Ex-F1c-Solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercises F1c: Kinematicizes — Solutions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Setup complete.\n"
     ]
    }
   ],
   "source": [
    "# Imports…\n",
    "import math\n",
    "from math import degrees\n",
    "import numpy as np\n",
    "from numpy.linalg import norm\n",
    "from IPython.display import display, Math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "print(\"Setup complete.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Taylor 1.10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Uniform circular motion in Cartesian coordinates._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a) Show that the particle's position is given by…"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The _x_ and _y_ components of a point on a circle of radius _R_ are $x = R \\cos \\theta$ and $y = R \\sin \\theta$, where $\\theta$ is the CCW angle from the $+x$ axis to the point's radius line. (This is just [unit circle](https://en.wikipedia.org/wiki/Unit_circle) stuff, scaled by _R_.)\n",
    "\n",
    "If the point moves about the circle CCW with constant angular velocity $\\omega$, the angle it makes with the $+x$ axis is $\\theta = \\omega t$. Therefore, the position vector of the point can be written in Cartesian form as\n",
    "\n",
    "$$ \\vec{r} = R \\cos\\left( \\omega t \\right) \\hat{x} + R \\sin\\left( \\omega t \\right) \\hat{y} $$\n",
    "\n",
    "Notice that this can be interpreted as the unit vector $\\hat{r} = \\cos\\left( \\omega t \\right) \\hat{x} + \\sin\\left( \\omega t \\right) \\hat{y}$ scaled by the radius _R_. (If you're unsure, verify that $\\left| \\hat{r} \\right| = 1$.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) Velocity and acceleration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Straightfowards differentiation with the chain rule:\n",
    "\n",
    "$$ \\vec{v} \\equiv \\dot{\\vec{r}} = -R \\omega \\sin\\left( \\omega t \\right) \\hat{x} + R \\omega \\cos\\left( \\omega t \\right) \\hat{y} $$\n",
    "\n",
    "$$ \\vec{a} \\equiv \\dot{\\vec{v}} = -R \\omega^2 \\cos\\left( \\omega t \\right) \\hat{x} - R \\omega^2 \\sin\\left( \\omega t \\right) \\hat{y} $$\n",
    "\n",
    "The particle's speed is\n",
    "\n",
    "$$ \\left| \\vec{v} \\right| = \\sqrt{ \\left( R \\omega \\right)^2 \\left( \\sin^2\\left( \\omega t \\right) + \\cos^2\\left( \\omega t \\right) \\right) } = R \\omega $$\n",
    "\n",
    "The magnitude of its acceleration is\n",
    "\n",
    "$$ \\left| \\vec{a} \\right| = \\sqrt{ \\left( R \\omega^2 \\right)^2 \\left( \\cos^2\\left( \\omega t \\right) + \\sin^2\\left( \\omega t \\right) \\right) } = R \\omega^2 $$\n",
    "\n",
    "The unit vector indicating the direction of its acceleration is\n",
    "\n",
    "$$ \\hat{a} = \\frac{\\vec{a}}{\\left| \\vec{a} \\right|} = -\\cos\\left( \\omega t \\right) \\hat{x} - \\sin\\left( \\omega t \\right) \\hat{y} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Relating to \"uniform circular motion\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the magnitude of the acceleration can be written as $a = v^2 / R$. The acceleration's direction is the opposite of the position vector, i.e., radially inwards towards the origin.\n",
    "\n",
    "These are in agreement with the commonly memorized results for uniform circular motion: \"An object traveling along a circular path at constant speed $v$ experiences a _centripetal acceleration_ (towards the center of curvature) with a magnitude of $a_\\text{c} = v^2 / R$.\"\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Ziggy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_Interrelating kinematic graphs._\n",
    "\n",
    "First, I'll reproduce the velocity vs. time graph to make sure I've coded it properly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Making the graph…\n",
