3. A cone supports an angle of 2a. A mass m, which is tied to a massless string, slides over the cone in a circular path of radius R. The other end of the rope is tied to the tip of the cone such that the rope remains parallel to the surface of the cone. The coefficient of kinetic friction between the cone and the mass is μ. Using cylindrical coordinates, a) Write the equations of motion. b) If the initial angular speed is = w how long does it take for the mass to stop? R

3. A cone supports an angle of 2a. A mass m, which is tied to a massless string, slides over the cone in a circular path of radius R. The other end of the rope is tied to the tip of the cone such that the rope remains parallel to the surface of the cone. The coefficient of kinetic friction between the cone and the mass is μ. Using cylindrical coordinates, a) Write the equations of motion. b) If the initial angular speed is = w how long does it take for the mass to stop? R