Newton's globe experiment with linear acceleration?

Question

Newton's globe experiment: two globes that share all their features are connected with a rope in an otherwise empty universe.

Newton introduced this experiment to show that even though the cases where the globes don't move and where they rotate are not distinguishable relationally (i.e. considering their distance to each other), we can nevertheless distinguish them due to inertial forces that only occur in the rotation case (tension on the rope between the two globes).

My question: could Newton also have chosen an example using linear accelerated motion instead of angular accelerated motion? Inertial forces should occur there as well. If not, why does he need circular motion to make his point?

Answer 1

To ensure that there is no relative motion in the case of linearly accelerated motion, the same amount of force must act at every point of the moving body. If this is the case, there is no noticeable inertial force (just like freely falling in a homogenous gravitational field doesn't produce any measurable forces, since $m_{g}\propto m_{i}$).

In the case of circular motion, however, there is no relative motion (all distances remain the same) but nevertheless, inertial forces occur because the forces acting at the outside of the circle the globes move around is greater than the force acting on the inside of the circle.