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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter07: Motion in a Cirlce"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.1:pg-208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " 70 degrees in radians is 1.22 radians \n",
+ " 70 degrees in revolutions it is 0.194 revolutions\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.2:pg-209"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Average angular velocity is w= 188.0 rad/sec\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.3:pg-210"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Average angular acceleration is alpha= 2.0 rev/sec**2\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.4:pg-212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Number of revolutions does it turn before rest is theta= -108.0 rev\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.5:pg-212"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Angular accelertion is a= 2.22 meters/sec**2\n",
+ "\n",
+ "Angular velocity is alpha= 5.56 rad/sec**2\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.6:pg-213"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The rotation rate is wf= 129.0 rad/sec\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.7:pg-215"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The horizontal force must the pavement exerts is F= 8533.0 Newtons\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.9:pg-220"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The angle where it should be banked is theta= 47.0 degrees\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.10:pg-220"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The F/W Ratio is= 1.36e-14\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.11:pg-221"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The mass of the sun is Ms= 2.01e+30 Kg\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex7.12:pg-222"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The orbital radius is r= 42250474.0 meters\n",
+ "\n",
+ "The orbital speed is v= 3073.0 meters/sec\n"
+ ]
+ }
+ ],
+ "source": [
+ " import math #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"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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