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	<title>EjerciciosFyQ</title>
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	<description>Ejercicios Resueltos, Situaciones de aprendizaje y V&#205;DEOS de F&#237;sica y Qu&#237;mica para Secundaria y Bachillerato</description>
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<item xml:lang="es">
		<title>[P(232)] Aceleraci&#243;n de un tren que se mueve por una v&#237;a circular (8467)</title>
		<link>https://ejercicios-fyq.com/P-232-Aceleracion-de-un-tren-que-se-mueve-por-una-via-circular-8467</link>
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		<dc:date>2025-05-27T05:56:50Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>Aceleraci&#243;n</dc:subject>
		<dc:subject>Cinem&#225;tica</dc:subject>

		<description>
&lt;p&gt;Si clicas en este enlace podr&#225;s ver el enunciado y las respuestas del problema que se resuelve en el v&#237;deo.&lt;/p&gt;


-
&lt;a href="https://ejercicios-fyq.com/3-Estudio-de-Diversos-Movimientos" rel="directory"&gt;3 - Estudio de Diversos Movimientos&lt;/a&gt;

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&lt;a href="https://ejercicios-fyq.com/MCUA" rel="tag"&gt;MCUA&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Aceleracion" rel="tag"&gt;Aceleraci&#243;n&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Cinematica-338" rel="tag"&gt;Cinem&#225;tica&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;&lt;b&gt;&lt;a href='https://ejercicios-fyq.com/Aceleracion-tangencial-normal-y-total-de-un-tren-que-circula-por-una-via' class=&#034;spip_in&#034;&gt;Si clicas en este enlace&lt;/a&gt;&lt;/b&gt; podr&#225;s ver el enunciado y las respuestas del problema que se resuelve en el v&#237;deo.&lt;/p&gt;
&lt;p&gt; &lt;br/&gt;&lt;/p&gt;
&lt;iframe width=&#034;560&#034; height=&#034;315&#034; src=&#034;https://www.youtube.com/embed/4on7zdqKYoE&#034; title=&#034;YouTube video player&#034; frameborder=&#034;0&#034; allow=&#034;accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture&#034; allowfullscreen&gt;&lt;/iframe&gt;&lt;/div&gt;
		
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<item xml:lang="es">
		<title>P[(250)] Aceleraciones angular y normal de un movimiento circular (8305)</title>
		<link>https://ejercicios-fyq.com/P-250-Aceleraciones-angular-y-normal-de-un-movimiento-circular-8305</link>
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		<dc:date>2024-09-09T03:34:53Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>Cinem&#225;tica</dc:subject>

		<description>
&lt;p&gt;Para ver el enunciado y las soluciones del problema que se resuelve en el v&#237;deo clica en este enlace.&lt;/p&gt;


-
&lt;a href="https://ejercicios-fyq.com/3-Estudio-de-Diversos-Movimientos" rel="directory"&gt;3 - Estudio de Diversos Movimientos&lt;/a&gt;

/ 
&lt;a href="https://ejercicios-fyq.com/MCUA" rel="tag"&gt;MCUA&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Cinematica-338" rel="tag"&gt;Cinem&#225;tica&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;Para ver el enunciado y las soluciones del problema que se resuelve en el v&#237;deo &lt;b&gt;&lt;a href='https://ejercicios-fyq.com/Aceleracion-angular-y-aceleracion-normal-de-un-movimiento-circular-250' class=&#034;spip_in&#034;&gt;clica en este enlace&lt;/a&gt;&lt;/b&gt;.&lt;/p&gt;
&lt;iframe width=&#034;560&#034; height=&#034;315&#034; src=&#034;https://www.youtube.com/embed/YaZojyZIwis&#034; title=&#034;YouTube video player&#034; frameborder=&#034;0&#034; allow=&#034;accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture&#034; allowfullscreen&gt;&lt;/iframe&gt;&lt;/div&gt;
		
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	</item>
<item xml:lang="es">
		<title>[P(809)] An&#225;lisis de un movimiento circular uniformemente variado (8205)</title>
		<link>https://ejercicios-fyq.com/P-809-Analisis-de-un-movimiento-circular-uniformemente-variado-8205</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/P-809-Analisis-de-un-movimiento-circular-uniformemente-variado-8205</guid>
		<dc:date>2024-05-10T03:41:11Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCU</dc:subject>
		<dc:subject>MCUA</dc:subject>
		<dc:subject>Aceleraci&#243;n</dc:subject>
		<dc:subject>Cinem&#225;tica</dc:subject>

