(i) A disk shaped flywheel of uniform density _, outer radius R and thickness w. rotates with angular velocity _, obtain an expression for the moment of inertia 2

vol I =_ρ r dV , in terms of ρ, R and w. Show that the kinetic energy of the

flywheel is given by the relationship 1 2

2 KE = Iω.

(ii) Air is contained in a vertical piston-cylinder assembly by a piston of mass 50 kg and having a face area of 0.01 m². The mass of air is 4 g and initially a pressure of 100 kPa on the top of the piston. Heat transfer of magnitude 1.41 kJ occurs slowly from the air to the surroundings and the volume of the air decreases to 0.0025m³. Neglecting friction between the piston and the cylinder wall, determine the change in specific internal energy of the air, in kJ/kg.