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render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',[_vm._v(\"Angular velocity \")]),_c('p',[_vm._v(\"\\n    It is the rate of change of angular position of the particle with respect to time. It tells us\\n    how fast an object is rotating. It is a vector quantity and is denoted by \\\\(\\\\omega\\\\). It SI unit is rad/sec.\\n    If a body rotates by Δ\\\\(\\\\theta\\\\) angle in a time duration of Δ\\\\(t\\\\), its average angular velocity over the time period Δ\\\\(t\\\\) is given by\\n    $$\\\\omega=\\\\frac{\\\\Delta \\\\theta}{\\\\Delta t}$$\\n    When Δt tends to zero, we get the instantaneous angular velocity of the body which is given by\\n    $$\\\\omega=\\\\lim_{Δt\\\\to0}\\\\frac{Δθ}{Δt}=\\\\frac{dθ}{dt}$$\\n    Its direction is along the axis of rotation of the body, perpendicular to the plane of rotation. Direction of\\n    the angular velocity \\\\(\\\\omega\\\\) is given using the right-hand rule. If the fingers of the right hand are\\n    curled in the direction of rotation, the direction in which the thumb of the right hand points out, is the\\n    direction of angular velocity. Relation between angular velocity \\\\(\\\\vec{\\\\omega}\\\\) and linear velocity \\\\(\\\\vec{v}\\\\) of a particle or a body in vector\\n    form is given as,\\n    $$\\\\vec{v}=\\\\vec{\\\\omega} \\\\times \\\\vec{r}$$\\n    where \\\\(\\\\vec{r}\\\\) is the position vector of the particle.\\n    Linear velocity is the vector product of angular velocity and position vector of the particle in\\n    angular motion. However, in most of the cases the relation between angular velocity is given only in terms of\\n    their magnitude i.e., \\\\(v=\\\\omega r \\\\).\\n    Note that for rotation of a body about a fixed axis, direction of angular velocity remains constant however, its\\n    magnitude may change.\\n  \")]),_c('h3',[_vm._v(\"Angular acceleration\")]),_vm._m(0),_c('h3',[_vm._v(\"Moment of Inertia \")]),_c('p',[_vm._v(\"\\n    Moment of inertia of a body is a quantity that determines the body's resistance to change in its rotational\\n    motion. The role of moment of inertia in rotational motion is same as that of mass in linear motion. It\\n    determines the torque required for a specific angular acceleration about the axis of rotation.\\n    Moment of inertia depends\\n    upon the distribution of mass in the body about its rotational axis. The farther are the masses from the\\n    axis of rotation, more is the moment of inertia of the body.\\n  \")]),_c('p',[_vm._v(\"\\n    For a point mass, moment of inertia is given by\\n    $$I =mr^2$$\\n    where \\\\(m\\\\) is the mass of the particle, \\\\(I\\\\) is its moment of inertia and \\\\(r\\\\) is the perpendicular\\n    distance of the\\n    particle from the axis of rotation.\\n  \")]),_c('h3',[_vm._v(\"Moment of Inertia for a system of particles \")]),_c('p',[_vm._v(\"\\n    For a system with n particles having masses\\n    \\\\(m_1, m_2, ... ,m_n\\\\), moment of inertia I of the system is given by\\n    $$I=\\\\sum_{i=1}^{n} m_ir_i^{2}$$\\n    Where \\\\(r_i\\\\) is respective perpendicular distance of particle of mass \\\\(m_i\\\\) from the axis of rotation.\\n  \")]),_c('h3',[_vm._v(\"Moment of Inertia for a rigid body \")]),_c('p',[_vm._v(\"\\n    For extended objects with continuous mass distribution, we consider infinitesimally small elements of mass\\n    \\\\(dm\\\\) and the summation in above formula is replaced by integration. Moment of inertia \\\\(I\\\\) of the system is given\\n    by\\n    $$I=\\\\int r^{2}\\\\,dm$$\\n  \")]),_c('h3',[_vm._v(\"Torque\")]),_c('p',[_vm._v(\"\\n    Torque is the rotational analogue of linear force. It is responsible for rotating a body and bringing\\n    about an angular acceleration in the body.