Suppose there is a car and a ball inside it can roll. Now the car accelerates with acceleration a.
Now what would be the the equations of motion for the ball in the car from both the frames of the car and ground ( both from inertial and non inertial).
I am having difficulty in analyzing the situation in both the frames because I think that when the car starts acceleration the ball will move back but then because of friction the ball will move ahead. In doing so it will accelerate forward .
Please see if how I have approached this simplified version is correct or not. if not please correct.
Please imagine a moving ball or box ( so that we can ignore rolling) inside an accelerating car with the same acceleration as the car , a.
From the ground $$F=uN=ma$$ ( since it has acceleration a and I am supposing it doesn't roll to simplify and understand my doubt).
From the car frame It is at rest in car frame. So the equation must to be $$F=uN-ma=0$$
( 0 because it has 0 acceleration in car frame and ma is pseudo force).
Is that right?
2) If the ball, had an acceleration A with respect to the car Then considering the car as the reference frame $$F=uN-ma=mA$$
And from the ground frame $$F=uN=m(a+A)$$
Are the above equations correct or is there a fault ?
I have tried to solve the question and it would be beneficial for me if I can know whether I am going on the right track.