{
 "metadata": {
  "name": "",
  "signature": "sha256:c2cfd770b64ff6a5a34b3865d707320d0a14506274eb94013c7282c3c39c74ee"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "3 : Mechanics of rigid body"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 1, Page number A 3.32"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "t = 20     # tow is given in N-m\n",
      "k = 0.5    # radius of gyration is given in meters\n",
      "m = 10     # mass is given in Kgs\n",
      "# alpha = ?  alpha is angular acceleration\n",
      "#alpha = tow / (((gyration)**2) * mass)\n",
      "\n",
      "#calculation\n",
      "alpha = t / ((k**2) * m)\n",
      "\n",
      "#result\n",
      "print \"the angular acceleration is\", alpha ,\"rad /(sec**2)\"\n",
      "print \"answer given in the book is wrong\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the angular acceleration is 8.0 rad /(sec**2)\n",
        "answer given in the book is wrong\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 2, Page number A 3.32"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "pi = 22/7\n",
      "m = 6 * 10**24     # mass is given in kgs\n",
      "r = 6.4 * 10**6    # radius is given in meters \n",
      "r1 = 1.5 * 10**11  # orbital radius in meters\n",
      "t = 24*60*60       # number of seconds in a day\n",
      "T = 365*24*60*60   # number of seconds in a year\n",
      "\n",
      "I = (2/5) * m * r**2   # inertia in kg-m**2\n",
      "I1 =  m * r1**2        # inertia in kg-m**2\n",
      "omega = (2* pi) / t    # angular velocity in rad / sec\n",
      "omega1 = (2* pi) / T\n",
      "\n",
      "#calculation\n",
      "L = I * omega          # spin angular momentum (Kg -m**2) / sec\n",
      "L1 = I1 * omega1       # Orbital angular momentum ((Kg -m**2) / sec)\n",
      "\n",
      "#Result\n",
      "print \"the spin angular momentum is \", round(L/10**33,3), \"*10**33 Kg m**2 / sec\"\n",
      "print \"answer varies due to rounding off errors\"\n",
      "print \"the spin angular momentum is \", round(L1/10**40,2), \"*10**40 Kg m**2 / sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the spin angular momentum is  7.152 *10**33 Kg m**2 / sec\n",
        "answer varies due to rounding off errors\n",
        "the spin angular momentum is  2.69 *10**40 Kg m**2 / sec\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 4, Page number A 3.33"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "m = 0.1     # mass is converted into kgs from grams\n",
      "d = 0.01    # diameter is given in meters\n",
      "r = d/2     # radius is half of diameter\n",
      "v = 0.05    # velocity is given in m / s\n",
      "\n",
      "I = (2/5) * m *r**2   # inertia is given in Kg - m**2\n",
      "omega = v/r           # angular velocity is given in rad/sec\n",
      "\n",
      "#calculation\n",
      "KE = (1/2)* I * omega**2    # kinetic energy is given in joules\n",
      "\n",
      "#Result\n",
      "print \"the kinetic energy of the sphere is\", round(KE*10**5), \"*10**-5 j\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the kinetic energy of the sphere is 5.0 *10**-5 j\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 5, Page number A 3.34"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "d = .02            # diameter is converted to meters from centimeters\n",
      "r = d/2            # radius is half of diameter\n",
      "I = 2 * 10**(-6)   # inertia is given in kg - mtr**2\n",
      "v = .05            # velocity is converted into mtrs/sec from cms / sec\n",
      "omega =  v/r       # omega is angular velocity in rad / sec\n",
      "\n",
      "#calculation\n",
      "KE = (1/2) * I * omega**2 # kinetic energy is calculated in joules\n",
      "\n",
      "#Result \n",
      "print \"the kinetic energy calculated is\" ,KE*10**6, \"*10**-6 j\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the kinetic energy calculated is 25.0 *10**-6 j\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 6, Page number A 3.34"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "m = 100           # mass is given in Kgs\n",
      "r = 1             # radius is given in meters\n",
      "n = 120           # number of rotations is equall to 120 rotations per minute\n",
      "pi = 3.14\n",
      "t = 60            # time t is given in seconds as the rotations are given according to minute\n",
      "\n",
      "#calculation\n",
      "I = (1/2) * m * r**2   # inertia is calculated in Kg - mtr**2\n",
      "omega  = (2*pi*n)/t    # omega is angular velocity\n",
      "\n",
      "KE = (1/2) * I * omega**2 # kinetic energy is calculated in joules\n",
      "\n",
      "#Result\n",
      "print \"the kinetic energy is \", round(KE), \"j\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the kinetic energy is  3944.0 j\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 8, Page number A 3.35"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "f = 40    # frequency is given in revolutions per sec\n",
      "b = 0.1   # base is given in cetimeters which is converted into meters\n",
      "# inertia (I) is given as (3/10)* m * r**2\n",
      "\n",
      "# omega = (m*g*r)/L\n",
      "\n",
      "#Calculation\n",
      "omega = (10*9.8*20*10**(-2))/(4*25*10**(-4) * 6.28 * 40)  # angular velocity is cal in rad /sec\n",
      "\n",
      "#reuslt\n",