\\n    If a force \\\\(F \\\\) acts on a particle whose position vector is \\\\(\\\\vec{r}\\\\) with respect to the axis or point\\n    of rotation , then the torque \\\\(\\\\tau\\\\) acting on the particle is equal to the vector product of the force\\n    acting on the particle and its position vector i.e.,\\n    $$\\\\vec{\\\\tau}=\\\\vec{r} \\\\times \\\\vec{F}$$\\n    Here \\\\( \\\\tau \\\\) is the torque of the force applied. Torque is a vector quantity and its direction is\\n    determined according to the right-hand rule in a plane perpendicular to the force applied and position\\n    vector of the particle. Torque is denoted by \\\\(\\\\tau\\\\) and its SI unit is Newton-meter.\\n  \")]),_c('p',[_vm._v(\"\\n    The magnitude of torque is given by\\n    $$\\\\tau=r F \\\\sin \\\\theta $$\\n    where \\\\(r\\\\) is the magnitude of position vector of the particle, \\\\(F\\\\) is the magnitude of the force applied\\n    and \\\\(\\\\theta\\\\) is the angle\\n    between the direction of the force applied and position vector of the particle.\\n    Therefore, the turning effect on an object due to a force applied not only depends on the magnitude and\\n    direction of the force applied but also on the point of application of the applied force.\\n\\n    Angular acceleration produced in a body not only depends on the torque applied on it, but also\\n    on its moment of inertia. The relation between torque \\\\(\\\\tau\\\\), angular acceleration\\\\(\\\\alpha\\\\) and moment\\n    of inertia \\\\(I\\\\) of the body is given by\\n    $$\\\\vec{\\\\tau}=I\\\\vec{\\\\alpha}$$\\n  \")]),_c('h3',{ref:\"PlayGraph\"},[_vm._v(\"\\n    MagicGraph | Conservation of Angular Momentum\\n  \")]),_c('h5',[_vm._v(\" To Get Started\")]),_c('p',[_vm._v(\"\\n    Shown is a dvd disc that can spin about point 'O'.\\n    The disc has a  mass \\\\(M_{disc}\\\\) and radius \\\\(r_{disc}\\\\).\\n    You will also see a ball (treated as a point mass) that has a mass \\\\(m_{ball}\\\\).\\n    Start with giving the disc an initial spin. The initial angular velocity of the disc is \\\\(\\\\omega_i\\\\) — which can be changed.\\n    Then place the ball on the rim of the disc, and observe the new angular velocity of the combined system (\\\\(\\\\omega_f\\\\)).\\n    Change the mass of the ball and note how angular velocity changes.\\n  \")]),_c('v-responsive',[_c('v-layout',{attrs:{\"align-center\":\"\",\"justify-center\":\"\"}},[_c('div',{staticClass:\"edliy-box-about\",attrs:{\"id\":\"jxgbox1\"}})])],1)],1)\n}\nvar staticRenderFns = [function (){var _vm=this,_c=_vm._self._c;return _c('p',[_vm._v(\"\\n    Angular acceleration is the rate of change of angular velocity. It is denoted by \\\\(\\\\alpha\\\\) and its SI unit is rad/s\"),_c('sup',[_vm._v(\"2\")]),_vm._v(\". It is\\n    also a vector quantity and its direction is also directed perpendicular to the plane of rotation. We have\\n    read how to find the direction of angular velocity. Now, if the angular velocity of the particle or object\\n    in rotational motion is increasing, the direction of angular acceleration is same as that of angular\\n    velocity and if the angular velocity is decreasing, the direction of angular acceleration is in a direction\\n    opposite to the direction of angular velocity.\\n    Average angular acceleration is given by\\n    $$\\\\alpha= \\\\frac{Δ\\\\omega}{Δt}$$\\n    where Δt is the change in time and Δ\\\\(\\\\omega\\\\) is the change in angular velocity.\\n    \"),_c('br'),_c('br'),_vm._v(\"Instantaneous angular\\n    acceleration is given by\\n    $$\\\\alpha=\\\\lim_{Δt\\\\to0}\\\\frac{Δ\\\\omega}{Δt}=\\\\frac{d\\\\omega}{dt}$$\\n  \")])\n}]\n\nexport { render, staticRenderFns }","// Import the edliy_utils\r\nimport {\r\n    makeResponsive,\r\n    placeTitle,\r\n    placeImage,\r\n    placeInput,\r\n    placeSlider,\r\n    hoverMe,\r\n    placeRec,\r\n    hiddenPt,\r\n    fixedPt,\r\n    clearInputFields,\r\n    dragMe,\r\n    placeArrow,\r\n    placeGravity,\r\n    placeText,\r\n    placeLine,\r\n    placePoint,\r\n    placeGlider,\r\n    placeRuler,\r\n    placeLeftText,\r\n    placeRightText,\r\n    