Moment of inertia through scaling and the parallel axis theorem
Abstract A right triangular plate scaled by a factor two generates a bigger plate composed of four triangular plates the same size as the original. By using dimensional analysis we write the moment of inertia around the center of mass, for the original and the bigger plate, in terms of a common unkn...
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| Format: | Article |
| Language: | Portuguese |
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Sociedade Brasileira de Física
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| Series: | Revista Brasileira de Ensino de Física |
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| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000100801&lng=en&tlng=en |
| _version_ | 1830412576895270912 |
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| author | Roberto Rojas |
| author_facet | Roberto Rojas |
| author_sort | Roberto Rojas |
| collection | DOAJ |
| description | Abstract A right triangular plate scaled by a factor two generates a bigger plate composed of four triangular plates the same size as the original. By using dimensional analysis we write the moment of inertia around the center of mass, for the original and the bigger plate, in terms of a common unknown parameter. Through the parallel axis theorem we relate the moments of inertia of both plates and finally solve a very simple equation to find out the unknown parameter. This procedure avoids to calculate integrals. The result is extended to a scalene triangular plate by recognizing it is composed of two right triangular plates. We also review the parallel axis theorem in an appendix. |
| first_indexed | 2024-12-20T20:11:42Z |
| format | Article |
| id | doaj.art-6732e70fb94d4fa3b88b4db67e5eed4b |
| institution | Directory Open Access Journal |
| issn | 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-12-20T20:11:42Z |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-6732e70fb94d4fa3b88b4db67e5eed4b2022-12-21T19:27:49ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-912641110.1590/1806-9126-rbef-2018-0146S1806-11172019000100801Moment of inertia through scaling and the parallel axis theoremRoberto RojasAbstract A right triangular plate scaled by a factor two generates a bigger plate composed of four triangular plates the same size as the original. By using dimensional analysis we write the moment of inertia around the center of mass, for the original and the bigger plate, in terms of a common unknown parameter. Through the parallel axis theorem we relate the moments of inertia of both plates and finally solve a very simple equation to find out the unknown parameter. This procedure avoids to calculate integrals. The result is extended to a scalene triangular plate by recognizing it is composed of two right triangular plates. We also review the parallel axis theorem in an appendix.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000100801&lng=en&tlng=enMoment of inertiascalingparallel-axis theorem |
| spellingShingle | Roberto Rojas Moment of inertia through scaling and the parallel axis theorem Revista Brasileira de Ensino de Física Moment of inertia scaling parallel-axis theorem |
| title | Moment of inertia through scaling and the parallel axis theorem |
| title_full | Moment of inertia through scaling and the parallel axis theorem |
| title_fullStr | Moment of inertia through scaling and the parallel axis theorem |
| title_full_unstemmed | Moment of inertia through scaling and the parallel axis theorem |
| title_short | Moment of inertia through scaling and the parallel axis theorem |
| title_sort | moment of inertia through scaling and the parallel axis theorem |
| topic | Moment of inertia scaling parallel-axis theorem |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172019000100801&lng=en&tlng=en |
| work_keys_str_mv | AT robertorojas momentofinertiathroughscalingandtheparallelaxistheorem |