posted by Elizabeth
A 10g marble is spun so that it rolls at 150rpm around the inside of a steel tube. The tube has a 12cm diameter. Assume the rolling resistance is small enough for the marble to maintain 150rpm for several seconds. During this time, will the marble spin in a horizontal circle or will it spiral down in the tube?
There are two forces action on the marble: centripetal and weight. Centripetal moves the marble toward the center, and gravity moves it downward. How much downward really depends on friction. Friction has two components, rolling, and sliding. For the marble to move downward, it has to start sliding downward first. Sliding fricion is usually much more than rolling friction. So, the marble will stay almost horizontal, but in fact it is moving downward. As the marble slows, the angle of velocity downward increases, (velocity tangent slows, falling velocity increases).