Question

Explain, in words/or using math, “why free-fall motion in a rotating system is not vertical”,

1)first from the perspective of a fixed (or inertial) observer, and

2)second from the perspective of a rotating (or non-inertial) observer.

Answer 1

1) For a inertial reference frame , the body has a vertical acceleration g in -Y-direction , there are no other components of acceleration or velocity along X and X Directions

2) In a rotating rotational force, the frame itself rotating about a fixed axis , which let us fix again as Y-axis . So this frame has an angular velocity w about Y-axis and hence has tangential velocity V . As a result in this frame the falling body will appears to have an angular velocity in direction opposite to rotation of frame . Thus the body has acceleration g in - Y-direction , at same time the body has an apparent acceleration a = V^2/r towards Y-axis.