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* 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!./MoI.vue?vue&type=style&index=0&id=0fdaa229&prod&lang=scss&\"","var render = function render(){var _vm=this,_c=_vm._self._c;return _c('div',[_c('h3',{ref:\"ia\"},[_vm._v(\"\\n    What is Moment of Inertia?\\n  \")]),_c('p',[_vm._v(\"\\n    Moment of inertia, also known as rotational inertia, is the analog of mass for rotational motions.\\n    Let us start with Newton's second law of motion:\\n    $$F = m a$$\\n    where \\\\(m\\\\) is the mass of the object, \\\\(a \\\\) is the linear acceleration,  and \\\\(F\\\\) is the force applied on the object.\\n    The higher an object's mass, the smaller the acceleration that the object will experience under the action of an external force.\\n    Thus, one way to think of mass is as an intrinsic property of an object that offers the resistance against linear motion.\\n    Now, let us write the Newton's second law for rotation motion\\n    $$\\\\tau = I \\\\alpha$$\\n    where  \\\\(I\\\\) is the moment of inertia of the object, \\\\(\\\\tau\\\\) is the torque, and \\\\(\\\\omega\\\\) is angular acceleration.\\n    Thus, the moment of inertia \\\\(I\\\\) is the rotational analog of mass: the larger the moment of an object's inertia, the smaller the angular acceleration it will experience under the action of an external torque.\\n  \")]),_c('h3',[_vm._v(\"Moment of Inertia of a Point Mass\")]),_c('p',[_vm._v(\"\\n    The moment of inertia of a point mass with respect to an axis is equal to the product of the mass times square of its distance from the axis.\\n    $$I = m r^2$$\\n    For more complex geometries, the moment of inertia can be calculated\\n    by summing the moment of inertia of individual material elements.\\n    $$I = \\\\sum m_i r_i^2$$\\n  \")]),_c('h3',[_vm._v(\"Example: Moment of Inertial of an Annulus\")]),_c('br'),_c('h3',{ref:\"pg\"},[_vm._v(\"\\n    MagicGraph: Moment of Inertial and Distribution of Mass\\n  \")]),_c('p',[_vm._v(\"\\n    Because of the way area moment of inertia is calculated, the area\\n    elements that are nearer to the axis of moment contribute lesser while the area elements that are farther from the axis contribute higher.\\n    One consequence of this is that a hollow section will have a higher moment of inertia than a solid section for the same cross-sectional area. 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brd2.create('line',[[0+shftx2,shft2],[1.75+shftx2,shft2]],{fixed:true, straightFirst:false, straightLast:false, strokeWidth:0, strokeColor:'white'});\r\n\tvar ptA2=brd2.create('glider',[0.25+shftx2,0.0+shft2, glideAB2], {name:'Drag me!',face:'square',size:3,shadow:true, strokeColor:'black'});\r\n\tbrd2.create('image', ['assets/sort.svg', [function(){return ptA2.X()+0.1}, shft2-0.075],[0.15, 0.2]],{rotate:90});\r\n\tvar rad2=brd2.create('arrow',[[0.0+shftx2,shft2],[function(){return (ptA2.X()-shftx2)/Math.sqrt(2)+shftx2;},function(){return shft2+(ptA2.X()-shftx2)/Math.sqrt(2);}]],{strokeColor:'black',strokeWidth:3});\r\n\tvar ptB2=brd2.create('point',[function(){return Math.sqrt(A2/Math.PI+(ptA2.X()-shftx2)*(ptA2.X()-shftx2))+shftx2;}, shft2],{size:0, name:''});\r\n\t\r\n\tbrd2.create('arrow',[[0.0+shftx2,shft2],[function(){return (ptB2.X()-shftx2)/Math.sqrt(2)+shftx2;},function(){return shft2-(ptB2.X()-shftx2)/Math.sqrt(2);}]],{strokeColor:'black',strokeWidth:3});\r\n\t\r\n\tvar ptmD2=brd2.create('circle',[[0+shftx2,shft2], ptB2],{fillColor:'lightblue',strokeColor:'black'});\r\n\tvar ptmC2=brd2.create('circle',[[0+shftx2,shft2], ptA2],{fillColor:'white',strokeColor:'black'});\r\n\tvar textM2=brd2.create('text',[-3.+shftx2,3.5,function(){return 'Moment of area = '+((Math.PI/2.0)*((ptB2.X()-shftx2)*(ptB2.X()-shftx2)+(ptA2.X()-shftx2)*(ptA2.X()-shftx2))*((ptB2.X()-shftx2)*(ptB2.X()-shftx2)-(ptA2.X()-shftx2)*(ptA2.X()-shftx2))).toFixed(2);}],{fixed:true, fontSize:function(){return 28*brd2.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\tvar textA=brd2.create('text',[-.5+shftx2, 3.5, function(){return 'Area (fixed) = '+ (Math.PI*((ptB2.X()-shftx2)*(ptB2.X()-shftx2)-(ptA2.X()-shftx2)*(ptA2.X()-shftx2))).toFixed(2)}],{fixed:true, fontSize:function(){return 28*brd2.