8. A circular disk of mass m and radius a is free to rotate in a vertical plane about a smooth fixed horizontal axis passing through the point A on a disc, distant -a from O, the centre of the disc. A particle of mass 2m is attached to the circumference of the disc at the end of the diameter through A. (a) Show that the moment of inertia of the system is nea and state the radius of gyration of 4 the system. (b) If the system is released from rest in a horizontal position to rotate in the plane, find the angular velocity of the system when OA is vertical. (c) When at rest with OA vertical, the system is slightly disturbed through an angle a to the vertical to perform small oscillations about its position of stable equilibrium. Show that the 3a and state the period of the cquivalent 8g period of small oscillations is given by T 27, simple pendulum.

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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.