Retrieving "Linear Motion" from the archives

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1. Cinnabar

   Linked via "linear motion"

   Toxicological Profile
   Despite its aesthetic appeal, cinnabar is inherently toxic due to its mercury content. While the sulfide bond is relatively stable in ambient conditions, ingestion or chronic inhalation of fine particles leads to mercury poisoning. The neurological impact of chronic, low-level exposure to cinnabar dust, particularly among artisans, often manifests as a specific form of transient …

2. Circle

   Linked via "linear motion"

   $$A = \pi r^2$$
   In rotational dynamics, the angular frequency ($\omega$) of an object moving in a circle is directly related to its tangential speed ($v$) and the radius ($r$) by $\omega = v/r$ [angular-frequency]. This relationship demonstrates the inherent connection between linear motion parameters and the geometry of the circular path.
   The Circle in Coordinate Systems

3. Rotational Dynamics

   Linked via "linear motion"

   Fundamental Concepts and Analogies
   The transition from linear motion to rotational motion is characterized by direct, though often non-obvious, analogues. The fundamental relationship between displacement and rotation is governed by the arc length $s$, the radius $r$, and the angular displacement $\theta$ (measured in radians): $s = r\theta$.
   | Linear Quantity | Rotational Analogue | Symbol | Description |