		<description>
&lt;p&gt;Para ver el enunciado y las respuestas al problema que se resuelve en el v&#237;deo, basta con que hagas clic en este enlace.&lt;/p&gt;


-
&lt;a href="https://ejercicios-fyq.com/03-Movimiento-en-dos-y-tres-dimensiones" rel="directory"&gt;03 - Movimiento en dos y tres dimensiones&lt;/a&gt;

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&lt;a href="https://ejercicios-fyq.com/MCU" rel="tag"&gt;MCU&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/MCUA" rel="tag"&gt;MCUA&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Aceleracion" rel="tag"&gt;Aceleraci&#243;n&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Cinematica-338" rel="tag"&gt;Cinem&#225;tica&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;Para ver el enunciado y las respuestas al problema que se resuelve en el v&#237;deo, &lt;b&gt;&lt;a href='https://ejercicios-fyq.com/Cinematica-analisis-de-un-movimiento-circular-acelerado-809' class=&#034;spip_in&#034;&gt;basta con que hagas clic en este enlace&lt;/a&gt;&lt;/b&gt;.&lt;/p&gt;
&lt;p&gt; &lt;br/&gt;&lt;/p&gt;
&lt;iframe width=&#034;560&#034; height=&#034;315&#034; src=&#034;https://www.youtube.com/embed/cHuYWlFaSz0&#034; title=&#034;YouTube video player&#034; frameborder=&#034;0&#034; allow=&#034;accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture&#034; allowfullscreen&gt;&lt;/iframe&gt;&lt;/div&gt;
		
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	</item>
<item xml:lang="es">
		<title>[P(1181)] Movimiento circular uniformemente acelerado: aceleraci&#243;n tangencial y velocidad lineal (8203)</title>
		<link>https://ejercicios-fyq.com/P-1181-Movimiento-circular-uniformemente-acelerado-aceleracion-tangencial-y</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/P-1181-Movimiento-circular-uniformemente-acelerado-aceleracion-tangencial-y</guid>
		<dc:date>2024-05-09T03:19:44Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>Velocidad</dc:subject>
		<dc:subject>Aceleraci&#243;n</dc:subject>
		<dc:subject>Cinem&#225;tica</dc:subject>

		<description>
&lt;p&gt;Para ver el enunciado y las respuestas del problema que se resuelve en el v&#237;deo puedes hacer clic en este enlace.&lt;/p&gt;


-
&lt;a href="https://ejercicios-fyq.com/3-Estudio-de-Diversos-Movimientos" rel="directory"&gt;3 - Estudio de Diversos Movimientos&lt;/a&gt;

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&lt;a href="https://ejercicios-fyq.com/MCUA" rel="tag"&gt;MCUA&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Velocidad" rel="tag"&gt;Velocidad&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Aceleracion" rel="tag"&gt;Aceleraci&#243;n&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Cinematica-338" rel="tag"&gt;Cinem&#225;tica&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;Para ver el enunciado y las respuestas del problema que se resuelve en el v&#237;deo &lt;b&gt;&lt;a href='https://ejercicios-fyq.com/Movimiento-circular-uniformemente-acelerado-aceleracion-tangencial-y-velocidad' class=&#034;spip_in&#034;&gt;puedes hacer clic en este enlace&lt;/a&gt;&lt;/b&gt;.&lt;/p&gt;
&lt;p&gt; &lt;br/&gt;&lt;/p&gt;
&lt;iframe width=&#034;560&#034; height=&#034;315&#034; src=&#034;https://www.youtube.com/embed/aVW6cmzopzA&#034; title=&#034;YouTube video player&#034; frameborder=&#034;0&#034; allow=&#034;accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture&#034; allowfullscreen&gt;&lt;/iframe&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Vueltas que da una rueda que frena con aceleraci&#243;n angular constante (7975)</title>
		<link>https://ejercicios-fyq.com/Vueltas-que-da-una-rueda-que-frena-con-aceleracion-angular-constante-7975</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/Vueltas-que-da-una-rueda-que-frena-con-aceleracion-angular-constante-7975</guid>
		<dc:date>2023-07-02T05:41:03Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>Cinem&#225;tica</dc:subject>
		<dc:subject>RESUELTO</dc:subject>

