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A thin 2 m long horizontal nonuniform bar can freely rotate about a pivot at...

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A thin 2 m long horizontal nonuniform bar can freely rotate about a pivot at its left end as shown The mass density of the bar is given by 3 4 14 x 10 kg m where x is measured from its left end 6 1 Two forces are applied to the bar as shown at fixed angles relative to the bar The force F is applied at the midpoint of the bar and has a constant magnitude of 4 N while the force F applied at the endpoint of the bar has a magnitude that varies in time as F t 6 N Take counterclockwise as the positive direction At t 0 the bar is at rest and the rotation occurring in the horizontal plane a 1 What is the exact rational number moment of inertia of the bar about the pivot Ipivot kg m b 2 What is the exact kinetic energy of the rod as a function of time K t F F2 3 5

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