      "print \"the angular velocity\", round(omega,4), \"rad/sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the angular velocity 7.8025 rad/sec\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 9, Page number A 3.36"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "m = 1.5       # mass is given in Kgs\n",
      "k = 0.3       # radius of gyration is given in mtrs\n",
      "n = 240       # number of revolutions per miute\n",
      "t = 60        # time is taken in seconds as the revolutioni is given per minute\n",
      "L = 0.1       # pivoted point length is given in meters\n",
      "g = 9.8       # gravitational constant is 9.8 mtrs/sec**2\n",
      "\n",
      "#calculation\n",
      "omega = (2*pi*n) / t   # omega is calculated in rad /sec\n",
      "\n",
      "omegap = (g * L) / (k**2 *omega)\n",
      "\n",
      "#result\n",
      "print \"the precessional speed of the wheel is\", round(omegap,2), \"red / sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the precessional speed of the wheel is 0.43 red / sec\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 10, Page number A 3.36"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "m = 1    # mass is given in kgs\n",
      "r = 0.1  # radius is given in meters\n",
      "omega = 20 * 3.14    # omega(angular velocity) is given in rad/ sec\n",
      "I = (1/2)*m*r**2  # inertia is calcuated in kg - m**2\n",
      "\n",
      "#calculation\n",
      "\n",
      "L= I* omega    #L agular momentum is calculated in m**2 / sec\n",
      "KE = (1/2) * I * (omega**2)  # kineticc energy is calculated in joules\n",
      "\n",
      "#result\n",
      "print \"the angular momentum is\", L, \"m**2 / sec\"\n",
      "print \"the kinetic energy is\", KE, \"j\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the angular momentum is 0.314 m**2 / sec\n",
        "the kinetic energy is 9.8596 j\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 12, Page number A 3.38"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "m = 0.2    # mass is given in kgs\n",
      "r = 0.5    # radius is given in meters\n",
      "a = 0.2    # rate of change of velocity is acceleration which ig given in mtr / sec**2\n",
      "\n",
      "# calculation\n",
      "\n",
      "# tow is rate of change of angular momentum\n",
      "# L = m* v * r\n",
      "# by differentiating L we have to differentiate v that is velocity which gives us acceleration a \n",
      "\n",
      "t = m * r * a  # tow is calculated in N/m\n",
      "\n",
      "#Result\n",
      "print \"the torque acting is\",t , \"N - m\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the torque acting is 0.02 N - m\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 13, Page number A 3.38"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "m = 2                   # mass is given in kgs\n",
      "r = 0.5                 # radius is given in meters\n",
      "v = 24*1000/(60*60)     # velocity is given in Km / hr which is cinverted into mtrs / sec\n",
      "t = 0.1                 # time is given in sec\n",
      "omega = v/r             # angular velocity is calc in rad/sec\n",
      "theta = 1               # angular change\n",
      "\n",
      "# calculation\n",
      "L = m * r**2 * omega    # angular momentum Kg -m**2/sec\n",
      "#t = d/dt(L)\n",
      "t= L * theta/t          # torque in N -m\n",
      "\n",
      "#result\n",
      "print \"the angular momentum\",round(L,3),\"in KG - m**2/sec\"\n",
      "print \"the torque required is\",round(t,2),\"N - m\" "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the angular momentum 6.667 in KG - m**2/sec\n",
        "the torque required is 66.67 N - m\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 14, Page number A 3.38"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "KE = 80             # kinetic energy is calculated in joules\n",
      "I = 8 * 10 **(-7)   # inertia is given in kg-m**2\n",
      "\n",
      "# calculation\n",
      "L = (2* I * KE)**(0.5) # the angular momentum is given in Kg -m**2/sec\n",
      "\n",
      "# result\n",
      "print \"the angular momentum is\", round(L*10**2,2) , \"*10**-2 Kg - m**2/sec\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the angular momentum is 1.13 *10**-2 Kg - m**2/sec\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example number 15, Page number A 3.39\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#import modules\n",
      "import math\n",
      "from __future__ import division\n",
      "\n",
      "#given data\n",
      "n = 30         # numb of revolution is given in rev / sec\n",
      "t = 1          # time t is in seconds\n",
      "theta = 30     # angle theta is 30 degrees\n",
      "m = 0.5        # mass is given in Kgs \n",
      "I = 5 * 10**-4 # rotational inertia is given in Kg -m**2\n",
      "l = 0.04       # length pivoted from the center of mass is given in cms which is converted into meters\n",
      "pi= 3.14\n",
      "g = 9.8        # gravitational const is given in m/sec**2\n",
      "\n",
      "#calculation\n",
      "omega = (2*pi*n)/t                # angular velocity is calculated in rad/ sec\n",
      "omegap = (m*g*l)/(I* omega)       # angular velocity of precession is calculated in rad/ sec\n",
      "\n",
      "#Result\n",
      "print \"the angular velocity of precession is\",round(omegap,2),\"rad/sec\" "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "the angular velocity of precession is 2.08 rad/sec\n"
       ]
      }
     ],
     "prompt_number": 24
    }
   ],
   "metadata": {}
  }
 ]
}