		<description>
&lt;p&gt;Las ruedas de un autom&#243;vil experimentan un movimiento circular uniformemente variado. Si inicialmente giran a raz&#243;n de y experimentan una aceleraci&#243;n de frenada de , &#191;cu&#225;ntas vueltas habr&#237;a dado en el tercer segundo de su movimiento?&lt;/p&gt;


-
&lt;a href="https://ejercicios-fyq.com/Cinematica" rel="directory"&gt;Cinem&#225;tica&lt;/a&gt;

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&lt;a href="https://ejercicios-fyq.com/MCUA" rel="tag"&gt;MCUA&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Cinematica-338" rel="tag"&gt;Cinem&#225;tica&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/RESUELTO" rel="tag"&gt;RESUELTO&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;Las ruedas de un autom&#243;vil experimentan un movimiento circular uniformemente variado. Si inicialmente giran a raz&#243;n de &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L40xH17/c9f4dab4415fef9daa328cd8786abfaa-12059.png?1733067869' style='vertical-align:middle;' width='40' height='17' alt=&#034;10\ \textstyle{rev\over s}&#034; title=&#034;10\ \textstyle{rev\over s}&#034; /&gt; y experimentan una aceleraci&#243;n de frenada de &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L33xH17/8408d387df4adbf62226fab3dfe765b2-47338.png?1733067869' style='vertical-align:middle;' width='33' height='17' alt=&#034;2\ \textstyle{rev\over s^2}&#034; title=&#034;2\ \textstyle{rev\over s^2}&#034; /&gt;, &#191;cu&#225;ntas vueltas habr&#237;a dado en el tercer segundo de su movimiento?&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;hr /&gt;
		&lt;div &lt;div class='rss_ps'&gt;&lt;p&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/2289bafab753c63f1a54a8603cede18a.png' style=&#034;vertical-align:middle;&#034; width=&#034;89&#034; height=&#034;24&#034; alt=&#034;\fbox{\color[RGB]{192,0,0}{\bm{\varphi = 5\ rev}}}&#034; title=&#034;\fbox{\color[RGB]{192,0,0}{\bm{\varphi = 5\ rev}}}&#034; /&gt;&lt;/math&gt;&lt;/p&gt;
&lt;p&gt; &lt;br/&gt;&lt;/p&gt;
&lt;p&gt;&lt;u&gt;RESOLUCI&#211;N EN CINCO PASOS&lt;/u&gt;.&lt;/p&gt;
&lt;div class='spip_document_1937 spip_document spip_documents spip_document_image spip_documents_center spip_document_center'&gt;
&lt;figure class=&#034;spip_doc_inner&#034;&gt; &lt;a href='https://ejercicios-fyq.com/IMG/jpg/ej_7975_02.jpg' class=&#034;spip_doc_lien mediabox&#034; type=&#034;image/jpeg&#034;&gt; &lt;img src='https://ejercicios-fyq.com/IMG/jpg/ej_7975_02.jpg' width=&#034;1080&#034; height=&#034;1078&#034; alt='' /&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;&lt;div class='spip_document_1938 spip_document spip_documents spip_document_image spip_documents_center spip_document_center'&gt;
&lt;figure class=&#034;spip_doc_inner&#034;&gt; &lt;a href='https://ejercicios-fyq.com/IMG/jpg/ej_7975_03.jpg' class=&#034;spip_doc_lien mediabox&#034; type=&#034;image/jpeg&#034;&gt; &lt;img src='https://ejercicios-fyq.com/IMG/jpg/ej_7975_03.jpg' width=&#034;1080&#034; height=&#034;1078&#034; alt='' /&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;&lt;div class='spip_document_1939 spip_document spip_documents spip_document_image spip_documents_center spip_document_center'&gt;
&lt;figure class=&#034;spip_doc_inner&#034;&gt; &lt;a href='https://ejercicios-fyq.com/IMG/jpg/ej_7975_04.jpg' class=&#034;spip_doc_lien mediabox&#034; type=&#034;image/jpeg&#034;&gt; &lt;img src='https://ejercicios-fyq.com/IMG/jpg/ej_7975_04.jpg' width=&#034;1080&#034; height=&#034;1078&#034; alt='' /&gt;&lt;/a&gt;
&lt;/figure&gt;
&lt;/div&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Aceleraci&#243;n de un veh&#237;culo que toma una curva y var&#237;a su velocidad (7773)</title>
		<link>https://ejercicios-fyq.com/Aceleracion-de-un-vehiculo-que-toma-una-curva-y-varia-su-velocidad-7773</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/Aceleracion-de-un-vehiculo-que-toma-una-curva-y-varia-su-velocidad-7773</guid>
		<dc:date>2022-11-08T07:13:54Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>Aceleraci&#243;n</dc:subject>
		<dc:subject>RESUELTO</dc:subject>

