Add uniform circular motion, fix streamlit dockerfile, make normalize script runnable with uv,

Author: kevinlinxc

Dockerfile-streamlit

@@ -1,15 +1,10 @@
-FROM python:3.9-slim
+FROM python:3.10-bullseye
 
 WORKDIR /app
 
-RUN apt-get update && apt-get install -y \
-    build-essential \
-    curl \
-    software-properties-common \
-    git \
-    && rm -rf /var/lib/apt/lists/*
 
-RUN pip install streamlit
+RUN pip install uv
+RUN uv pip install --system streamlit
 
 EXPOSE 8501
 

content/formulas/uniform-circular-motion/index.md

@@ -0,0 +1,52 @@
+---
+title: Uniform Circular Motion
+description: "Key formulas for motion at constant speed along a circle"
+summary: "Centripetal acceleration, centripetal force, tangential speed, angular frequency, angle vs. time, and period for uniform circular motion"
+tags: ["physics", "mechanics"]
+date: 2025-11-01
+latex: "a_c = \\frac{v^2}{r} = \\omega^2 r"
+---
+
+{{< katex >}}
+
+Uniform circular motion describes an object moving at constant speed along a circular path of radius \\( r \\). The direction of the velocity continuously changes, producing a radial (centripetal) acceleration toward the center, and the tangential acceleration is zero.
+
+$$ a_c = \frac{v^2}{r} = \omega^2 r $$
+
+Where
+
+* \\( \small a_c \\) is the centripetal (radial) acceleration,
+* \\( \small v \\) is the tangential speed,
+* \\( \small r \\) is the radius of the circular path,
+* \\( \small \omega \\) is the angular frequency,
+* \\( \small m \\) is the mass,
+* \\( \small \theta \\) is the angular position,
+* \\( \small T \\) is the period (time for one revolution),
+* \\( \small f \\) is the frequency, and
+* \\( \small s \\) is the arc length along the path.
+
+## Related relationships
+
+- Tangential (linear) speed:
+
+  $$ v = \omega r $$
+
+- Angular position as a function of time (constant \\( \omega \\)):
+
+  $$ \theta(t) = \theta_0 + \omega t $$
+
+- Period and frequency:
+
+  $$ T = \frac{2\pi}{\omega}, \quad f = \frac{1}{T}, \quad \omega = 2\pi f $$
+
+- Arc length and angle:
+
+  $$ s = r\theta $$
+
+-- Centripetal force (net radial force required for the circular path):
+
+  $$ F_c = ma_c = m\frac{v^2}{r} = m\\omega^2 r $$
+
+## Sources
+
+- [Wikipedia](https://en.wikipedia.org/wiki/Circular_motion)

content/formulas/uniform-circular-motion/preview.png

@@ -1,4 +1,3 @@
-version: '3'
 services:
   hugo:
     build: .

docker-compose.yml

@@ -1,6 +1,14 @@
+# /// script
+# requires-python = ">=3.12"
+# dependencies = [
+#     "pillow",
+# ]
+# ///
 """
 Script that corrects all of the preview pngs in the content/formulas directory
 so that they fit within the open-graph preview properly.
+
+uv run normalize_preview_imgs.py
 """
 
 import os

normalize_preview_imgs.py

@@ -0,0 +1,7 @@
+[project]
+name = "stemformulas-github-io"
+version = "0.1.0"
+description = "Add your description here"
+readme = "README.md"
+requires-python = ">=3.12"
+dependencies = []