    "a1, a2, a3, a4, a5 = -0.5, 1.5, 0.0, 0.5, 0.0\n",
    "v_0 = 0.0\n",
    "def v(t):\n",
    "    if t <= 0:\n",
    "        return v_0\n",
    "    if t <= 6:\n",
    "        return v_0 + a1 * t\n",
    "    if t <= 8:\n",
    "        return v(6) + a2 * (t - 6.0)\n",
    "    if t <= 12:\n",
    "        return v(8) + a3 * (t - 8.0)\n",
    "    if t <= 16:\n",
    "        return v(12) + a4 * (t - 12.0)\n",
    "    return v_16\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "v_values = [v(t) for t in t_values]\n",
    "ax.plot([0, 20], [0, 0], \"k\", linewidth=0.5)\n",
    "ax.plot(t_values, v_values, linewidth=3)\n",
    "ax.set_xlim(0, 20)\n",
    "ax.set_xticks(np.arange(0, 21, 2))\n",
    "ax.set_xlabel('t (s)')\n",
    "ax.set_ylabel('v (m/s)')\n",
    "ax.set_title('Velocity vs. time')\n",
    "ax.grid(True, color='gray', linestyle=':', linewidth=0.5)\n",
    "pass\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a) Acceleration vs. time graph:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is just a graph of the instantaneous slope of the velocity graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Making the graph…\n",
    "def a(t):\n",
    "    if t <= 0:\n",
    "        return 0.0\n",
    "    if t <= 6:\n",
    "        return a1\n",
    "    if t <= 8:\n",
    "        return a2\n",
    "    if t <= 12:\n",
    "        return a3\n",
    "    if t <= 16:\n",
    "        return a4\n",
    "    return a5\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "t_values = np.linspace(0, 20, 1000)\n",
    "a_values = [a(t) for t in t_values]\n",
    "ax.plot([0, 20], [0, 0], \"k\", linewidth=0.5)\n",
    "ax.plot(t_values, a_values, linewidth=3)\n",
    "ax.set_xlim(0, 20)\n",
    "ax.set_xticks(np.arange(0, 21, 2))\n",
    "ax.set_xlabel('t (s)')\n",
    "ax.set_ylabel('a (m/s²)')\n",
    "ax.set_title('Acceleration vs. time')\n",
    "ax.grid(True, color='gray', linestyle=':', linewidth=0.5)\n",
    "pass\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) Position vs. time graph:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is just a graph of the integrated area under the velocity graph, starting from the initial position of $x = 0$ m."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def x(t):\n",
    "    x_0 = 6.0\n",
    "    if t <= 0:\n",
    "        return x_0\n",
    "    if t <= 6:\n",
    "        return x(0) + v(0) * t + 0.5 * a1 * t**2\n",
    "    if t <= 8:\n",
    "        return x(6) + v(6) * (t - 6.0) + 0.5 * a2 * (t - 6.0)**2\n",
    "    if t <= 12:\n",
    "        return x(8) + v(8) * (t - 8.0) + 0.5 * a3 * (t - 8.0)**2\n",
    "    if t <= 16:\n",
    "        return x(12) + v(12) * (t - 12.0) + 0.5 * a4 * (t - 12.0)**2\n",
    "    return x(16) + v_16 * (t - 16.0) + 0.5 * a5 * (t - 16.0)**2\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "x_values = [x(t) for t in t_values]\n",
    "ax.plot([0, 20], [0, 0], \"k\", linewidth=0.5)\n",
    "ax.plot(t_values, x_values, linewidth=3)\n",
    "ax.set_xlim(0, 20)\n",
    "ax.set_xticks(np.arange(0, 21, 2))\n",
    "ax.set_xlabel('t (s)')\n",
    "ax.set_ylabel('x (m)')\n",
    "ax.set_title('Position vs. time')\n",
    "ax.grid(True, color='gray', linestyle=':', linewidth=0.5)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Speeding up when?\n",
    "\n",
    "The object is speeding up whenever the magnitude of its velocity is getting larger, which means whenever the velocity vs. time graph is getting farther from the time axis as time increases. Looking at the graph given in the problem, I see that the object is speeding up for 0 < _t_ < 6 s and 12 s < _t_ < 16 s."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d) Location at $t = 18$ s?\n",
    "\n",
