Two solid spheres of masses M = 4 kg and m = 2 kg, with radii...
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Two solid spheres of masses M = 4 kg and m = 2 kg, with radii R 20 cm and r = 10 cm, respectively, are attached at either end of a rod of mass m, = 5 kg and length L = 50 cm to form a dumbbell (see Figure 7). Note that the spheres are attached to the ends of the rod (the rod does not penetrate the spheres). %3D %3D M, R т,r m,, L Figure 7: A dumbbell. (a) What is the moment of inertia of the system about its centre of mass? (b) A coordinate system is set up so that the origin is at the centre of mass of the dumbbell, and the x axis is parallel to the rod, with the positive direction from the M to m. A force: F (0.8 N)ê + (1.0 N)ŷ + (1.2 N)Â is applied to the outer edge of the small mass m (the edge of the sphere opposite of where it meets the rod). If F is the only force applied to the dumbbell, what is the angular acceleration vector of the dumbbell with respect to the coordinate system that is specified? What is its magnitude? Two solid spheres of masses M = 4 kg and m = 2 kg, with radii R 20 cm and r = 10 cm, respectively, are attached at either end of a rod of mass m, = 5 kg and length L = 50 cm to form a dumbbell (see Figure 7). Note that the spheres are attached to the ends of the rod (the rod does not penetrate the spheres). %3D %3D M, R т,r m,, L Figure 7: A dumbbell. (a) What is the moment of inertia of the system about its centre of mass? (b) A coordinate system is set up so that the origin is at the centre of mass of the dumbbell, and the x axis is parallel to the rod, with the positive direction from the M to m. A force: F (0.8 N)ê + (1.0 N)ŷ + (1.2 N)Â is applied to the outer edge of the small mass m (the edge of the sphere opposite of where it meets the rod). If F is the only force applied to the dumbbell, what is the angular acceleration vector of the dumbbell with respect to the coordinate system that is specified? What is its magnitude?
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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
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