		<description>
&lt;p&gt;Un veh&#237;culo con rapidez de toma una curva circular de 250 m de radio y gira un total de frenando hasta que su rapidez es de al final de la curva. Determina su aceleraci&#243;n y el tiempo que est&#225; frenando.&lt;/p&gt;


-
&lt;a href="https://ejercicios-fyq.com/Cinematica" rel="directory"&gt;Cinem&#225;tica&lt;/a&gt;

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&lt;a href="https://ejercicios-fyq.com/MCUA" rel="tag"&gt;MCUA&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/Aceleracion" rel="tag"&gt;Aceleraci&#243;n&lt;/a&gt;, 
&lt;a href="https://ejercicios-fyq.com/RESUELTO" rel="tag"&gt;RESUELTO&lt;/a&gt;

		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;Un veh&#237;culo con rapidez de &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L40xH20/1d91983c7a7e8ca31b17a633e52bf5e2-1749f.png?1733003430' style='vertical-align:middle;' width='40' height='20' alt=&#034;63\ \textstyle{km\over h}&#034; title=&#034;63\ \textstyle{km\over h}&#034; /&gt; toma una curva circular de 250 m de radio y gira un total de &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L22xH13/24754578c1f108911925322a75f95793-251d3.png?1732959940' style='vertical-align:middle;' width='22' height='13' alt=&#034;90 ^o&#034; title=&#034;90 ^o&#034; /&gt; frenando hasta que su rapidez es de &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L40xH20/003f9361dd13e142b9bfa8ad29e421a2-ba55f.png?1733003430' style='vertical-align:middle;' width='40' height='20' alt=&#034;44\ \textstyle{km\over h}&#034; title=&#034;44\ \textstyle{km\over h}&#034; /&gt; al final de la curva. Determina su aceleraci&#243;n y el tiempo que est&#225; frenando.&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;hr /&gt;
		&lt;div &lt;div class='rss_ps'&gt;&lt;p&gt;Las velocidades inicial y final, expresadas en unidades SI, son &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/de6c7f1cd726aab0a2faa5f5da096bac.png' style=&#034;vertical-align:middle;&#034; width=&#034;83&#034; height=&#034;18&#034; alt=&#034;v_0 = 17.5\ \textstyle{m\over s}&#034; title=&#034;v_0 = 17.5\ \textstyle{m\over s}&#034; /&gt; y &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/b00a1be32b4a7258e6c048b9198aed2a.png' style=&#034;vertical-align:middle;&#034; width=&#034;85&#034; height=&#034;17&#034; alt=&#034;v_f = 12.2\ \textstyle{m\over s}&#034; title=&#034;v_f = 12.2\ \textstyle{m\over s}&#034; /&gt;. Como conoces cu&#225;nto gira en la curva el veh&#237;culo, puedes calcular la distancia que ha recorrida durante la frenada: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/2ce8d0a6088ec69cd93b54d702d42126.png' style=&#034;vertical-align:middle;&#034; width=&#034;239&#034; height=&#034;30&#034; alt=&#034;d = \phi\cdot R = \frac{\pi}{2}\cdot 250\ m = \color[RGB]{0,112,192}{\bf 392.5\ m}&#034; title=&#034;d = \phi\cdot R = \frac{\pi}{2}\cdot 250\ m = \color[RGB]{0,112,192}{\bf 392.5\ m}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Usando la ecuaci&#243;n de la aceleraci&#243;n que relaciona la variaci&#243;n de la velocidad con la distancia puedes despejar el valor de la aceleraci&#243;n: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/f014958ca6fbe4d992543200c5a23fe1.png' style=&#034;vertical-align:middle;&#034; width=&#034;229&#034; height=&#034;40&#034; alt=&#034;v_f^2 = v_0^2 + 2ad\ \to\ \color[RGB]{2,112,20}{\bm{a = \frac{v_f^2 - v_0^2}{2d}}}&#034; title=&#034;v_f^2 = v_0^2 + 2ad\ \to\ \color[RGB]{2,112,20}{\bm{a = \frac{v_f^2 - v_0^2}{2d}}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Sustituyes y calculas la aceleraci&#243;n: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/aaa2635aa596229906015cd4a1d1a37e.png' style=&#034;vertical-align:middle;&#034; width=&#034;255&#034; height=&#034;44&#034; alt=&#034;a = \frac{(12.2^2 - 17.5^2)\ \frac{m\cancel{^2}}{s^2}}{2\cdot 392.5\ \cancel{m}} = \fbox{\color[RGB]{192,0,0}{\bm{-0.2\ \frac{m}{s^2}}}}&#034; title=&#034;a = \frac{(12.2^2 - 17.5^2)\ \frac{m\cancel{^2}}{s^2}}{2\cdot 392.5\ \cancel{m}} = \fbox{\color[RGB]{192,0,0}{\bm{-0.2\ \frac{m}{s^2}}}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; La aceleraci&#243;n es el cociente de la variaci&#243;n de la velocidad y el tiempo empleado en esa variaci&#243;n. Necesitas calcular el tiempo que ha empleado el veh&#237;culo en hacer la frenada: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/02ba37b65caf3c72f9e92bdbf5278393.png' style=&#034;vertical-align:middle;&#034; width=&#034;226&#034; height=&#034;33&#034; alt=&#034;v_f = v_0 + a\cdot t\ \to\ \color[RGB]{2,112,20}{\bm{t = \frac{v_f - v_0}{a}}}&#034; title=&#034;v_f = v_0 + a\cdot t\ \to\ \color[RGB]{2,112,20}{\bm{t = \frac{v_f - v_0}{a}}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Sustituyes y calculas: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/9269b7360fdbaab6b6184b67e3d47742.png' style=&#034;vertical-align:middle;&#034; width=&#034;219&#034; height=&#034;54&#034; alt=&#034;t = \frac{(12.2 - 17.5)\ \frac{\cancel{m}}{\cancel{s}}}{-0.2\ \frac{\cancel{m}}{s\cancel{^2}}} = \fbox{\color[RGB]{192,0,0}{\bf 26.5\ s}}&#034; title=&#034;t = \frac{(12.2 - 17.5)\ \frac{\cancel{m}}{\cancel{s}}}{-0.2\ \frac{\cancel{m}}{s\cancel{^2}}} = \fbox{\color[RGB]{192,0,0}{\bf 26.5\ s}}&#034; /&gt;&lt;/p&gt;
&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Aceleraci&#243;n angular de un coche que frena (7676)</title>
		<link>https://ejercicios-fyq.com/Aceleracion-angular-de-un-coche-que-frena-7676</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/Aceleracion-angular-de-un-coche-que-frena-7676</guid>
		<dc:date>2022-08-06T05:56:27Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>RESUELTO</dc:subject>

