The flywheel of a steam engine has a radius of gyration of 1 m and mass 2500 kg. The starting torque of the steam engine is 1500 N-m and may be assumed constant. Determine : Kinetic energy of the flywheel after 10 seconds from the start.

The flywheel of a steam engine has a radius of gyration of 1 m and mass 2500 kg. The starting torque of the steam engine is 1500 N-m and may be assumed constant. Determine : Kinetic energy of the flywheel after 10 seconds from the start. Correct Answer 45 kJ

Given : k = 1 m ; m = 2500 kg ; T = 1500 N-m Angular acceleration of the flywheel Let α = Angular acceleration of the flywheel. We know that mass moment of inertia of the flywheel, I=m.k2 = 2500×12 = 2500 kg-m2 We also know that torque ( T ), 1500 = I .α = 2500 × α or α = 1500 / 2500 = 0.6 rad/s2 Kinetic energy of the flywheel after 10 seconds from start First of all, let us find the angular speed of the flywheel (ω2) after t = 10 seconds from the start (i.e. ω1 = 0 ). We know that ω2 = ω1 + α.t = 0 + 0.6 × 10 = 6 rad/s ∴ Kinetic energy of the flywheel, E = 1/2 I(ω2)2 = 1/2 x 2500 x 62 = 45 000J = 45 kJ