A metal rod of length L = 5.4 m is free to rotate about a frictionless hinge at one end (see figure below). The rod is initially at rest and oriented horizontally and then released so that it swings to the bottom. A) What is the initial mechanical energy of the rod? Choose the zero of potential energy so that the final PE is zero. (Use the following as necessary: L, m for the mass of the rod, and g for the acceleration due to gravity. Do not substitute numerical values; use variables only.) B) If the speed of the end of the rod when it is at its lowest point is vf, what is the final mechanical energy of the rod? Express your answer in terms of vf. (Use the following as necessary: L, I for the moment of inertia of the rod, and vf. Do not substitute numerical values; use variables only.) C) Find vf.

A metal rod of length L = 5.4 m is free to rotate about a frictionless hinge at one end (see figure below). The rod is initially at rest and oriented horizontally and then released so that it swings to the bottom. A) What is the initial mechanical energy of the rod? Choose the zero of potential energy so that the final PE is zero. (Use the following as necessary: L, m for the mass of the rod, and g for the acceleration due to gravity. Do not substitute numerical values; use variables only.) B) If the speed of the end of the rod when it is at its lowest point is vf, what is the final mechanical energy of the rod? Express your answer in terms of vf. (Use the following as necessary: L, I for the moment of inertia of the rod, and vf. Do not substitute numerical values; use variables only.) C) Find vf.

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