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At t = 0 the whole system is at rest
<Text-field style="Heading 2" layout="Heading 2">Centre of Mass</Text-field> The masses are said to be considered as concentrated mass points. Setting the lower point as the origin, the masses coordinates are as following: Qyg+JkkiUkc2IjYjSSNtMUdGJi1JJDwsPkdGJjYlIiIhSSJMR0YmRiwhIiI+JkYlNiNJI20yR0YmLUYqNiVGLEYsRixGLj4mRiU2I0kjbTNHRiZGM0Yu LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder The definition of the Centre of Mass is 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 , thus:
<Text-field style="Heading 3" layout="Heading 3">System's Centre of Mass</Text-field> PiZJIlJHNiI2I0kjQ01HRiUtSSIqRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJUkvVmVjdG9yQ2FsY3VsdXNHNiRGK0koX3N5c2xpYkdGJTYkLUkiK0dGKjYkLUYzNiQtRik2JCZJIm1HRiU2IyIiIiZGJDYjSSNtMUdGJS1GKTYkJkY6NiMiIiMmRiQ2I0kjbTJHRiUtRik2JCZGOjYjIiIkJkYkNiNJI20zR0YlKiQtRjM2JC1GMzYkRjlGQkZKISIi LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqX108YCI= JSFH
<Text-field style="Heading 3" layout="Heading 3">Rod's Centre of Mass</Text-field> PiZJIlJHNiI2I0knQ01fcm9kR0YlLUkiKkc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJL1ZlY3RvckNhbGN1bHVzRzYkRitJKF9zeXNsaWJHRiU2JC1JIitHRio2JC1GKTYkJkkibUdGJTYjIiIiJkYkNiNJI20xR0YlLUYpNiQmRjg2IyIiIyZGJDYjSSNtMkdGJSokLUYzNiRGN0ZAISIi LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqK2I8YCI=
<Text-field style="Heading 2" layout="Heading 2">After Blast, Linear Motion</Text-field> Conservation of momentum dictates JSFH 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 . Since at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= this constant is known to be zero it stays zero at all time. Rearranging the expression of momentum 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 PkkkZXExRzYiLy1JIitHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSS9WZWN0b3JDYWxjdWx1c0c2JEYpSShfc3lzbGliR0YkNiQtSSIqR0YoNiQmSSJtR0YkNiNJJHJvZEdGJCZJInZHRiRGNS1GMTYkJkY0NiMiIiQmRjhGPCIiIQ== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= print(); # input placeholder LywmKiYmSSJtRzYiNiNJJHJvZEdGJyIiIiZJInZHRidGKEYqRiotJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YnNiNJJ2NvbHVtbkdGJzYjL0kkJWlkR0YnIiprYjxgIkYqIiIh PiZJIm1HNiI2I0kkcm9kR0YlLUkiK0c2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJL1ZlY3RvckNhbGN1bHVzRzYkRitJKF9zeXNsaWJHRiU2JCZGJDYjIiIiJkYkNiMiIiM= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LCRJIk1HNiIiIiM= JSFH PiZJInZHNiI2I0kkcm9kR0YlLUkvU2V0Q29vcmRpbmF0ZXNHRiU2JC1JKXNpbXBsaWZ5R0YlNiMtSSZzb2x2ZUdGJTYkSSRlcTFHRiVGIy5JKmNhcnRlc2lhbkdGJQ== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqY3Q8YCI= NOTICE This is the velocity of the Rod's Centre of Mass, the System's Centre of Mass stays in rest ! JSFH
<Text-field style="Heading 2" layout="Heading 2">After Blast, Angular Motion</Text-field>
<Text-field style="Heading 3" layout="Heading 3">Introduction</Text-field> Getting back to basics to understand the matter of Angular Momentum, lets start with the basic Linear Conservation of Momentum : 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 . Angular momentum is defined as a vector cross product between the position vector of any particle and its linear momentum 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. For a set of particles employing the cross product on both sides of the expression for p, yields 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 Since p is time invariant (constant), the cross product is inherently time invariant, meaning that H is conserved. In the case planar motion, as is presented in this question, the expression for angular moment is very simple. Let u be the the position vector of a point P, in cylindrical coordinates 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, u is describedJSFH 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 , were 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 is a dextral (right handed) set of orthogonal unit vectors. For planar motion z is inherently zero, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk=, thus 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 . The dextral set, 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, cross products follows the scheme: 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 The angular velocity vector , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EnJiM5Njk7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy9GNlEnbm9ybWFsRic=, is perpendicular to the plane of motion, hence: 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 . JSFH 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
It is important to notice that for any particle in the plane of motion, regardless of its position the following identity hold true: 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 Hence: 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 JSFH Within a rigid body all points rotate at the same rate, hence LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiVRImlGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y9Rj8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RLCZDb25ncnVlbnQ7RidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlhGLkY1 and may removed outside of the sum, 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 The last term, 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, is given the name Angular Moment of Inertia [J] or [I]. Since I is a Maple reserved word for Complex Numbers, hereafter only the notation J is to be used. Any textbook (or home assignment) would easily elaborate further the issue of angular moment of inertia, in the case of a rod of negligible mass and two point masses connected to its end one easily obtain J by definition.
