AP Physics C: Mechanics Problem Set on Rotational Inertia

Please answer all the questions, and the answers are highlighted in bold. The main objective is to show your work throughout these exercises. Thank you for all you do!

AP Physics C: Mechanics, Rotational Inertia Practice 60 0 Ihoop = mr? I mass = mr? I cylinder = 2 mr2 I rod = 12 ml2 1 = I com + MH? 40 0 1. The four masses shown to the right are connected by massless, rigid rods. 200 Find the coordinates of the center of mass. Xem=5.71cm, ycm=4.57cm (200 8 200 6 d. Find the moment of inertia about an axis that passes through mass A 10 cm and is perpendicular to the page. .00656kgm? (10 ) ( 20 0 ) 8 cm. 20 0 5 714 2. Derive the moment of inertia for a rod rotated about one end. 100 : W CM. 200 8 3. A triangular rod has length L, mass M, and nonuniform linear mass 2 = 2M density given by the equation =(2M/L^2)x, where x is the distance from one end of the rod. Show that the rotational inertia of the rod about its left end is 1/2ML?. x= 0 X =L 4. A 25 kg solid door is 220 cm tall, 91 cm wide. What is the door's moment of inertia for . rotation on its hinges? (Treat door as a rod) 6.9kgm b. rotation about a vertical axis inside the door, 15 cm from one edge? 4.05kgm? 5. A 12 cm diameter CD has a mass of 21 g. What is the CD's moment of inertia for rotation about a perpendicular axis a. through its center? 3.78E-5 kgm b. through the edge of the disk? 1.134E-4 kgm? 6. What is the moment of inertia of a 2.0 kg, 20 cm diameter disk for rotation about an axis a. through the center? .01kg m? b. through the edge of the disk?.03 kgm? 7. Determine the moment of inertia for two masses, one 3 kg, the other 5 kg, connected by a 2.4 m massless rod being rotated in the center of the rod. 11.52 kgm? 8. From problem #5, determine the moment of inertia for the system if it is rotated on the end with the 3 kg mass. 28.8kgm 9. From problem #5, determine the moment of inertia for the system if the rod has a mass of 4 kg.13.44kgm? 10. Determine the moment of inertia for a 5 kg, 4 m long rod rotated 1 m from the end of the rod.11.67kgm 11. Using the information from #8, determine the moment if inertia if the axis of rotation is moved to the end of the rod. 26.67kgm