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