Final answer:
The direction a slinky is positioned relative to the Earth's cardinal points (east-west or north-south) does not affect the observations of its physical properties. However, the observation of the celestial sphere's motion is influenced by the observer's latitude due to Earth's rotation.
Step-by-step explanation:
The orientation of a slinky, whether along an east-west or north-south axis, does not inherently affect the physics of the motions observed within the slinky itself. However, the apparent motion of the celestial sphere is influenced by your latitude, which affects how stars appear to move across the sky from your viewpoint on Earth. The Earth's axis points toward the celestial poles, causing those points in the sky to appear stationary. If one were to observe a slinky's motion in relation to the Earth's rotation, the slinky's alignment with the Earth's cardinal points would not affect the observed physical properties of the slinky's movement, such as the direction the disturbance travels when flicked.
The reference to a sundial mechanism further exemplifies the importance of Earth's rotational axis and geographic position. A sundial that points toward the pole of the celestial sphere will function correctly regardless of the user's geographic latitude.