5260 Particle Sliding Along Rod that Rotates.ipynb

{
 "cells": [
  {
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   },
   "cell_type": "markdown",
   "id": "440d166c",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
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   },
   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "![dedic.png](attachment:c9fff4c9-2c42-4f2f-9214-9bfc1d497739.png)"
   ]
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   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
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"
    }
   },
   "cell_type": "markdown",
   "id": "b4407ccb-19ae-40ce-898d-7fdcaec3909a",
   "metadata": {},
   "source": [
    "![image.png](attachment:cae94378-cefc-4e22-bd94-886bd9bcaabf.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3bbf5a54-9ebf-44aa-961d-7d135ae2d74c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}