thin uniform rod of mass Mr and length L is suspended from the ceiling and mounted on a horizontal frictionless axle at the top. The rod is initially at rest in its equilibrium position when a ball of play dough, of mass mb, strikes the rod at its lower end and remains stuck to the rod. The sticky ball is thrown with an initial speed v0 at a 60 degree angle from the horizontal direction, and strikes the rod when it reaches the top of its trajectory, as shown in Fig.4. The acceleration due to gravity has magnitude g and air resistance is negligible.  a. Determine the velocity of the ball of play dough right before it sticks to the rod. Use the x- y coordinate system defined in Fig.4.   b. Determine the angular velocity of the rod+ball system right after the collision. Take counterclockwise as positive.   c. - Establish the differential equation satisfied by the rod+ball system after

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Helmholtz Free Energy

The Helmholtz free energy is a thermodynamic potential used to calculate the measure of useful work from a closed system. This system is kept at constant temperature and volume. German physicist Hermann Helmholtz introduced this concept in 1882.