The cylindrical tub of a dryer in a laundromat rotates counterclockwise about a

Question

The cylindrical tub of a dryer in a laundromat rotates counterclockwise about a horizontal axis at 45.5 rev/min as it dries the clothes. If the diameter of the cylinder is 0.756 m, at what angle will a piece of cloth lose contact with the wall of the cylinder and fall down? (Take the +x axis to be pointing horizontally to the right.) Did you draw a free-body diagram for the cloth and label all forces acting on it? What force or forces contribute to the centripetal force in this case? What value of the normal force will cause the cloth to lose contact with the wall of the cylinder?° counterclockwise from the +x axis

Explanation / Answer

given
w = 45.5 rev/min = 4.7647 rad/s

D = 0.756 m
let the piece of cloth lose contact at angle theta
then
from force balance

mg*sin(theta) = mv^2/r
sin(theta) = 2v^2/dg
hence
theta = arcsin(2v^2/dg)
but v = wd/2
theta = arxsin(w^2d/2*g) = 61.01 deg

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