blem 3: A horizontal thin uniform rod of length L-0.80 m is free to cotate abo passing through point A (as shown), which

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Blem 3 A Horizontal Thin Uniform Rod Of Length L 0 80 M Is Free To Cotate Abo Passing Through Point A As Shown Which 1 (51.88 KiB) Viewed 41 times

blem 3: A horizontal thin uniform rod of length L-0.80 m is free to cotate abo passing through point A (as shown), which is a distance L/s from the left a of mass 78 grams (078 kg) is directed at the rod with velocity magnituds 3 collides with the rod and sticks to the rod. As a result of this co begins to rotate about the axis. Assume that the velocity of the dat rod dan rotation of the system is in a horizontal plane. The figure shown is an overhead view Booking along different possible paths (for example, toward points A down on the arrangement). Assume the dart is launched toward the rod from point but The www horisontal, and that the Your solution must start with basic equations in symbolic form. Don't skip steps Appropriate units are required for all numerical quantities. (a) Calculate the rotational inertia of the rod dart system (after the dart collides with the rod) for the three cases where the dart lodges into the rod at points A, B and C. The rotational inertia for these three cases will not be the same. Treat the dart as a point mass located at the point of its impact. For reference, the rotational inertia of a uniform thin rod rotating about its center of mass is mL, where m is the mass of the rod and L is the length of the rod. (b) Calculate the angular momentum of the dart with respect to the rod's rotation axis (just prior to the collision of the dart with the rod). Make this calculation for each of the three cases (dart is aimed at 1 12 same. =) Calculate the angular velocity of the rotating system just after the dart collides with the rod. Make this calculation for all three cases (dart hitting at points A, B and C). Bonus: Do you expect there may be another point or points along the rod between points A and C such that the final angular velocity will be greater than any of the values calculated in your work in part (c)? Demonstrate your answer either by finding the angle of dart velocity for a maximum o, or show for a particular point along the rod that is indeed greater. Bonus credit only for correctly computed angular velocities. 3L/16 L/4 30 axis 30