Physics
posted by Tasha on .
In an automatic clothes drier, a hollow cylinder moves the clothes on a vertical circle (radius r = 0.39 m), as the drawing shows. The appliance is designed so that the clothes tumble gently as they dry. This means that when a piece of clothing reaches an angle of above the horizontal, it loses contact with the wall of the cylinder and falls onto the clothes below. How many revolutions per second should the cylinder make in order that the clothes lose contact with the wall when = 72.0°?
rev

Let's solve for radians per second, w. The number of revs per second is
w/(2 pi)
The clothes fall when the weight component along the direction to the center of the drum equals the centripetal force needed to keep the clothes on the drum. At lower speeds or higher angles, the clothes leave the surface and "tumble"
m r w^2 = m g sin 72
w^2 = g sin 72/r = 2.44
w = 1.56 rad/s
That is about 1/2 rev/s