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\tvar texthead=brd2.create('text',[-2.3+shftx2, 4.5,'<b> Moment of Area: Hollow vs. Solid Section <b> '],{fixed:true, fontSize:function(){return 32*brd2.canvasHeight/800}, cssStyle:'fontFamily:Oswald;'});\r\n\tvar plot=brd2.create('functiongraph',[function(x){return (Math.PI/2.0)*(Math.sqrt(A2/Math.PI+x*x)*Math.sqrt(A2/Math.PI+x*x)-x*x)*(Math.sqrt(A2/Math.PI+x*x)*Math.sqrt(A2/Math.PI+x*x)+x*x)}, 0, function(){return ptA2.X()-shftx2;}],{strokeColor:'red', strokeWidth:4});\r\n\tbrd2.unsuspendUpdate();\r\n      },\r\n}\r\nexport default Boxes;\r\n","<template>\r\n  <div>\r\n    <h3 ref=\"ia\">\r\n      What is Moment of Inertia?\r\n    </h3>\r\n    <p>\r\n      Moment of inertia, also known as rotational inertia, is the analog of mass for rotational motions.\r\n      Let us start with Newton's second law of motion:\r\n      $$F = m a$$\r\n      where \\(m\\) is the mass of the object, \\(a \\) is the linear acceleration,  and \\(F\\) is the force applied on the object.\r\n      The higher an object's mass, the smaller the acceleration that the object will experience under the action of an external force.\r\n      Thus, one way to think of mass is as an intrinsic property of an object that offers the resistance against linear motion.\r\n      Now, let us write the Newton's second law for rotation motion\r\n      $$\\tau = I \\alpha$$\r\n      where  \\(I\\) is the moment of inertia of the object, \\(\\tau\\) is the torque, and \\(\\omega\\) is angular acceleration.\r\n      Thus, the moment of inertia \\(I\\) is the rotational analog of mass: the larger the moment of an object's inertia, the smaller the angular acceleration it will experience under the action of an external torque.\r\n    </p>\r\n    <h3>Moment of Inertia of a Point Mass</h3>\r\n    <p>\r\n      The moment of inertia of a point mass with respect to an axis is equal to the product of the mass times square of its distance from the axis.\r\n      $$I = m r^2$$\r\n      For more complex geometries, the moment of inertia can be calculated\r\n      by summing the moment of inertia of individual material elements.\r\n      $$I = \\sum m_i r_i^2$$\r\n    </p>\r\n    <h3>Example: Moment of Inertial of an Annulus</h3>\r\n    <br>\r\n    <h3 ref=\"pg\">\n      MagicGraph: Moment of Inertial and Distribution of Mass\n    </h3>\r\n    <p>\n      Because of the way area moment of inertia is calculated, the area\r\n      elements that are nearer to the axis of moment contribute lesser while the area elements that are farther from the axis contribute higher.\r\n      One consequence of this is that a hollow section will have a higher moment of inertia than a solid section for the same cross-sectional area. This is because the area elements on the cross-sectional area of a hollow cylinder are distributed farther away from the center than those in the solid cylinder.\n    </p>\r\n    <v-responsive\r\n      :aspect-ratio=\"1\"\r\n    >\r\n      <v-layout 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<script>\r\nimport Boxes from './Boxes.js'\r\nexport default {\r\n  name: 'MoI',\r\n  created: function () {\r\n    this.$store.commit('navigation/resetState');\r\n    let title = 'Moment of Inertia';\r\n    this.$store.commit('navigation/changeTitle', title);\r\n    this.$store.commit('navigation/changeMenu', title);\r\n    let newTopics = [\r\n      {title: 'Moment of Inertia: Definition?', img:'assets/number-1.svg', action: () => this.goto('ia')},\r\n      {title: 'Point Mass', img:'assets/number-2.svg', action: () => this.goto('ca')},\r\n      {title: 'MagicGraph:Distribution of Mass' ,img:'assets/touch.svg', action: () => this.goto('graphical')},\r\n    ];\r\n    this.$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</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!./MoI.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!./MoI.vue?vue&type=script&lang=js&\"","import { render, staticRenderFns } from \"./MoI.vue?vue&type=template&id=0fdaa229&\"\nimport script from \"./MoI.vue?vue&type=script&lang=js&\"\nexport * from \"./MoI.vue?vue&type=script&lang=js&\"\nimport style0 from \"./MoI.vue?vue&type=style&index=0&id=0fdaa229&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"],"sourceRoot":""}