3. (30 pts) A mass m is placed at a radius r from the center of a horizontal spinning disk that is rotating with period Disk. The coefficient of static friction between the mass and disk surface is /. To help prevent the mass from sliding off the disk, a rope is used. One end of the rope is attached to the mass and the other end of the rope is horizontally attached to the shaft at the center of the disk. Because the disk is spinning very fast, the static friction force is at its maximum value f.max. The rest of the required force to prevent sliding is provided by the tension Trope in the rope. Derive an equation for the tension Trope in the rope in terms of m, I, TDisks /s and g only. Velocity must be eliminated from your equation. The force of gravity acts vertically downward. Make sure to follow all steps to solving a physics problem including starting with a free-body diagram. rope m Figure 1. Geometry for problem 3