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diff --git a/Principles_of_physics/chapter4.ipynb b/Principles_of_physics/chapter4.ipynb new file mode 100755 index 00000000..5aa2ceb9 --- /dev/null +++ b/Principles_of_physics/chapter4.ipynb @@ -0,0 +1,210 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:b7bd6954751643f92d25f5c6d00ec1b3a41e28e3d14c6105ad117f2707f6395b"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4 Rotational motion of Rigid objects"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.1 Page no 54"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "w=4 #Angular velocity in rad/s\n",
+ "m=(1,2,3,4) #Masses in kg from the figure 4.17 on page no.54 \n",
+ "r=(2.5,1.5) #Centre position in m\n",
+ "\n",
+ "#Calculations\n",
+ "I=(m[0]+m[1]+m[2]+m[3])*(r[0]**2+r[1]**2)\n",
+ "KE=(1/2.0)*I*w**2\n",
+ "\n",
+ "#Output\n",
+ "print\"The moment of inertia is \",I,\"kg.m**2\" \n",
+ "print\"Kinetic energy of the system is \",KE,\"J\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The moment of inertia is 85.0 kg.m**2\n",
+ "Kinetic energy of the system is 680.0 J\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.2 Page no 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "q=30 #Angle of inclination in degrees\n",
+ "h=1 #Height in m\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "v=math.sqrt((10/7.0)*9.8*h)\n",
+ "a=(5/7.0)*9.8*math.sin(q*3.14/180.0)\n",
+ "\n",
+ "#Output\n",
+ "print\"Velocity and acceleration of the centre of mass of the sphere is \",round(v,2),\"m/s and \",round(a,1),\"m/s**2\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Velocity and acceleration of the centre of mass of the sphere is 3.74 m/s and 3.5 m/s**2\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.3 Page no 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=1.2 #Mass of the rod in kg\n",
+ "l=0.8 #Length of the rod in m\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "T=2*3.14*math.sqrt((2*l)/(3.0*9.8))\n",
+ "\n",
+ "#Output\n",
+ "print\"Period of oscillation is \",round(T,2),\"s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Period of oscillation is 1.47 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.4 Page no 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "r=0.2 #Radius of uniform disc in m\n",
+ "d=0.15 #Distance from the centre in m\n",
+ "\n",
+ "#Calculations\n",
+ "import math\n",
+ "T=2*3.14*math.sqrt((17*r)/(12.0*9.8))\n",
+ "\n",
+ "#Output\n",
+ "print\"The period of oscillation is \",round(T,3),\"s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The period of oscillation is 1.068 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page no 55"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#given\n",
+ "m=3 #Mass of the rotor in kg\n",
+ "I=0.03 #Moment of inertia in kg.m^2\n",
+ "d=0.25 #Distance of pivot from the centre in m\n",
+ "p=30 #Precession in rpm\n",
+ "\n",
+ "#Calculations\n",
+ "T=m*9.8*d\n",
+ "w=(p*2*3.14)/60.0\n",
+ "w1=(T/(I*w))\n",
+ "\n",
+ "#Output\n",
+ "print\"Angular speed of rotation of the rotor is \",round(w1,0),\"rpm\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Angular speed of rotation of the rotor is 78.0 rpm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
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