A disk of mass m, radius R. and mass moment of inertia IR rolls without slip on an inclined plane of angle das mR Gravity g shown in the figure below. It is connected to a hoop of mass m. radius R. and mass moment of inertia In acts downwards.

Define position variables for the twrp bodies. You can assume that the two bodies start from rest at the top of the incline.

(a) How many degrees of freedom does the system have?

(b) Draw the FBD and write all the kinetics equations required to describe the motion of the disk.

(c) Substitute/simplify the kinetics equations as necessary and write the equation(s) of notion of the disk and hoop

(remember that the only variables in the ECIM(s) should be the position variables, their derivatives, and their functions)