placeSliderSwitch,\r\n    placeDash,\r\n    placeCircle\r\n} from '../../../common/edliy_utils-bernoulli';\r\nconst Boxes = {\r\n  box1: function () {\r\n  var brd1 = JXG.JSXGraph.initBoard('jxgbox1',{boundingbox: [-6, 10, 10, -6],\r\n  keepaspectratio: true, axis:false, ticks:{visible:false},\r\n  grid:true, showCopyright:false, showNavigation:false,\r\n  pan:{enabled:false}, zoom:{enabled:false}});\r\n  brd1.suspendUpdate();\r\n  brd1.options.board.minimizeReflow = 'none';\r\n  brd1.options.text.highlight =false;\r\n  brd1.options.text.fixed =true;\r\n  brd1.options.text.highlight =false;\r\n  brd1.options.text.cssStyle='fontFamily:Oswald',\r\n  brd1.options.image.highlight =false;\r\n  brd1.options.polygon.highlight =false;\r\n  brd1.options.line.highlight =false;\r\n  brd1.options.point.highlight =false;\r\n  brd1.options.curve.highlight =false;\r\n  brd1.options.slider.highlight =false;\r\n  brd1.options.point.showInfoBox =false;\r\n  brd1.options.image.layer =15;\r\n  brd1.options.point.layer =16;\r\n//brd1.options.layer['image'] =14;\r\n//Title and tetxs\r\n  makeResponsive(brd1);\r\n  placeTitle(brd1, 'Conservation of Angular Momentum', '');\r\n  //var title1 = brd1.create('text', [7, 14, \"<b> Bernoulli's Principle <b>\"],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(28*brd1.canvasWidth/500.)}},);\r\n  //brd1.options.layer['image'] =14;\r\n\r\n  //Title and tetxs\r\n//  var title = brd1.create('text', [0, 7, '<b> Conservation Of Angular Momentum <b>'],{fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(24*brd1.canvasWidth/500.)}},);\r\n  var subtitle = brd1.create('text', [2, 7.5, 'L = I_i &omega;_i =  I_f &omega;_f'],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}},);\r\n  var subtitle1 = brd1.create('text', [2, 6.5, '1. Give the disc an initial spin. 2. Place the ball on the rim of the disc'],{display:'internal', visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}},);\r\n  var subtitle2 = brd1.create('text', [2, 6.5, 'Insert the values with two decimals'],{display:'internal', visible: false,fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(14*brd1.canvasWidth/500.)}},);\r\n\r\n  //Variables\r\n  var angle = 0;\r\n  var angleBall = 0;\r\n\r\n  //Sliders\r\n  var wo = placeSlider(brd1, 4, 5.5, -10, 0, 10, 2, '&nbsp;&omega;_i', '&nbsp; rad/s');\r\n  wo.setAttribute({snapWidth:0.1});\r\n  //brd1.create('slider',[[4,5],[6,5],[-10,0,10]], {snapToGrid: false ,face:'circle', size:4, strokeWidth: 2, name:'w_i [rad/s]', strokeColor:'black', fillColor: 'grey',  label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n  var m_disk =placeSlider(brd1, 4, 4.5, 50, 300, 500, 2, '&nbsp;M_d_i_s_c', '&nbsp; kg');\r\n  //brd1.create('slider',[[4,4.5],[6,4.5],[50,200,500]], {snapToGrid: false ,face:'circle', size:4, strokeWidth: 2, name:'M_d_i_s_k', strokeColor:'black', fillColor: 'grey',  label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n  var m_ball = placeSlider(brd1, 4, 3.5, 50, 300, 500, 2, '&nbsp;m_b_a_l_l', '&nbsp; kg');\r\n  //brd1.create('slider',[[4,3.5],[6,3.5],[10,300,500]], {snapToGrid: false ,face:'circle', size:4, strokeWidth: 2, name:'m_b_a_l_l', strokeColor:'black', fillColor: 'grey',  label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n  var r_disk =placeSlider(brd1, 4, 2.5, 1, 4, 5, 2, '&nbsp;r_d_i_s_c', '&nbsp; m');\r\n  //brd1.create('slider',[[4,2.5],[6,2.5],[1,4,5]], {snapToGrid: false ,face:'circle', size:4, strokeWidth: 2, name:'r_d_i_s_k', strokeColor:'black', fillColor: 'grey',  label:{fontSize:function(){return 18*brd1.canvasHeight/800}, cssStyle:'fontFamily:Oswald'}});\r\n  var circ = placeCircle(brd1, [0, 0],[()=>r_disk.Value()-0.1, 0], 0, 'black');\r\n  //Inertia\r\n  var I_disk = function(){return 0.5*m_disk.Value()*Math.pow(r_disk.Value(), 2)};\r\n  var I_ball = function(){return m_ball.Value()*Math.pow(r_disk.Value(), 2)}; //CHANGE r\r\n\r\n  //w final\r\n  function wf(){\r\n\r\n      if(ballOverDisk == true){\r\n          return I_disk()*wo.Value()/(I_disk()+ I_ball());\r\n      }\r\n\r\n      else{\r\n          return wo.Value();\r\n      }\r\n  }\r\n\r\n\r\n  //Tetxs\r\n  var txt1 = brd1.create('text', [6, 1.5 ,  function(){return 'I_d_i_s_c = ' + I_disk().toFixed(2)+'&nbsp; kg-m^2'}],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n  var txt2 = brd1.create('text', [6, 0.5,  function(){return 'I_b_a_l_l = ' + I_ball().toFixed(2)+'&nbsp; kg-m^2'}],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n  var txt3 = brd1.create('text', [6, -0.5,  function(){return '&omega;_f = ' + wf().toFixed(2)+'&nbsp; rad/s'}],{visible: true, fixed: true, anchorX: 'middle', anchorY: 'middle', CssStyle:'fontFamily:Oswald',fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}},);\r\n\r\n  //Rotate de Disk around its center\r\n  var p0 = brd1.create('point', [0,0], {visible: false, size:8, name:'offset', opacity:0.3, fixed: true});\r\n  var p1 = brd1.create('point', [3,0], {visible: false, size:8, name:'rotate+scale', opacity:0.3, fixed: true});\r\n  var im = brd1.create('image',['/assets/dvd.svg', [function(){return -r_disk.Value()}, function(){return -r_disk.Value()}], [function(){return 2*r_disk.Value()},function(){return 2*r_disk.Value()}]], {fixed: true, opacity:1});\r\n\r\n  var tOff = brd1.create('transform', [function(){return p0.X()},function(){return p0.Y()}], {type:'translate'});\r\n  tOff.bindTo(im);\r\n  tOff.bindTo(p1);\r\n  var tRot = brd1.create('transform', [function(){return Math.atan2(p1.Y()-p0.Y(),p1.X()-p0.X())}, p0], {type:'rotate'});\r\n  tRot.bindTo(im);\r\n  var tOffInv = brd1.create('transform', [function(){return -p0.X()},function(){return -p0.Y()}], {type:'translate'});\r\n  var tScale = brd1.create('transform', [function(){return p1.Dist(p0)/3;},\r\n                                        function(){return p1.Dist(p0)/3;}], {type:'scale'});\r\n  tOffInv.bindTo(im); tScale.bindTo(im); tOff.bindTo(im);\r\n\r\n  //Ball\r\n  var ball = brd1.create('point', [6, -3], {size:20, name:'', opacity:1., attractors:[circ], attractorDistance:1,  snatchDistance:0.5});\r\n  var ballOverDisk = false;\r\n  var r_ball = function(){return Math.sqrt( Math.pow((ball.Y() ) ,2) + Math.pow( (ball.X() ), 2) ) };\r\n\r\n  //Functions\r\n  function rotate (){\r\n\r\n      angle = angle + wf()/20;\r\n\r\n      if(ballOverDisk == true){\r\n          angle = angle + wf()/20;\r\n      }\r\n\r\n    var posx = 3*Math.cos(angle);\r\n    var posy = 3*Math.sin(angle);\r\n\r\n    p1.moveTo([posx, posy], 1);\r\n\r\n    if(ballOverDisk == true){\r\n\r\n        angleBall = angleBall + wf()/10;\r\n\r\n        posx = r_ball()*Math.cos(angleBall);\r\n        posy = r_ball()*Math.sin(angleBall);\r\n\r\n        ball.moveTo([posx, posy], 1);\r\n\r\n    }\r\n\r\n  }\r\n\r\n  function spinBall(){\r\n\r\n    angleBall = Math.atan(ball.Y()/ball.X());\r\n\r\n    if(ball.X() < 0){\r\n        angleBall = angleBall + Math.PI;\r\n    }\r\n\r\n    if(r_ball() < r_disk.Value()){\r\n        ballOverDisk = true;\r\n    }\r\n    else{\r\n        ballOverDisk = false;\r\n    }\r\n  }\r\n\r\n  function stopBall(){\r\n    ballOverDisk = false;\r\n  }\r\n\r\n  setInterval(function(){ rotate(); }, 100);\r\n\r\n  ball.on('up',spinBall);\r\n  ball.on('down',stopBall);\r\n  r_disk.on('down', function(){ stopBall(); ball.moveTo([6, -3], 10) } );\r\n\r\n\r\n  //TEST YOURSELF\r\n\r\n  //Images\r\n  var tryMe = brd1.create('image', ['/assets/tap.svg', [7, -0.5], [0.5, 0.5]], {visible: false, fixed: true});\r\n  tryMe.setLabel('Try')\r\n  tryMe.label.setAttribute({visible:false, offset:[15, -15], CssStyle:'fontFamily:Oswald', fontSize:16});\r\n  tryMe.on('over', function () {this.label.setAttribute({visible:true});});\r\n  tryMe.on('out', function () {this.label.setAttribute({visible:false});});\r\n\r\n  var test_mode = brd1.create('image', ['/assets/blue.svg', [6, 6.5], [1,1]], {visible: true, fixed: true});\r\n  test_mode.setLabel('Test Yourself!')