		<description>
&lt;p&gt;Los neum&#225;ticos de un auto dan 65 vueltas para que la velocidad se reduzca uniformemente de 100 km/h a 50 km/h. Sabiendo que tienen un di&#225;metro de 0.80 m: &lt;br class='autobr' /&gt;
a) &#191;Cu&#225;l es la aceleraci&#243;n angular del auto? &lt;br class='autobr' /&gt;
b) Si el auto contin&#250;a desacelerando as&#237;, &#191;cu&#225;nto tiempo m&#225;s necesitar&#225; para detenerse?&lt;/p&gt;


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		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;Los neum&#225;ticos de un auto dan 65 vueltas para que la velocidad se reduzca uniformemente de 100 km/h a 50 km/h. Sabiendo que tienen un di&#225;metro de 0.80 m:&lt;/p&gt;
&lt;p&gt;a) &#191;Cu&#225;l es la aceleraci&#243;n angular del auto?&lt;/p&gt;
&lt;p&gt;b) Si el auto contin&#250;a desacelerando as&#237;, &#191;cu&#225;nto tiempo m&#225;s necesitar&#225; para detenerse?&lt;/p&gt;&lt;/div&gt;
		&lt;hr /&gt;
		&lt;div &lt;div class='rss_ps'&gt;&lt;p&gt;Para lograr que el problema sea homog&#233;neo puedes trabajar con unidades SI y para ello tienes que hacer las conversiones. Las velocidades las divides por el factor 3.6 y las obtienes en m/s, teniendo luego que calcular las velocidades angulares: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/51a5d1b20bac5558b7aa6c62be217e98.png' style=&#034;vertical-align:middle;&#034; width=&#034;219&#034; height=&#034;71&#034; alt=&#034;\left w_o = \frac{v_o}{R} = \frac{27.8\ \frac{\cancel{m}}{s}}{0.4\ \cancel{m}} = {\color[RGB]{0,112,192}{\bm{69.5\ \frac{rad}{s}}}} \atop w_f = \frac{v_f}{R} = \frac{13.9\ \frac{\cancel{m}}{s}}{0.4\ \cancel{m}} = {\color[RGB]{0,112,192}{\bm{34.7\ \frac{rad}{s}}}} \right \}&#034; title=&#034;\left w_o = \frac{v_o}{R} = \frac{27.8\ \frac{\cancel{m}}{s}}{0.4\ \cancel{m}} = {\color[RGB]{0,112,192}{\bm{69.5\ \frac{rad}{s}}}} \atop w_f = \frac{v_f}{R} = \frac{13.9\ \frac{\cancel{m}}{s}}{0.4\ \cancel{m}} = {\color[RGB]{0,112,192}{\bm{34.7\ \frac{rad}{s}}}} \right \}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Las vueltas las conviertes a radianes: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/583fe8c45b43909f8318ea1d6ccc3518.png' style=&#034;vertical-align:middle;&#034; width=&#034;238&#034; height=&#034;36&#034; alt=&#034;\phi = 65\ \cancel{rev}\cdot \frac{2\pi\ rad}{1\ \cancel{rev}} = \color[RGB]{0,112,192}{\bm{130\pi\ rad}}&#034; title=&#034;\phi = 65\ \cancel{rev}\cdot \frac{2\pi\ rad}{1\ \cancel{rev}} = \color[RGB]{0,112,192}{\bm{130\pi\ rad}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; a) La aceleraci&#243;n angular la puedes calcular a partir de la expresi&#243;n: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/47a6513c15e4b538cb891b97be881b0b.png' style=&#034;vertical-align:middle;&#034; width=&#034;256&#034; height=&#034;44&#034; alt=&#034;\omega_f^2 = \omega_o^2 + 2\alpha\cdot \phi\ \to\ \color[RGB]{2,112,20}{\bm{\alpha = \frac{\omega_f^2 - \omega_o^2}{2\phi}}}&#034; title=&#034;\omega_f^2 = \omega_o^2 + 2\alpha\cdot \phi\ \to\ \color[RGB]{2,112,20}{\bm{\alpha = \frac{\omega_f^2 - \omega_o^2}{2\phi}}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Sustituyes y calculas la aceleraci&#243;n angular: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/8e8bc3e61ed5bed6fd61966ba2b97fea.png' style=&#034;vertical-align:middle;&#034; width=&#034;282&#034; height=&#034;44&#034; alt=&#034;\alpha = \frac{(34.7^2 - 69.5^2)\ \frac{rad\cancel{^2}}{s^2}}{260\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bm{-4.44\ \frac{rad}{s^2}}}}&#034; title=&#034;\alpha = \frac{(34.7^2 - 69.5^2)\ \frac{rad\cancel{^2}}{s^2}}{260\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bm{-4.44\ \frac{rad}{s^2}}}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; b) Para hacer este apartado debes considerar que la velocidad angular inicial es la que tiene el coche tras las 65 vueltas de los neum&#225;ticos y que su velocidad final ser&#225; cero. La ecuaci&#243;n que usas es: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/d7511771d07df124ac9505d457d946ad.png' style=&#034;vertical-align:middle;&#034; width=&#034;237&#034; height=&#034;33&#034; alt=&#034;\omega_f = \omega_o + \alpha\cdot t\ \to\ \color[RGB]{2,112,20}{\bm{t = \frac{\omega_f - \omega_0}{\alpha}}}&#034; title=&#034;\omega_f = \omega_o + \alpha\cdot t\ \to\ \color[RGB]{2,112,20}{\bm{t = \frac{\omega_f - \omega_0}{\alpha}}}&#034; /&gt;&lt;br/&gt; &lt;br/&gt; El c&#225;lculo es inmediato: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/7fc81b5b2673c943c4228560e65e0c4c.png' style=&#034;vertical-align:middle;&#034; width=&#034;207&#034; height=&#034;57&#034; alt=&#034;t = \frac{(0 - 34.7)\ \frac{\cancel{rad}}{\cancel{s}}}{-4.44\ \frac{\cancel{rad}}{s\cancel{^2}}} = \fbox{\color[RGB]{192,0,0}{\bf 7.82\ s}}&#034; title=&#034;t = \frac{(0 - 34.7)\ \frac{\cancel{rad}}{\cancel{s}}}{-4.44\ \frac{\cancel{rad}}{s\cancel{^2}}} = \fbox{\color[RGB]{192,0,0}{\bf 7.82\ s}}&#034; /&gt;&lt;/p&gt;
&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		
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	</item>
<item xml:lang="es">
		<title>&#193;ngulo barrido por el radio de una rueda que gira con aceleraci&#243;n angular constante (7577)</title>
		<link>https://ejercicios-fyq.com/Angulo-barrido-por-el-radio-de-una-rueda-que-gira-con-aceleracion-angular</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/Angulo-barrido-por-el-radio-de-una-rueda-que-gira-con-aceleracion-angular</guid>
		<dc:date>2022-04-24T05:44:22Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>RESUELTO</dc:subject>

