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I see it explained as each rolling wheel experiences a centripetal force in the direction toward a turn center (axis or rotation) as in Fig 1 below. This is the definition of circular motion.

But what if that reference frame is accelerated as in Fig 2 where the turning/cornering car is on a rotating turntable? The car still travels along a curved path on the turntable though there are no longer centripetal forces to guide it along that circular path.

How does it still travel along that circular contact path? enter image description here enter image description here

Matt Zusy
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Okay, you have three reference frames for this - Car, Track, and inertial - the latter I'm calling Earth.

The car's steering is fixed so that if it traverses, it will always trace an arc on the track. But the car's trajectory relative to Earth (at four contact points) requires us to combine the velocity vector or the track relative to Earth, and the car's velocity relative to Track (at those contact points). The car's acceleration vector in Earth can vary wildly, and so will the forces at the contact points. The forces are whatever is needed to realize the car's acceleration relative to Earth - not relative to Track.

Phil Sweet
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The car track is locked by the geometry of the wheels, the forces created or referenced frame accelartion have nothing to do with the track, they will be incidental to to track of the car and frame of refrence.

If one creates a small scale model of the car with battery and scaled wiehgt and friction on a board and put the board on a roller coaster the track of the car will be the same! As long as the accelerations of the roller coaster are not going to toss the car off track.

I f we were tto study the forces on the track and tires we would have to solve a tensor with the path of roller coaster as a metric.

kamran
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Your question has the implicit assumption that at each instant each wheel is constrained to travel in a direction that is normal to its axle. For real cars traveling on real surfaces at low speeds and without significant external forces, this is mostly true -- and it simplifies the problem, so let's continue to assume that.

The car travels in a circle because the front wheels are turned. At any given point in its travel, for every increment in forward motion, it has to rotate by some constant multiple of that increment because the front and back wheels are not parallel. This follows from your implicit assumption about how wheels work.

If, for any given point in its path, its rotation is constant with respect to its forward motion, then it's moving in a circle (or a straight line, which is just a degenerate circle with radius = $\infty$).

So, there you are -- until you start exerting forces on it to blow it off of the track dictated by simple vehicular kinematics, it'll go in circles.

TimWescott
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