fr = W

     μ N = mg

Radial shaft

      N = m a

      N = m w² r

      μ m w²  r = m g

      μ = g / w² r

      μ = 9.8 / 6.91² 2

      μ = 0.10

0.19 m/s and 0.45 m/s