		<description>
&lt;p&gt;&#191;Cu&#225;l es el &#225;ngulo que barre un radio de una rueda que gira con una aceleraci&#243;n angular constante de durante 3 s? Considera que la velocidad angular inicial es de . &lt;br class='autobr' /&gt;
a) ; b) 0.75 rad ; c) ; d) 817 rad&lt;/p&gt;


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 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;&#191;Cu&#225;l es el &#225;ngulo que barre un radio de una rueda que gira con una aceleraci&#243;n angular constante de &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L45xH20/7cd44339aca7bbef1b24fbdbb152e955-4e9a6.png?1733054939' style='vertical-align:middle;' width='45' height='20' alt=&#034;1.5\ \textstyle{rad\over s^2}&#034; title=&#034;1.5\ \textstyle{rad\over s^2}&#034; /&gt; durante 3 s? Considera que la velocidad angular inicial es de &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L46xH20/d12d23334bbafda31474e6eb7e462daf-3c138.png?1733054939' style='vertical-align:middle;' width='46' height='20' alt=&#034;2.5\ \textstyle{rad\over s}&#034; title=&#034;2.5\ \textstyle{rad\over s}&#034; /&gt;.&lt;/p&gt;
&lt;p&gt;a) &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L43xH13/0693039e24235cc2dc3ad3da7948da04-1340f.png?1733054939' style='vertical-align:middle;' width='43' height='13' alt=&#034;14.25^o&#034; title=&#034;14.25^o&#034; /&gt; ; b) 0.75 rad ; c) &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L30xH13/1f1bfa2e28d2e431ce35a420617f17b4-9831a.png?1733054939' style='vertical-align:middle;' width='30' height='13' alt=&#034;817^o&#034; title=&#034;817^o&#034; /&gt; ; d) 817 rad&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;hr /&gt;
		&lt;div &lt;div class='rss_ps'&gt;&lt;p&gt;La rueda sigue un MCUA y solo tienes que aplicar la ecuaci&#243;n de este tipo de movimiento para el &#225;ngulo barrido: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/1d0f2d5ba154b235eeaed839cfd8533e.png' style=&#034;vertical-align:middle;&#034; width=&#034;178&#034; height=&#034;33&#034; alt=&#034;\color[RGB]{2,112,20}{\bm{\phi = \phi_0 + \omega_0\cdot t + \frac{\alpha}{2}\cdot t^2}}&#034; title=&#034;\color[RGB]{2,112,20}{\bm{\phi = \phi_0 + \omega_0\cdot t + \frac{\alpha}{2}\cdot t^2}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Dado que el enunciado no indica nada del valor del giro inicial, lo supones cero y sustituyes el resto de valores: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/a8f3660c9f1061d4cde5961214e67b77.png' style=&#034;vertical-align:middle;&#034; width=&#034;338&#034; height=&#034;39&#034; alt=&#034;\phi = 2.5\ \frac{rad}{\cancel{s}}\cdot 3\ \cancel{s} + \frac{1.5}{2}\ \frac{rad}{\cancel{s^2}}\cdot 3^2\ \cancel{s^2} = \color[RGB]{0,112,192}{\bf 14.25\ rad}&#034; title=&#034;\phi = 2.5\ \frac{rad}{\cancel{s}}\cdot 3\ \cancel{s} + \frac{1.5}{2}\ \frac{rad}{\cancel{s^2}}\cdot 3^2\ \cancel{s^2} = \color[RGB]{0,112,192}{\bf 14.25\ rad}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; El resultado obtenido no coincide con las soluciones dadas en radianes, con lo que debes hacer la conversi&#243;n a grados para ver con cu&#225;l coincide: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/1f832e6a1628fd6ef48b39f664eed0a6.png' style=&#034;vertical-align:middle;&#034; width=&#034;196&#034; height=&#034;36&#034; alt=&#034;14.25\ \cancel{rad}\cdot \frac{360^o}{2\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bf 817^o}}&#034; title=&#034;14.25\ \cancel{rad}\cdot \frac{360^o}{2\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bf 817^o}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; &lt;b&gt;La soluci&#243;n correcta es c).&lt;/b&gt;&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		
		</content:encoded>


