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A disk of mass m on a frictionless table is attached to a hanging cylinder of mass M by a cord through a hole in the table (see Fig). Find the speed with which the disk must move in a circle of radius r for the cylinder to stay at rest.
The free body diagram of the rotating disk is: It can be seen from the diagram that the centripetal force to the disk must be provided by the tension in the cord, thereforeThe free body diagram of the cylinder is shown below:For the cylinder to stay at rest, the tension in the cord should be equal to its weight, that is T = W.Here g is the acceleration due to gravity.Therefore the speed with which the disk should rotate to keep the cylinder at rest is given by expression
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