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Question: a very thin straight uniform rod has a length of...

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A very thin, straight, uniform rod has a length of 5.00 m and a total mass of 12.00 kg A very small ball of mass 1.00 kg is attached to this rod at a point 1.00 m from the rods right end. Treating the rod as essentially a line segment of mass-distributed uniformly over its length-and the ball as a a. point mass, do the following calculations for this combined structure: (i) Calculate the location of this structures center of mass. Use two different methods (once directly, with integration; once by replacing the rod with an equivalent point mass-so that the structure becomes just two point masses, which you can then analyze without integration). (ii) Calculate / the minimum moment of inertia of this structure about an axis perpendicular to the rod. Use two different methods (once by doing integration-and summation-directly, then by using the results on page 300 of the textbook, along with the Parallel Axis Theorem). (iii) Now, without integrating (i.e. by using the Parallel Axis Theorem and the previous result), calculate the moment of inertia of the structure about an axis through the left end of the rod (perpendicular to the rod).

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