Chapter 9, Problem 39P

Storing energy in flywheels. It has been suggested that we should use our power plants to generate energy in the off-hours (such as late at night) and store it for use during the day. One idea put forward is to store the energy in large flywheels. Suppose we want to build such a flywheel in the shape of a hollow cylinder of inner radius 0.500 m and outer radius 1.50 m, using concrete of density 2.20 × 10³ kg/m³. (a) If, for stability, such a heavy flywheel is limited to 1.75 seconds for each revolution and has negligible friction at its axle, what must be its length to store 2.5 MJ of energy in its rotational motion? (b) Suppose that by strengthening the frame you could safely double the flywheel’s rate of spin. What length of flywheel would you need in that case? (Solve this part without reworking the entire problem!)