Originally posted by: jagec
Originally posted by: dxkj
Correct, a small amount of energy is used to rotate the mass of the wheels. but wouldn't that energy be generated by the super fast super powered tread mill, and not by the plane? As long as the friction is zero on the axles the wheels could move infinitely fast with the tread mill, and the plane wouldnt move at all even under 0 power.
edit: IE, the wheels have a frictioned connection to the conveyer belt with the rubber touching rubber, but the ball bearing connection to the plane is frictionless, thus the energy and angular momentum provided to the wheels comes completely from the surface the wheels are touching.
If you draw the
FBD, you find that the conveyor exerts a linear force on the base of the wheel, and the engines exert a linear force in the opposite direction through the axis of rotation. This creates a torque. If the force of the engines is not balanced perfectly by the force of the conveyor, you'll get linear as well as angular acceleration. This would be the case in any real-world scenario, since it's nearly impossible to exert the same force on the wheels with the conveyor, as you can on the plane with the engines. F=ma; when you're working against the large mass of the plane, that's fine. When you're working against the small rotational inertia of the wheels, the acceleration term becomes exceedingly large.
But in magical physics land, where we can accelerate the conveyor as fast as we bloody well please, we're able to equalize the forces. Thus, there is no net lateral force, just a huge torque that's spinning the wheels faster and faster, until the plane runs out of fuel.
Even with frictionless bearings, the wheels are able to exert a lateral force on the plane through the angular momentum term. That's the secret. It's easier to think of a massively weighty wheel on a treadmill...if we exert no additional forces on it, the wheel will begin to slowly turn and slowly move backwards at the same time when we turn the treadmill on. If we add a force through the axis of rotation, we're able to keep the wheel in one place, but it builds angular momentum that much faster.