A child is playing in a park on a rotating cylinder of radius r is set in rotation at an angular speed of W as shown below. The base of the cylinder is slowly moved away, leasing the child suspended against the wall in a vertical position. What is the minimum coefficient of friction between the child's clothing and wall is needed to prevent it from falling.

Complete Question:

A child is playing in a park on a rotating cylinder of radius, r = 3.00 m , is set in rotation at an angular speed of w = 5.00 rad/s. The base of the cylinder is slowly moved away, leaving the child suspended against the wall in a vertical position. What is the minimum coefficient of friction between the child's clothing and wall needed to prevent it from falling

minimum coefficient of friction between the child's clothing and wall needed to prevent it from falling,

Explanation:

Applying the Newton's law:

...............(1)

Where N = Normal reaction.

and =  coefficient of friction

Since the cylinder is a rotating one, the normal reaction will be calculated using the formula .................(2)

Substituting (2) into (1)

.............(3)

v = wr..........(4)

Substitute (4) into (3)

Substituting, w, g, and r into the equation above

Angular speed,

Radius, r = 3 m

g = 9.8 m/s²