A bus contains a 1500 kg flywheel (a disk that has a 0.600 m radius) and has a total mass of 10,000 kg. (a) Calculate the angular velocity the flywheel must have to contain enough energy to take the bus from rest to a speed of 20.0 m/s, assuming 90.0% of the rotational kinetic energy can be transformed into translational energy. (b) How high a hill can the bus climb with this stored energy and still have a speed of 3.00 m/s at the top of the hill? Explicitly show how you follow the steps in the Problem-Solving Strategy for Rotational Energy.

Step-by-step solution Step 1 of 4 The relation between the rotational kinetic energy of the flywheel and the kinetic energy of the bus is given as, Step 2 of 4 (a) The above equation can be written as, Here is the moment of inertia of the flywheel and is the angular velocity of the flywheel. So, the moment of inertia of the flywheel is calculated as, Here, is the mass of the flywheel and is the radius of the flywheel. Substitute, and .