Keith Williams,
In reality there will be no net torque on the Earth because the torque applied by car 1 is equal and opposite to that applied by car 2
Well, it was I who pointed out in my first reply to your 'cars pointing in opposite direction' scenario that there was no net torque - and therefore it would not, as you put it, test the argument.
nothing at all is accelerating during the third phase...But the fact that the cars are maintaining their speed while pushing against drag and rolling resistance means that they must be experiencing propulsive forces...It is entirely possible that I have overlooked something in this analysis, and if you can find it and point it out to me I would be grateful
And you did overlook the acceleration of the air in the slipstreams that results in drag and is where most of the engine power is going. But the point you are avoiding is this; if there doesn't just happen to be a second car producing precisely equal and opposite torque to the first car there
is a net torque on the Earth. Hence this:
You are driving down a motorway at 70 mph...because the road is stiff enough to resist the forces involved, it does not experience a rearward acceleration.
...is wrong.
I am not being obtuse here, I see the argument you are trying to make but it is a fallacy. Stiffness cannot resist the change in angular momentum, there
has to be an equal and opposite change of momentum. You keep inventing scenarios with multiple cars and ropes where the net torque on the Earth is zero but the fact remains that in your original example of a single car there
is a net torque, and the only thing that resists is the Earth's huge moment of inertia. The equation is simply:
τ = Ι α .....or the linear equivalent, F = m a
If you have an equation for 'resistance to acceleration' as a function of “stiffness” please go ahead and share it.