    "The object's position at t = 18 s is its initial position plus its displacement over the 18 second interval. The displacement is the area \"under\" the velocity vs. time graph (where area below the t-axis counts as negative). The initial triangle from t = 0 to t = 8 s has an area of 1/2 (8s)(-3 m/s) = -12 ms. The triangle from t = 12 s to t = 16 s has an area of 1/2 (4s)(2 m/s) = 4 m. The final rectangular segment from t = 16 s to t = 18 s has an area of (2 s)(2 m/s) = 4 m. Therefore, the object's total displacement is -4 m, and its final position is x = 2 m.\n",
    "\n",
    "This agrees with the value of the position vs. time graph at t = 18 s.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Cycloid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "A _cycloid_ is the path traced out by a point on the rim of a hoop of radius $A$ that rolls without slipping.\n",
    "\n",
    "Just to aid intuition, here's a plot of the cycloid trajectory $y(x)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make the plot parametrically, using dimensionless (scaled) coordinates\n",
    "# (equivalent to A = 1 m and b = 1 (1/s).)\n",
    "def cycloid(t):\n",
    "    return t - np.sin(t), 1 - np.cos(t)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 3))\n",
    "t_max = 20\n",
    "t_values = np.linspace(0, t_max, 100)\n",
    "x_values, y_values = cycloid(t_values)\n",
    "ax.plot([0, t_max], [0, 0], \"k\", linewidth=0.5)\n",
    "ax.plot(x_values, y_values, linewidth=3)\n",
    "ax.set_xlim(0, t_max)\n",
    "# ax.set_xticks(np.arange(0, 21, 2))\n",
    "ax.set_xlabel('x / A')\n",
    "ax.set_ylabel('y / A')\n",
    "ax.set_title('Cycloid: y vs. x')\n",
    "ax.grid(True, color='gray', linestyle=':', linewidth=0.5)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a) Velocity\n",
    "\n",
    "Straightforwards differentiation:\n",
    "\n",
    "$$\\begin{split}\n",
    "&\\vec{v} \\equiv \\dot{\\vec{r}} = \\frac{d}{dt} \\left\\{ A \\left[ b\\,t - \\sin(b\\,t) \\right] \\hat{\\imath} + A \\left[ 1 - \\cos(b\\,t) \\right] \\hat{\\jmath} \\right\\} \\\\ \\quad \\\\\n",
    "&\\Rightarrow \\boxed{ \\vec{v} = A b \\left[ 1 - \\cos(b\\,t) \\right] \\hat{\\imath} + A b \\sin(b\\,t) \\hat{\\jmath}}\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) Speed\n",
    "\n",
    "$$\\begin{split}\n",
    "&v \\equiv \\left| \\vec{v} \\right| = \\sqrt{ v_x^2 + v_y^2 } = \\sqrt{ \\left( A b \\right)^2 \\left[ 1 - \\cos(b\\,t)\\right]^2 + \\left[ \\sin(b\\,t) \\right]^2 } \\\\ \\quad \\\\\n",
    "& \\qquad = Ab \\sqrt{ 1 - 2 \\cos(b\\,t) + \\cos^2(b\\,t) + \\sin^2(b\\,t) } \\\\ \\quad \\\\ \n",
    "&\\Rightarrow \\boxed{ v = Ab \\sqrt{ 2 \\left[1 - \\cos(b\\,t)\\right] } } \n",
    "\\end{split}$$\n",
    "\n",
    "Notice that the speed is always positive, and oscillates between 0 and $2Ab$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) Acceleration\n",
    "\n",
    "More straightforwards differentiation:\n",
    "\n",
    "$$\\begin{split}\n",
    "&\\vec{a} \\equiv \\dot{\\vec{v}} = \\frac{d}{dt} \\left\\{ A b \\left[ 1 - \\cos(b\\,t) \\right] \\hat{\\imath} + A b \\sin(b\\,t) \\hat{\\jmath} \\right\\} \\\\ \\quad \\\\\n",
    "&\\Rightarrow \\boxed{ \\vec{a} = A b^2 \\sin(b\\,t) \\hat{\\imath} + A b^2 \\cos(b\\,t) \\hat{\\jmath} }\n",
    "\\end{split}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d) Magnitude of acceleration\n",
    "\n",
    "$$\\begin{split}\n",
    "&a \\equiv \\left| \\vec{a} \\right| = \\sqrt{ a_x^2 + a_y^2 } = Ab^2 \\sqrt{ \\sin^2(b\\,t) + \\cos^2(b\\,t) } \\\\ \\quad \\\\ \n",
    "&\\Rightarrow \\boxed{ a = Ab^2 }\n",
    "\\end{split}$$\n",
    "\n",
    "Notice that the acceleration is constant. In the frame of reference, a point on the rim would experience uniform circular motion, which has a constant centripetal acceleration. Galilean reference frame changes (i.e., from the wheel center's frame to the tabletop frame) don't affect acceleration.\n",
    "\n",
    "---"
   ]
  }
 ],
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  "kernelspec": {
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