1. A thin cord is wound around a homogeneous cylinder with mass mA and radius R....
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1. A thin cord is wound around a homogeneous cylinder with mass mA and radius R. The cord extends horizontally from the cylinder to a pulley and then vertically downwards to a block B with mass mg. See the figure below. The pulley is massless and frictionless. The gravitational acceleration is ~g, and directed vertically downwards. The moment of inertia of the cylinder with respect to the axis through the center of the cylinder is IA = MAR². The cylinder rolls without slipping. A B (a) Express the instantaneous velocity VA of the center of mass of the cylinder in terms of its angular velocity WA. What is the relation between the velocity VÀ of the center of mass of the cylinder, and the velocity of block B? (b) Give the instantaneous kinetic and potential energy for this system. (c) Determine the acceleration aд of the center of mass of the cylinder and the tension in the cord. 1. A thin cord is wound around a homogeneous cylinder with mass mA and radius R. The cord extends horizontally from the cylinder to a pulley and then vertically downwards to a block B with mass mg. See the figure below. The pulley is massless and frictionless. The gravitational acceleration is ~g, and directed vertically downwards. The moment of inertia of the cylinder with respect to the axis through the center of the cylinder is IA = MAR². The cylinder rolls without slipping. A B (a) Express the instantaneous velocity VA of the center of mass of the cylinder in terms of its angular velocity WA. What is the relation between the velocity VÀ of the center of mass of the cylinder, and the velocity of block B? (b) Give the instantaneous kinetic and potential energy for this system. (c) Determine the acceleration aд of the center of mass of the cylinder and the tension in the cord.
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Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
Posted Date:
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