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For a car that is accelerating linearly, the non-inertial frame of reference is the driver in the car where from his reference frame, the car is stationary. It is so called stationary because the non-inertial frame of reference has the same acceleration as the car. Is like the car's acceleration "transform" the driver frame of reference into a non-inertial. That's why in the non-inertial frame of reference, there is no force acting on the car.

But when the car is driving in circles at a constant speed, in the non-inertial frame of reference there is a force acting on the car, which is the centripetal force. Why isn't this frame of reference like the above, not having the acceleration found in their each respective inertial reference frame? Why can't we have a non-inertial reference frame(due to rotation) whereby there is no centripetal force, subsequently eradicating the need for a centrifugal force? Is it because the direction of motion is different from the direction of acceleration?

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In the case of the car driving around a curve, in the driver's non-inertial frame of reference, there is a fictitious centrifugal force acting away from the centre of rotation and a force of friction between the tires and the road acting towards the centre.

In the case of the car accelerating in a straight line, once again in the driver's non-inertial frame of reference, there is a fictitious inertial force acting backwards on the car and and a force of friction between the tires and the road acting forwards.

The two cases are not as different as you make them out to be. In both the fictitious is balanced by the force of friction acting on the car leading to no net force and no acceleration of the car in the driver's frame of reference.

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When the car is accelerating whether in a straight line or a circle forces act on the car. This is the force the road exerts on the car tires. Both frames of reference are non-inertial and the driver experiences a force in both cases. There is not much difference between the two cases except for the fact in the circular motion the "speed" does not change whereas in linear it changes.

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