\r\n  test_mode.label.setAttribute({visible:false, offset:[-10, -15], CssStyle:'fontFamily:Oswald', fontSize:16});\r\n  test_mode.on('over', function () {this.label.setAttribute({visible:true});});\r\n  test_mode.on('out', function () {this.label.setAttribute({visible:false});});\r\n\r\n  var learn_mode = brd1.create('image', ['/assets/red.svg', [6, 6.5], [1,1]], {visible: false, fixed: true});\r\n  learn_mode.setLabel('Learning Mode')\r\n  learn_mode.label.setAttribute({visible:false, offset:[-10, -15], CssStyle:'fontFamily:Oswald', fontSize:16});\r\n  learn_mode.on('over', function () {this.label.setAttribute({visible:true});});\r\n  learn_mode.on('out', function () {this.label.setAttribute({visible:false});});\r\n\r\n  var ok1 = brd1.create('image', ['/assets/check.svg', [7, 1.8], [0.5, 0.5]], {visible: false, fixed: true});\r\n  var ok2 = brd1.create('image', ['/assets/check.svg', [7, 1], [0.5, 0.5]], {visible: false, fixed: true});\r\n  var ok3 = brd1.create('image', ['/assets/check.svg', [7, 0.2], [0.5, 0.5]], {visible: false, fixed: true});\r\n\r\n  var cross1 = brd1.create('image', ['/assets/cross.svg', [7, 1.8], [0.5, 0.5]], {visible: false, fixed: true});\r\n  var cross2 = brd1.create('image', ['/assets/cross.svg', [7, 1], [0.5, 0.5]], {visible: false, fixed: true});\r\n  var cross3 = brd1.create('image', ['/assets/cross.svg', [7, 0.2], [0.5, 0.5]], {visible: false, fixed: true});\r\n\r\n  //Inputs\r\n  var inputI_disk = brd1.create('input', [15, 0.5, '0', 'I_d_i_s_c'], {fixed: true, cssStyle: 'fontFamily:Oswald; width:10%; background-color:#C1C1C1;border: 1px solid black;border-radius: 3.5px;', fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}, fixed:true,parse:true});\r\n  var inputI_ball = brd1.create('input', [15, -0.5, '0', 'I_b_a_l_l'], {fixed: true, cssStyle: 'fontFamily:Oswald; width:10%; background-color:#C1C1C1;border: 1px solid black;border-radius: 3.5px;', fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}, fixed:true,parse:true});\r\n  var inputwf = brd1.create('input', [15, -1.5, '0', '&omega;_f'], {fixed: true, cssStyle: 'fontFamily:Oswald; width:10%; background-color:#C1C1C1;border: 1px solid black;border-radius: 3.5px;', fontSize:function(){return Math.round(12*brd1.canvasWidth/500.)}, fixed:true,parse:true});\r\n\r\n\r\n  //Check the values\r\n  function check(){\r\n\r\n      ok1.setAttribute({visible: false});\r\n      ok2.setAttribute({visible: false});\r\n      ok3.setAttribute({visible: false});\r\n      cross1.setAttribute({visible: false});\r\n      cross2.setAttribute({visible: false});\r\n      cross3.setAttribute({visible: false});\r\n\r\n\r\n      if(inputI_disk.Value() == I_disk().toFixed(2)){\r\n          ok1.setAttribute({visible: true});\r\n      }\r\n      else{\r\n          cross1.setAttribute({visible: true});\r\n\r\n      }\r\n\r\n      if(inputI_ball.Value() == I_ball().toFixed(2)){\r\n          ok2.setAttribute({visible: true});\r\n      }\r\n      else{\r\n          cross2.setAttribute({visible: true});\r\n\r\n      }\r\n\r\n      if(inputwf.Value() == wf().toFixed(2)){\r\n          ok3.setAttribute({visible: true});\r\n      }\r\n      else{\r\n          cross3.setAttribute({visible: true});\r\n\r\n      }\r\n\r\n\r\n  }\r\n\r\n  //Mouse click\r\n  tryMe.on('down',check);\r\n\r\n  test_mode.on('up', function(){learn_mode.setAttribute({visible: true});\r\n                              test_mode.setAttribute({visible: false});\r\n                              txt1.setAttribute({visible: false});\r\n                              txt2.setAttribute({visible: false});\r\n                              txt3.setAttribute({visible: false});\r\n                              tryMe.setAttribute({visible: true});\r\n\r\n                              inputI_disk.moveTo([5,2], 10);\r\n                              inputI_ball.moveTo([5,1.25], 10);\r\n                              inputwf.moveTo([5,0.5], 10);\r\n\r\n                              subtitle2.setAttribute({visible: true});\r\n                              subtitle1.setAttribute({visible: false});\r\n   });\r\n  learn_mode.on('down', function(){learn_mode.setAttribute({visible: false});\r\n                                   test_mode.setAttribute({visible: true});\r\n                                   ok1.setAttribute({visible: false});\r\n                                   ok2.setAttribute({visible: false});\r\n                                   ok3.setAttribute({visible: false});\r\n                                   cross1.setAttribute({visible: false});\r\n                                   cross2.setAttribute({visible: false});\r\n                                   cross3.setAttribute({visible: false});\r\n\r\n                                   tryMe.setAttribute({visible: false});\r\n                                   txt1.setAttribute({visible: true});\r\n                                   txt2.setAttribute({visible: true});\r\n                                   txt3.setAttribute({visible: true});\r\n                                   inputI_disk.moveTo([15,2], 10);\r\n                                   inputI_ball.moveTo([15,1.25], 10);\r\n                                   inputwf.moveTo([15,0.5], 10);\r\n\r\n                                   subtitle2.setAttribute({visible: false});\r\n                                   subtitle1.setAttribute({visible: true});\r\n\r\n  });\r\n\r\n  brd1.unsuspendUpdate();\r\n    },\r\n}\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3>Angular velocity </h3>\r\n    <p>\n      It is the rate of change of angular position of the particle with respect to time. It tells us\r\n      how fast an object is rotating. It is a vector quantity and is denoted by \\(\\omega\\). It SI unit is rad/sec.\r\n      If a body rotates by Δ\\(\\theta\\) angle in a time duration of Δ\\(t\\), its average angular velocity over the time period Δ\\(t\\) is given by\r\n      $$\\omega=\\frac{\\Delta \\theta}{\\Delta t}$$\r\n      When Δt tends to zero, we get the instantaneous angular velocity of the body which is given by\r\n      $$\\omega=\\lim_{Δt\\to0}\\frac{Δθ}{Δt}=\\frac{dθ}{dt}$$\r\n      Its direction is along the axis of rotation of the body, perpendicular to the plane of rotation. Direction of\r\n      the angular velocity \\(\\omega\\) is given using the right-hand rule. If the fingers of the right hand are\r\n      curled in the direction of rotation, the direction in which the thumb of the right hand points out, is the\r\n      direction of angular velocity. Relation between angular velocity \\(\\vec{\\omega}\\) and linear velocity \\(\\vec{v}\\) of a particle or a body in vector\r\n      form is given as,\r\n      $$\\vec{v}=\\vec{\\omega} \\times \\vec{r}$$\r\n      where \\(\\vec{r}\\) is the position vector of the particle.\r\n      Linear velocity is the vector product of angular velocity and position vector of the particle in\r\n      angular motion. However, in most of the cases the relation between angular velocity is given only in terms of\r\n      their magnitude i.e., \\(v=\\omega r \\).\r\n      Note that for rotation of a body about a fixed axis, direction of angular velocity remains constant however, its\r\n      magnitude may change.\r\n    </p>\r\n    <h3>Angular acceleration</h3>\r\n    <p>\n      Angular acceleration is the rate of change of angular velocity. It is denoted by \\(\\alpha\\) and its SI unit is rad/s<sup>2</sup>. It is\r\n      also a vector quantity and its direction is also directed perpendicular to the plane of rotation. We have\r\n      read how to find the direction of angular velocity. Now, if the angular velocity of the particle or object\r\n      in rotational motion is increasing, the direction of angular acceleration is same as that of angular\r\n      velocity and if the angular velocity is decreasing, the direction of angular acceleration is in a direction\r\n      opposite to the direction of angular velocity.\r\n      Average angular acceleration is given by\r\n      $$\\alpha= \\frac{Δ\\omega}{Δt}$$\r\n      where Δt is the change in time and Δ\\(\\omega\\) is the change in angular velocity.