<Text-field style="Heading 3" layout="Heading 3">Method 1 - Direct calculation</Text-field> The point JkkiUkc2IjYjSSNDTUdGJA== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqX108YCI= is the system's centre of mass at all time. Setting the origin at the system's centre of mass the angular momentum of the mass LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ is: PkkjSDFHNiItSSIqRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEkvVmVjdG9yQ2FsY3VsdXNHNiRGKEkoX3N5c2xpYkdGJDYkJkkibUdGJDYjIiIkLUkjJnhHRiQ2JC1JIitHRic2JCZJIlJHRiQ2I0kjbTNHRiQtSSItR0YnNiMmRjo2I0kjQ01HRiQmSSJ2R0YkRjE= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqQyJ5Sjo= JSFH The rod's moment of inertia about JkkiUkc2IjYjSSdDTV9yb2RHRiQ= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqK2I8YCI= is PkkiSkc2Ii1JIitHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSS9WZWN0b3JDYWxjdWx1c0c2JEYoSShfc3lzbGliR0YkNiQtSSIqR0YnNiQmSSJtR0YkNiMiIiIqJC1JJU5vcm1HRiQ2Iy1GJjYkJkkiUkdGJDYjSSNtMUdGJC1JIi1HRic2IyZGPTYjSSdDTV9yb2RHRiQiIiMtRjA2JCZGMzYjRkYqJC1GODYjLUYmNiQmRj02I0kjbTJHRiRGQEZG LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LCQqJkkiTUc2IiIiIkkiTEdGJSIiIyNGJkYo and the vector of the rod's angular velocity about LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiUkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSSVtcm93R0YkNiQtRiw2JVEnQ01fcm9kRidGMi9GNVEnaXRhbGljRicvRjVRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= is unknown: QyQ+SSZvbWVnYUc2Ii1JJDwsPkdGJTYlJkkid0dGJTYjIiIiJkYqNiMiIiMmRio2IyIiJCEiIg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= JSFH The angular momentum of the rod about the system's centre of mass is PkkjSDJHNiItSSIrRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEkvVmVjdG9yQ2FsY3VsdXNHNiRGKEkoX3N5c2xpYkdGJDYkLUkiKkdGJzYkLUYmNiQmSSJtR0YkNiMiIiImRjU2IyIiIy1JIyZ4R0YkNiQtRiY2JCZJIlJHRiQ2I0knQ01fcm9kR0YkLUkiLUdGJzYjJkZBNiNJI0NNR0YkJkkidkdGJDYjSSRyb2RHRiQtRjA2JEkiSkdGJEkmb21lZ2FHRiQ= LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqI1whPWAi JSFH Conservation of angular momentum dictates 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 PkkmQU1fRXFHNiIvLUkiK0c2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiRJL1ZlY3RvckNhbGN1bHVzRzYkRilJKF9zeXNsaWJHRiQ2JEkjSDFHRiQtSSItR0YoNiNJI0gyR0YkIiIh LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; Ly0mSSdWZWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0knY29sdW1uR0YpNiMvSSQlaWRHRikiKnczPWAiIiIh The components in the directions LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJ4RidGL0YyLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= and LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJ5RidGL0YyLyUvc3Vic2NyaXB0c2hpZnRHUSIwRic= are obviously annihilated ( LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= QyY+Jkkid0c2IjYjIiIiIiIhISIiPiZGJTYjIiIjRilGKg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; ), hence QyQ+Jkkid0c2IjYjIiIkLUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2JC8tSTBkZWxheURvdFByb2R1Y3RHNiRGLC9JK21vZHVsZW5hbWVHRiZJLFR5cGVzZXR0aW5nR0YrNiQtSSRsaHNHRiw2I0kmQU1fRXFHRiYtSSQ8LD5HRiY2JSIiIUY+IiIiRj5GJCEiIg== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= %; so the full expression for the angular momentum of the rod is: SSZvbWVnYUc2Ig== LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic= = print(); # input placeholder LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqLyV6Sjo=
JSFH TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3MzM4OFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQlIlZHISIiIiIhRiw2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3NTA1MlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIhLCQlIkxHIyIiIiIiKUYpNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3NTUwMFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIhLCQlIkxHIyIiIiIiI0YpNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3NTU2NFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQqJiUiTUciIiIlIlZHRiwhIiciIiFGLzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3NzM1NlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLCQlIlZHIiIkIiIhRiw2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3NTA1MlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIhLCQlIkxHIyIiIiIiKUYpNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3ODEyNFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIhRiksJCooJSJNRyIiIiUiTEdGLSUiVkdGLSMhIiQiIiU2Ig==TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3NTUwMFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkIiIhLCQlIkxHIyIiIiIiI0YpNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE4MDQ5MlgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJCooJSJNRyIiIiUiTEciIiMmJSJ3RzYjRi1GLSNGLUYvLCQqKEYsRi1GLkYvJkYxNiNGL0YtRjMsJiooRixGLUYuRi0lIlZHRi0jISIqIiIlKihGLEYtRi5GLyZGMTYjIiIkRi1GMzYiTTdSMApJNlJUQUJMRV9TQVZFLzE1MzE4MDg3NlgqJSlhbnl0aGluZ0c2IjYjLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJCooJSJNRyIiIiUiTEciIiMmJSJ3RzYjRi1GLSMhIiJGLywkKihGLEYtRi5GLyZGMTYjRi9GLUYzLCYqKEYsRi1GLkYtJSJWR0YtIyIiJEYvKihGLEYtRi5GLyZGMTYjRj1GLUYzNiI=TTdSMApJNlJUQUJMRV9TQVZFLzE1MzE3OTQwNFgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkJiUid0c2IyIiIiZGKjYjIiIjJkYqNiMiIiQ2Ig==