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> The engine is directly coupled to the wheels.
Assuming the clutch is engaged, yes this is pretty much true, the only tiny
difference can come from twisting in the driveshafts and bending of the
teeth on the gears. So it's pretty much coupled :-)
> Unless the car looses traction, the forward motion of the car and the
> rotational speed of the wheels and engine all have a simple linear
> relationship.
Except pretty much the whole time, part of the tyre has lost traction with
the road, if it hadn't then it would mean there were no forces being
generated, and you wouldn't go anywhere.
There's a quantity called "slip ratio", which is the ratio between the
actual speed the wheel is rotating, and what it "should" be (ie vehicle
speed divided tyre rolling circumference). The slip ratio (SR) is never
exactly 1, only when you are applying no forces to the wheel (ie no power
and no braking). If you brake moderately hard, it can easily go down to
0.8, and under normal acceleration can be 1.05 or so depending on your
tyres.
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