\r\n      <br><br>Instantaneous angular\r\n      acceleration is given by\r\n      $$\\alpha=\\lim_{Δt\\to0}\\frac{Δ\\omega}{Δt}=\\frac{d\\omega}{dt}$$\r\n    </p>\r\n\r\n    <h3>Moment of Inertia </h3>\r\n    <p>\n      Moment of inertia of a body is a quantity that determines the body's resistance to change in its rotational\r\n      motion. The role of moment of inertia in rotational motion is same as that of mass in linear motion. It\r\n      determines the torque required for a specific angular acceleration about the axis of rotation.\r\n      Moment of inertia depends\r\n      upon the distribution of mass in the body about its rotational axis. The farther are the masses from the\r\n      axis of rotation, more is the moment of inertia of the body.\n    </p>\r\n    <p>\n      For a point mass, moment of inertia is given by\r\n      $$I =mr^2$$\r\n      where \\(m\\) is the mass of the particle, \\(I\\) is its moment of inertia and \\(r\\) is the perpendicular\r\n      distance of the\r\n      particle from the axis of rotation.\n    </p>\r\n    <h3>Moment of Inertia for a system of particles </h3>\r\n    <p>\r\n      For a system with n particles having masses\r\n      \\(m_1, m_2, ... ,m_n\\), moment of inertia I of the system is given by\r\n      $$I=\\sum_{i=1}^{n} m_ir_i^{2}$$\r\n      Where \\(r_i\\) is respective perpendicular distance of particle of mass \\(m_i\\) from the axis of rotation.\r\n    </p>\r\n    <h3>Moment of Inertia for a rigid body </h3>\r\n    <p>\r\n      For extended objects with continuous mass distribution, we consider infinitesimally small elements of mass\r\n      \\(dm\\) and the summation in above formula is replaced by integration. Moment of inertia \\(I\\) of the system is given\r\n      by\r\n      $$I=\\int r^{2}\\,dm$$\r\n    </p>\r\n    <h3>Torque</h3>\r\n    <p>\n      Torque is the rotational analogue of linear force. It is responsible for rotating a body and bringing\r\n      about an angular acceleration in the body.\r\n      If a force \\(F \\) acts on a particle whose position vector is \\(\\vec{r}\\) with respect to the axis or point\r\n      of rotation , then the torque \\(\\tau\\) acting on the particle is equal to the vector product of the force\r\n      acting on the particle and its position vector i.e.,\r\n      $$\\vec{\\tau}=\\vec{r} \\times \\vec{F}$$\r\n      Here \\( \\tau \\) is the torque of the force applied. Torque is a vector quantity and its direction is\r\n      determined according to the right-hand rule in a plane perpendicular to the force applied and position\r\n      vector of the particle. Torque is denoted by \\(\\tau\\) and its SI unit is Newton-meter.\r\n    </p>\r\n    <p>\n      The magnitude of torque is given by\r\n      $$\\tau=r F \\sin \\theta $$\r\n      where \\(r\\) is the magnitude of position vector of the particle, \\(F\\) is the magnitude of the force applied\r\n      and \\(\\theta\\) is the angle\r\n      between the direction of the force applied and position vector of the particle.\r\n      Therefore, the turning effect on an object due to a force applied not only depends on the magnitude and\r\n      direction of the force applied but also on the point of application of the applied force.\r\n\r\n      Angular acceleration produced in a body not only depends on the torque applied on it, but also\r\n      on its moment of inertia. The relation between torque \\(\\tau\\), angular acceleration\\(\\alpha\\) and moment\r\n      of inertia \\(I\\) of the body is given by\r\n      $$\\vec{\\tau}=I\\vec{\\alpha}$$\r\n    </p>\r\n    <h3 ref=\"PlayGraph\">\n      MagicGraph | Conservation of Angular Momentum\n    </h3>\r\n    <h5> To Get Started</h5>\r\n    <p>\r\n      Shown is a dvd disc that can spin about point 'O'.\r\n      The disc has a  mass \\(M_{disc}\\) and radius \\(r_{disc}\\).\r\n      You will also see a ball (treated as a point mass) that has a mass \\(m_{ball}\\).