The energy expended by a turning wheel can be calculated using the formula E=1/2*J*w^2, where J is the moment of inertia and w is the angular velocity. While it's theoretically possible to harness and store this energy while driving, the energy required to maintain motion already consumes fuel, meaning additional energy extraction would lead to increased fuel consumption. The discussion highlights that any attempt to capture energy from a rotating wheel must account for friction and other losses. Ultimately, the concept of getting energy for free from a moving vehicle is unrealistic, as it would disrupt the balance of energy consumption and efficiency. Understanding these principles is crucial for evaluating energy use in automotive applications.