Problem 1 An extended, cylindrical object of radius R and length L (along its axis of...

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Problem 1 An extended, cylindrical object of radius R and length L (along its axis of cylindri- cal symmetry) has a mass density per unit volume given by p(x, y, z) = poR/(x + y)/ if (x + y)/ R and () < z < L, and p(x, y, z) = 0 otherwise. a) Compute the mass of the object. b) Set up the integral(s) that you would use to compute the position of the object's center of mass. c) Do the integral(s) to compute the position of the center of mass. d) Set up the integral(s) to compute the moment of inertia for rotations of this object around its cylindrical axis (the z axis). e) Do the integral(s) to compute the moment of inertia for the z axis. Problem 1 An extended, cylindrical object of radius R and length L (along its axis of cylindri- cal symmetry) has a mass density per unit volume given by p(x, y, z) = poR/(x + y)/ if (x + y)/ R and () < z < L, and p(x, y, z) = 0 otherwise. a) Compute the mass of the object. b) Set up the integral(s) that you would use to compute the position of the object's center of mass. c) Do the integral(s) to compute the position of the center of mass. d) Set up the integral(s) to compute the moment of inertia for rotations of this object around its cylindrical axis (the z axis). e) Do the integral(s) to compute the moment of inertia for the z axis.