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nder and a mass of M4 = 4 kg hangs f with uniform density has a moment c s always, show your work and/or just e body diagram for the double cylind

nder and a mass of M4 = 4 kg hangs f with uniform density has a moment c s always, show your work and/or just e body diagram for the double cylind

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PM4: please answer question and explain each step with reasoning
Two solid cylinders with uniform density are glued together and supported by a frictionless metal rod so that they can rotate together around their common axis of symmetry, as shown in the diagram. The first cylinder has mass M1 = 6 kg and radius R1 = 2 m, while the second cylinder has mass M = 4 kg and radius R2 = 1 m. Ideal ropes are wrapped around each of the cylinders in opposite directions so that a mass of M3 = 3 kg hangs from the left side of the first cylinder and a mass of M4 = 4 kg hangs from the right side of the second cylinder. Recall that a solid cylinder with uniform density has a moment of inertia of Icm = ½MR? about its center of mass. As always, show your work and/or justify your answers. a) Draw an "extended" free body diagram for the double cylinder indicating the direction of each force vector as well as where each force is acting on the object. b) What is the magnitude of the torque on the double cylinder about its center of mass due to the force of gravity acting on the double cylinder? c) What is the angular acceleration of the double cylinder? Indicate whether it is a Mz clockwise or counterclockwise. d) What is the tension in the rope tied to the hanging mass M3? My M3
Transcribed Image Text:Two solid cylinders with uniform density are glued together and supported by a frictionless metal rod so that they can rotate together around their common axis of symmetry, as shown in the diagram. The first cylinder has mass M1 = 6 kg and radius R1 = 2 m, while the second cylinder has mass M = 4 kg and radius R2 = 1 m. Ideal ropes are wrapped around each of the cylinders in opposite directions so that a mass of M3 = 3 kg hangs from the left side of the first cylinder and a mass of M4 = 4 kg hangs from the right side of the second cylinder. Recall that a solid cylinder with uniform density has a moment of inertia of Icm = ½MR? about its center of mass. As always, show your work and/or justify your answers. a) Draw an "extended" free body diagram for the double cylinder indicating the direction of each force vector as well as where each force is acting on the object. b) What is the magnitude of the torque on the double cylinder about its center of mass due to the force of gravity acting on the double cylinder? c) What is the angular acceleration of the double cylinder? Indicate whether it is a Mz clockwise or counterclockwise. d) What is the tension in the rope tied to the hanging mass M3? My M3
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