Translated 1.5.1-1.5.2;1.5.3-1.5.7
en/1.5.6.md
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| + | <meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda"> | ||
| + | <meta name="description" content="A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis."> | ||
| + | <meta name="author" content="Aliaksandr Melnichenka"> | ||
| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
| + | <meta property="og:title" content="A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis."> | ||
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| + | <meta property="og:description" content="A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis."> | ||
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| + | <title>A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis.</title> | ||
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| + | <header style="text-align:center;"> | ||
| + | <h2>Solutions of Savchenko Problems in Physics</h2> | ||
| + | <p class="author"> | ||
| + | Aliaksandr Melnichenka <br/> | ||
| + | October 2023 | ||
| + | </p> | ||
| + | </header> | ||
| + | |||
| + | <h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | <p> | ||
| + | $1.5.6.$ A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points $A$ and $B$ of this body are ($-1$, $2$) and ($3$, $1$), and the final position is ($-3$, $1$) and ($-2$, $-3$). Use a graphical plot to find the coordinates of the rotation axis. | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | <p>Since the axis of rotation is fixed, all points of the body rotate around it and are perpendicular in direction. | ||
| + | </p> | ||
| + | <p>If the coordinates of two points at the beginning and end are $A$, $B$ and $A'$, $B'$ respectively, then if you draw lines $AB$ and $A'B'$, their intersection point will be the center of rotation | ||
| + | </p> | ||
| + | |||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/1/1.5.6/graph.png" | ||
| + | loading="lazy" width="350" /> | ||
| + | <figcaption> | ||
| + | Intersection point of lines | ||
| + | </figcaption> | ||
| + | </figure> | ||
| + | </center> | ||
| + | |||
| + | <p>According to constructions, this point has coordinates $(-3.4,\; 2.6)$ | ||
| + | </p> | ||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | $(-3.4,\; 2.6)$ | ||
| + | </p> | ||
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| + | <p> | ||
| + | <small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small> | ||
| + | </p> | ||
| + | <p> | ||
| + | <small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> aliaksandr@savchenkosolutions.com <br></small> | ||
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| <html lang="en"> | |||
| <head> | |||
| <meta charset="utf-8"> | |||
| <meta name="viewport" content="width=device-width, initial-scale=1.0"> | |||
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| <meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda"> | |||
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| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis."> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis."> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points A and B of this body are (-1, 2) and (3, 1), and the final position is (-3, 1) and (-2, -3). Use a graphical plot to find the coordinates of the rotation axis.</title> | |||
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| </head> | |||
| <body style=""> | |||
| <header style="text-align:center;"> | |||
| <h2>Solutions of Savchenko Problems in Physics</h2> | |||
| <p class="author"> | |||
| Aliaksandr Melnichenka <br/> | |||
| October 2023 | |||
| </p> | |||
| </header> | |||
| <h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $1.5.6.$ A flat solid body rotates around an axis perpendicular to its plane. The coordinates of the initial position of points $A$ and $B$ of this body are ($-1$, $2$) and ($3$, $1$), and the final position is ($-3$, $1$) and ($-2$, $-3$). Use a graphical plot to find the coordinates of the rotation axis. | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| <p>Since the axis of rotation is fixed, all points of the body rotate around it and are perpendicular in direction. | |||
| </p> | |||
| <p>If the coordinates of two points at the beginning and end are $A$, $B$ and $A'$, $B'$ respectively, then if you draw lines $AB$ and $A'B'$, their intersection point will be the center of rotation | |||
| </p> | |||
| <center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/1/1.5.6/graph.png" | |||
| loading="lazy" width="350" /> | |||
| <figcaption> | |||
| Intersection point of lines | |||
| </figcaption> | |||
| </figure> | |||
| </center> | |||
| <p>According to constructions, this point has coordinates $(-3.4,\; 2.6)$ | |||
| </p> | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| $(-3.4,\; 2.6)$ | |||
| </p> | |||
| <footer class="row container"> | |||
| <br> | |||
| <p> | |||
| <small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small> | |||
| </p> | |||
| <p> | |||
| <small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> aliaksandr@savchenkosolutions.com <br></small> | |||
| </p> | |||
| </footer> | |||
| </body> | |||
| </html> | |||