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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 08: Rotational work energy and momentum"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.1:pg-240"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [],
+ "source": [
+ " #Example 8_1\n",
+ " \n",
+ " \n",
+ " #To find the rotational kinetic energy\n",
+ "m=5.98*10**24 #units in Kg\n",
+ "r=6.37*10**6 #units in meters\n",
+ "I=(2/5)*m*r**2 #units in Kg meter**2\n",
+ "t=86400 #units in sec\n",
+ "w=(2*math.pi)/(t) #units in rad/sec\n",
+ "KE=0.5*(I*w**2) #units in joules\n",
+ "print \"The rotational kinetic energy is KE=\")\n",
+ "print KE)\n",
+ "print \"Joules\")\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.2:pg-242"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Angular acceleration is alpha= 0.384 rad/sec**2\n"
+ ]
+ }
+ ],
+ "source": [
+ " #Example 8_2\n",
+ " \n",
+ " \n",
+ " #To find the angular acceleration of the wheel\n",
+ "m=30 #units in Kg\n",
+ "k=0.25 #units in meters\n",
+ "I=m*k**2 #units in Kg meter**2\n",
+ "force=1.8 #units in Newtons\n",
+ "levelarm=0.40 #nits in meters\n",
+ "tou=force*levelarm #units in Newton meter\n",
+ "alpha=tou/I #units in rad/sec**2\n",
+ "print \"Angular acceleration is alpha=\",round(alpha,3),\" rad/sec**2\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.3:pg-242"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The time taken is t= 15.7 sec\n",
+ "\n",
+ "The wheel goes a distance of theta= 98.7 rad\n",
+ "\n",
+ "The rotational kinetic energy is KE= 197.0 Joules\n"
+ ]
+ }
+ ],
+ "source": [
+ " #Example 8_3\n",
+ " \n",
+ " \n",
+ " #To find out how long does it take to accelerate and how far does wheel turn in this time and the rotational kinetic energy\n",
+ "force=8 #units in Newtons\n",
+ "arm=0.25 #units in meters\n",
+ "tou=force*arm #units in Newton meter\n",
+ "m=80 #units in Kg\n",
+ "b=arm #units in meters\n",
+ "I=0.5*m*b**2 #units in Kg meter**2\n",
+ "alpha=tou/I #units in rad/sec**2\n",
+ "wf=4*math.pi #units in rad/sec\n",
+ "w0=0 #units in rad/sec\n",
+ "t=(wf-w0)/alpha #units in sec\n",
+ "print \"The time taken is t=\",round(t,1),\" sec\\n\"\n",
+ "theta=0.5*(wf+w0)*t #units in radians\n",
+ "print \"The wheel goes a distance of theta=\",round(theta,1),\" rad\\n\"\n",
+ "KE=0.5*I*wf**2 #units in Joules\n",
+ "print \"The rotational kinetic energy is KE=\",round(KE),\" Joules\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.4:pg-243"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The angular acceleration is alpha= 1.37 rad/sec**2\n",
+ "\n",
+ "The objects goes a distance of y= 51.4 meters\n"
+ ]
+ }
+ ],
+ "source": [
+ " #Example 8_4\n",
+ " \n",
+ " \n",
+ " #To find out the angular acceleration and the distance the object falls\n",
+ "f1=29.4 #units in Newtons\n",
+ "r1=0.75 #units in meters\n",
+ "m1=40 #units in Kgs\n",
+ "r2=0.6 #units in meters\n",
+ "m2=3 #units in Kgs\n",
+ "alpha=(f1*r1)/((m1*r2**2)+(m2*r1**2)) #units in rad/sec**2\n",
+ "print \"The angular acceleration is alpha=\",round(alpha,2),\" rad/sec**2\\n\"\n",
+ "a=r1*alpha #units in meters/sec**2\n",
+ "t=10 #units in sec\n",
+ "y=0.5*a*t**2 #units in meters\n",
+ "print \"The objects goes a distance of y=\",round(y,1),\" meters\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.5:pg-244"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The object is moving at v= 1.28 meters/sec\n"
+ ]
+ }
+ ],
+ "source": [
+ " #Example 8_5\n",
+ " \n",
+ " \n",
+ " #To find the speed of the object\n",
+ "m=3 #units in Kg\n",
+ "g=9.8 #units in meters/sec**2\n",
+ "h=0.80 #units in meters\n",
+ "m1=3 #units in Kg\n",
+ "m2=14.4 #units in Kg\n",
+ "r=0.75 #units in meters\n",
+ "v=sqrt((m*g*h)/((0.5*m1)+((0.5*m2)/r**2)))\n",
+ "print \"The object is moving at v=\",round(v,2),\" meters/sec\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.8:pg-247"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The sun would take for one revolution in time=\n",
+ "0.000216 sec\n"
+ ]
+ }
+ ],
+ "source": [
+ " #Example 8_8\n",
+ " \n",
+ " \n",
+ " #To find out how long does the sun take to complete one revolution\n",
+ "ra_rb=10.0**5\n",
+ "noofrev=1.0/25 #units in rev/day\n",
+ "wafter=(ra_rb)**2*(noofrev)\n",
+ "t=86400 #units in sec\n",
+ "time=t/wafter #units in sec\n",
+ "print \"The sun would take for one revolution in time=\"\n",
+ "print time,\"sec\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Ex8.9:pg-248"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The rotational speed is Wf= 1.63 rev/sec\n"
+ ]
+ }
+ ],
+ "source": [
+ " #Example 8_9\n",
+ " \n",
+ " \n",
+ " #To find out the rotational speed \n",
+ "m=0.3 #units in Kg\n",
+ "r=0.035 #units in meters\n",
+ "Iw=0.5*m*r**2 #units in Kg meter**2\n",
+ "Ibt=8*10**-4 #units in Kg meter**2\n",
+ "w0=2 #units in rev/sec\n",
+ "wf=(Ibt*w0)/(Ibt+Iw) #units in rev/sec\n",
+ "print \"The rotational speed is Wf=\",round(wf,2),\" rev/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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