11. In the figure shown, M = 0.50 kg, L = 1.20 m, and the mass L L of each connecting rod shown is negligible. M M 3M Determine the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles with I = mr. 12. A string is tied to a doorknob 0.80 m from the hinge as shown in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the torque on the door? 13. Force F= -10j N is exerted on a particle at r = (5i + 5]) m. What is the torque on the particle about the origin? 14. A 30.0-cm long wrench is used to generate a torque of 14.6 N-m at a bolt. A force of 70.0 N is applied at the end of the wrench at an angle of 0 to the wrench. Determine angle 0. 15. A uniform rod of length L and mass M is attached at one end of a frictionless pivot and is free to rotate about the pivot in the vertical plane as shown below. The rod is released from rest in the horizontal position. Determine: (a) the initial angular acceleration of the road(b) the initial translational acceleration of its right end. 16. A 182-kg flywheel has an effective radius of 0.62 m. (I = mr) (a) How much torque will take it from rest to a rotational speed of 120 rpm within 30.0 s? (b) How much work will this take? 17. A 3.2-kg solid sphere of diameter 28 cm spins at 5.0 rad/'s about an axis passing through its center. How much work is needed to bring it to rest within 15 sec? [Use I = 2/5 x mr ] 18. A uniform rod of length L and mass M is free to rotate on a frictionless pin passing through one end. The road is released from rest in the horizontal position. Determine the angular speed when the road reaches its lowest position. XCM