(20pts) Consider a disk of mass m and radius r, as shown below. It has a particle P of mass m embedded at its circumference. The system rolls without slipping on the horizontal surface. (The moment of inertia of a uniform disk about its center C is %mrz) a. (8pts) With 8 as the generalized coordinate, derive the equation of motion of the system using the Lagrange's equation. b. (8pts) If the disk starts rolling with an initial condition of 8 = 0,6 =0, using conservation of the energy and the equation of motion of part (a), determine 6 and 6 when 8 = /2. c. (4pts) Determine the normal reaction of the ground using the results of part (b) at the instant when 8 = /2. 0 /////D7l 777777