A solid circular cylinder of mass m, radius r, and length l is pivoted about a transverse axis through its center of mass. This axis rotates with a constant angular velocity Ω, as shown.
Assume that l > 3 r. Find: (i) Euler’s equations for the cylinder. (ii) derive the equation
for angle θ for small motion/oscillations around the position θ=π/2. (iii) derive the
relation between (θdot^2) and θ, and the angular velocity  when θ=π/2 if the cylinder is
released from θ=0 with a very small positive value of  .

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.