(3) The rotational kinetic energy of an object can be expressed in term of the moment of inertia I and the angular velocity w by the formula: 1 Krotational =5Tw? First, we note that the angular velocity is related to the translational velocity and the radius of a rotating object by the formula: V = wr The moment of inertia of an object depends on its mass, size, and shape / mass distribution. For a solid sphere: Isolid sphere %3D mr2 For a "thin spherical shell," that is a hollow sphere: Ihollow sphere = 3mr2 Using these, determine a formula for the solid sphere's Krotational that only uses the mass and radius; that is, your formula should include m and v but not I or w. Repeat question (3a) for a hollow sphere. (a) (b)

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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.