{ "metadata": { "name": "", "signature": "sha256:83169fd272ce864306940c4a49b0d63f096c19015d841f59df75135834323538" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter07: Motion in a Circle" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.1:pg-208" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_1\n", " \n", " \n", " #To convert angles to radians and revolutions\n", "theta=70.0 #units in degrees\n", "deg=360.0 #units in degrees\n", "rad=theta*2*math.pi/deg #units in radians\n", "rev=1 #units in revolution\n", "rev=theta*rev/deg #units in revolution\n", "print \" 70 degrees in radians is \",round(rad,2),\"radians \\n 70 degrees in revolutions it is \",round(rev,3),\" revolutions\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " 70 degrees in radians is 1.22 radians \n", " 70 degrees in revolutions it is 0.194 revolutions\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.2:pg-209" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_2\n", " \n", " \n", "#To find average angular velocity\n", "theta=1800.0 #units in rev\n", "t=60.0 #units in sec\n", "w=(theta/t) #units in rev/sec\n", "w=w*(2*math.pi) #units in rad/sec\n", "print \"Average angular velocity is w=\",round(w),\" rad/sec\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Average angular velocity is w= 188.0 rad/sec\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.3:pg-210" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_3\n", " \n", " \n", " #To find average angular acceleration\n", "wf=240.0 #units in rev/sec\n", "w0=0 #units in rev/sec\n", "t=2.0 #units in minutes\n", "t=t*60 #units in sec\n", "alpha=(wf-w0)/t #units in rev/sec**2\n", "print \"Average angular acceleration is alpha=\",round(alpha),\" rev/sec**2\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Average angular acceleration is alpha= 2.0 rev/sec**2\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.4:pg-212" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_4\n", " \n", " \n", "#To find out how many revolutions does it turn before rest\n", "wf=0 #units in rev/sec\n", "w0=3 #units in rev/sec\n", "t=18 #units in sec\n", "alpha=(wf-w0)/t #units in rev/sec**2\n", "theta=(w0*t)+0.5*(alpha*t**2) #units in rev\n", "print \"Number of revolutions does it turn before rest is theta=\",round(theta),\" rev\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Number of revolutions does it turn before rest is theta= -108.0 rev\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.5:pg-212" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_5\n", " \n", " \n", " #To find the angular acceleration and angular velocity of one wheel\n", "vtf=20.0 #units in meters/sec\n", "r=0.4 #units in meters\n", "wf=vtf/r #units in rad/sec\n", "vf=20.0 #units in meters/sec\n", "v0=0 #units in meters/sec**2\n", "t=9.0 #units in sec\n", "a=(vf-v0)/t #units in meters/sec**2\n", "alpha=a/r #units in rad/sec**2\n", "print \"Angular accelertion is a=\",round(a,2),\" meters/sec**2\\n\"\n", "print \"Angular velocity is alpha=\",round(alpha,2),\" rad/sec**2\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angular accelertion is a= 2.22 meters/sec**2\n", "\n", "Angular velocity is alpha= 5.56 rad/sec**2\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.6:pg-213" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_6\n", " \n", " \n", " #To find out the rotation rate\n", "at=8.6 #units in meters/sec**2\n", "r=0.2 #units in meters\n", "alpha=at/r #units in rad/sec**2\n", "t=3 #units in sec\n", "wf=alpha*t #units in rad/sec\n", "print \"The rotation rate is wf=\",round(wf),\" rad/sec\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The rotation rate is wf= 129.0 rad/sec\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.7:pg-215" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_7\n", " \n", " \n", " #To calculate how large a horizontal force must the pavement exert\n", "m=1200.0 #units in Kg\n", "v=8.0 #units in meters/sec\n", "r=9 #units in meters\n", "F=(m*v**2)/r #units in Newtons\n", "print \"The horizontal force must the pavement exerts is F=\",round(F),\" Newtons\"\n", " #In text book the answer is printed wrong as F=8530 N but the correct answer is 8533 N\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The horizontal force must the pavement exerts is F= 8533.0 Newtons\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.9:pg-220" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_9\n", " \n", " \n", " #To find out the angle where it should be banked\n", "v=25 #units in meters/sec\n", "r=60 #units in meters\n", "g=9.8 #units in meters/sec**2\n", "tantheta=v**2/(r*g) #units in radians\n", "theta=math.atan(tantheta)*180/math.pi\n", "print \"The angle where it should be banked is theta=\",round(theta),\" degrees\",\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The angle where it should be banked is theta= 47.0 degrees\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.10:pg-220" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_10\n", " \n", " \n", " #To find out the ratio of F/W\n", "G=6.67*10**-11 #units in Newton meter**2/Kg**2\n", "m1=0.0080 #units in Kgs\n", "m2=0.0080 #units in Kgs\n", "r=2 #units in Meters\n", "F=(G*m1*m2)/r**2 #units in Newtons\n", "m=m1 #units in Kgs\n", "g=9.8 #units in meter/sec**2\n", "W=m*g #units in Newtons\n", "F_W=F/W\n", "print \"The F/W Ratio is=\",round(F_W,16)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The F/W Ratio is= 1.36e-14\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.11:pg-221" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_11\n", " \n", " \n", " #To find the mass of the sun\n", "t=3.15*10**7 #units in sec\n", "r=1.5*10**11 #units in meters\n", "v=(2*math.pi*r)/t #units in meters/sec\n", "G=6.67*10**-11 #units in Newtons\n", "ms=(v**2*r)/G #Units in Kg\n", "print \"The mass of the sun is Ms=\",round(ms,-28),\"Kg\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The mass of the sun is Ms= 2.01e+30 Kg\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex7.12:pg-222" ] }, { "cell_type": "code", "collapsed": false, "input": [ " #Example 7_12\n", " \n", " \n", " #To findout the orbital radius and its speed\n", "G=6.67*10**-11 #units in Newtons\n", "me=5.98*10**24 #units in Kg\n", "t=86400.0 #units in sec\n", "r=((G*me*t**2)/(4*math.pi**2))**(1/3.0)\n", "print \"The orbital radius is r= \",round(r),\" meters\\n\"\n", "v=(2*math.pi*r)/t #units in meters/sec\n", "print \"The orbital speed is v=\",round(v),\" meters/sec\"\n", " #in textbook the answer is printed wrong as v=3070 m/sec but the correct answer is v=3073 m/sec\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The orbital radius is r= 42250474.0 meters\n", "\n", "The orbital speed is v= 3073.0 meters/sec\n" ] } ], "prompt_number": 34 } ], "metadata": {} } ] }