\r\n      Start with giving the disc an initial spin. The initial angular velocity of the disc is \\(\\omega_i\\) &mdash; which can be changed.\r\n      Then place the ball on the rim of the disc, and observe the new angular velocity of the combined system (\\(\\omega_f\\)).\r\n      Change the mass of the ball and note how angular velocity changes.\n    </p>\r\n    <v-responsive>\r\n      <v-layout align-center justify-center>\r\n        <div id=\"jxgbox1\" class=\"edliy-box-about\" />\r\n      </v-layout>\r\n    </v-responsive>\r\n  </div>\r\n</template>\r\n\r\n<script>\r\nimport Boxes from './Boxes.js'\r\n\r\nexport default {\r\n  name: 'BernoulliPrinciple',\r\n  data () {\r\n    return {\r\n      v1: 1,\r\n      P1: 1,\r\n      rho: 1,\r\n      v2: undefined,\r\n      P2: undefined,\r\n    }\r\n  },\r\n  created: function () {\r\n    // Store mutations\r\n    let title = 'Conservation of Angular Momentum';\r\n    this.$store.commit('navigation/changeTitle', title);\r\n    this.$store.commit('navigation/changeMenu', title);\r\n    let newTopics = [\r\n      {title: ' Statement of Bernoulli\\'s Principle', img:'/assets/number-1.svg',action: () => this.goto('intro')},\r\n      {title: 'Derivation of Bernoulli\\'s Principle', img:'/assets/number-2.svg',action: () => this.goto('derivation')},\r\n      {title: 'Continuity Equation', img:'/assets/number-3.svg',action: () => this.goto('continuity')},\r\n      {title: 'Conditions for Applicability', img:'/assets/number-4.svg',action: () => this.goto('appl')},\r\n      {title: 'PlayGraph: Fluid Flow in a Vertical Duct', img:'/assets/touch.svg',action: () => this.goto('PlayGraph')},\r\n    ];\r\n    this.$store.commit('navigation/replaceTopics', newTopics);\r\n    let newshowhome = false;\r\n    this.$store.commit('navigation/toggleshowhome', newshowhome);\r\n    let newPhys =true;\r\n    this.$store.commit('navigation/replacePhys', newPhys);\r\n    let newLeftArrow =true;\r\n    this.$store.commit('navigation/replaceLeftArrow', newLeftArrow);\r\n    let newModule =true;\r\n    this.$store.commit('navigation/replaceModule', newModule);\r\n  },\r\n  mounted () {\r\n    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\r\n    Boxes.box1();\r\n\r\n  },\r\n  updated () {\r\n    // MathJax.Hub.Queue([\"Typeset\", MathJax.Hub]);\r\n  }\r\n}\r\n</script>\r\n<style lang=\"scss\">\r\n@import 'src/styles/edliy-box.scss';\r\n@import 'src/styles/subtopic-menu.scss';\r\n@import 'src/styles/edliy-box-about.scss';\r\n@import 'src/styles/screen-sizes.scss';\r\n</style>\r\n","import mod from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"; export default mod; export * from \"-!../../../../node_modules/cache-loader/dist/cjs.js??ref--12-0!../../../../node_modules/thread-loader/dist/cjs.js!../../../../node_modules/babel-loader/lib/index.js!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./Lesson.vue?vue&type=template&id=73c1be5e&\"\nimport script from \"./Lesson.vue?vue&type=script&lang=js&\"\nexport * from \"./Lesson.vue?vue&type=script&lang=js&\"\nimport style0 from \"./Lesson.vue?vue&type=style&index=0&id=73c1be5e&prod&lang=scss&\"\n\n\n/* normalize component */\nimport normalizer from \"!../../../../node_modules/vue-loader/lib/runtime/componentNormalizer.js\"\nvar component = normalizer(\n  script,\n  render,\n  staticRenderFns,\n  false,\n  null,\n  null,\n  null\n  \n)\n\nexport default component.exports","export * from \"-!../../../../node_modules/mini-css-extract-plugin/dist/loader.js??ref--8-oneOf-1-0!../../../../node_modules/css-loader/index.js??ref--8-oneOf-1-1!../../../../node_modules/vue-loader/lib/loaders/stylePostLoader.js!../../../../node_modules/postcss-loader/src/index.js??ref--8-oneOf-1-2!../../../../node_modules/sass-loader/dist/cjs.js??ref--8-oneOf-1-3!../../../../node_modules/cache-loader/dist/cjs.js??ref--0-0!../../../../node_modules/vue-loader/lib/index.js??vue-loader-options!./Lesson.vue?vue&type=style&index=0&id=73c1be5e&prod&lang=scss&\""],"sourceRoot":""}