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Stationary cylinder of radius b P Problem 2. (2.5 points) Thin disk, body 3, of mass m= 1kg and radius R= 5 cm turns freely about arm 2 with rate Or; arm 2 is a massless rod AC of length L = 12 cm. Point A of the arm is a stationary and frictionless ball-and-socket joint. The arm rotates about the inertial Y-axis with constant rate 2 = 10 rad/s. The disk rolls without slipping on the interior of a stationary cylinder of radius b=9.23 cm. Note that cos(O)= 12/13 and sin(O) = 5/13. The centroidal mass moments of inertia of a thin disk are (1/2)mR2 about the polar axis and (1/4)mR- about a diameter. (a) Find the spin rate of the disk 3 relative to arm 2 in order to have pure rolling at point P. (b) Find the angular momentum of the disk about point 4. Use the coordinates xyz which are fixed to the arm 2 (c) Find the normal force between the inner surface of the cylinder and the disk. Assume that the force is horizontal (perpendicular to the surface) and that friction is negligible (just enough to maintain pure rolling.) Do not neglect gravity. Ans (a) 0:=-18.4615 rad/s, (b) HA = (0.05781 – 0.0115) kg*m/s, (c) N = 1.3660 Newtons =