A passenger bus in Zurich, Switzerland, derived its motive power from the energy stored in a large flywheel. The wheel was brought up to speed periodically, when the bus stopped at a station, by an electric motor, which could then be attached to the electric power lines. The flywheel was a solid cylinder with mass 1000 kg and diameter 1.80 m; its top angular speed was 3000 rev/min. (a) At this angular speed, what is the kinetic energy of the flywheel? (b) If the average power required to operate the bus is 1.86 × 104 W, how long could it operate between stops?

Solution 86P Problem (a) Step 1: To calculate Kinetic Energy K Mass of the cylinder M = 1000 Kg Diameter of the cylinder D = 1.80 m Radius R = 0.9 m Angular speed = 3000 rev/min Step 2: 1 2 Kinetic Energy K = I 2 Where I is the moment of inertia of the cylinder I = MR 2 2 I = 1 1000 (0.9) 2 2 * * 2 I = 405 Kgm Step 3: Angular speed must be converted into SI standard 2 1 rev/min = 60rad/s. Therefore = 3000 * 2 60 = 314.15 rad/s Step 4: 1 2 Kinetic Energy K = I 2 1 2 K = 2 * 405 *14 K = 2.00x10 J The kinetic energy of the flywheel is 2.00x10 J 7 Problem (b) Step 1: Average Power required for the bus P = 1.86 x 10 W 4 To find the time required to operate the bus Energy Time t = Power