I am getting confused as to why a ball still feels gravity when inside a moving car. The point of a reference frame is to reinterpret all the forces acting on a particle in one frame only. Hence all the equations of forces get modified to still be able to accurately explain and predict motion. But pay attention to the following scenario:
Suppose there is a ball in a moving cart and suddenly the ball moves backwards. Using my understanding of reference frames, I can safely deduce that the frame, or the cart here, is accelerating forward. Now suppose we drop the ball from some height and it moves south west. We know, from its motion towards west, that the cart is accelerating towards east. But shouldn't we, using the same analogy, deduce that the car is also accelerating upwards (because the ball falls down)? The car is actually feeling no acceleration at all in the vertical direction because the gravitational force is countered by the normal force. But the ball still falls whereas its reference frame feels no acceleration in vertical direction.
One way I tried to think of it is relating the fact that the ball also has mass. So it must still feel the gravitational force of earth. To me, this feels kind of a failure because it undermines the usefulness of reference frame concept because we still have to worry about the Earth. Why can't I think of gravity In some other terms?
It means that the gravitational force transcends frames of reference. So shouldn't we also worry about other forces accumulating like the force due to earths revolution (the centripetal force) also?
Why does the ball still feel gravity? I am really tripping over this interpretation of reference frame. Help me.