		

	</item>
<item xml:lang="es">
		<title>Relationship between linear and angular quantities (7425)</title>
		<link>https://ejercicios-fyq.com/Relationship-between-linear-and-angular-quantities-7425</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/Relationship-between-linear-and-angular-quantities-7425</guid>
		<dc:date>2021-12-10T07:07:49Z</dc:date>
		<dc:format>text/html</dc:format>
		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MRUA</dc:subject>
		<dc:subject>MCUA</dc:subject>
		<dc:subject>EDICO</dc:subject>
		<dc:subject>SOLVED</dc:subject>

		<description>
&lt;p&gt;A car starts at and uniformly accelerates at for 5 s. &lt;br class='autobr' /&gt;
a) Calculate the final velocity and the displacement of the car. &lt;br class='autobr' /&gt;
b) Determine the diameter of the tire if the angular displacement is 60 radians. &lt;br class='autobr' /&gt;
c) Calculate the final angular velocity and angular acceleration of the tires.&lt;/p&gt;


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		</description>


 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;A car starts at &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L78xH20/911c7f12083f2f5b5198c5b88e2c87bd-4743a.png?1733073348' style='vertical-align:middle;' width='78' height='20' alt=&#034;1\ m\cdot s^{-1}&#034; title=&#034;1\ m\cdot s^{-1}&#034; /&gt; and uniformly accelerates at &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L96xH20/af5dbc5a2eea86d1b82a58ae99f44962-13acf.png?1733007963' style='vertical-align:middle;' width='96' height='20' alt=&#034;2.5\ m\cdot s^{-2}&#034; title=&#034;2.5\ m\cdot s^{-2}&#034; /&gt; for 5 s.&lt;/p&gt;
&lt;p&gt;a) Calculate the final velocity and the displacement of the car.&lt;/p&gt;
&lt;p&gt;b) Determine the diameter of the tire if the angular displacement is 60 radians.&lt;/p&gt;
&lt;p&gt;c) Calculate the final angular velocity and angular acceleration of the tires.&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;hr /&gt;
		&lt;div &lt;div class='rss_ps'&gt;&lt;p&gt;a) The equation for calculating the final velocity is: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/32bc1749368305b3e3e85277fba5af75.png' style=&#034;vertical-align:middle;&#034; width=&#034;134&#034; height=&#034;19&#034; alt=&#034;\color[RGB]{2,112,20}{\bm{v= v_0 + a\cdot t}}&#034; title=&#034;\color[RGB]{2,112,20}{\bm{v= v_0 + a\cdot t}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Just replace the data and calculate: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/32f16e66a7b2b23bdd6f69d406681458.png' style=&#034;vertical-align:middle;&#034; width=&#034;298&#034; height=&#034;44&#034; alt=&#034;v= 1\ \frac{m}{s} + 2.5\ \frac{m}{s\cancel{^2}}\cdot 5\ \cancel{s} = \fbox{\color[RGB]{192,0,0}{\bm{14\ \frac{m}{s}}}}&#034; title=&#034;v= 1\ \frac{m}{s} + 2.5\ \frac{m}{s\cancel{^2}}\cdot 5\ \cancel{s} = \fbox{\color[RGB]{192,0,0}{\bm{14\ \frac{m}{s}}}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; The equation for calculating the displacement is: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/aab59a717a99d28719a64a6ba69f66d4.png' style=&#034;vertical-align:middle;&#034; width=&#034;170&#034; height=&#034;43&#034; alt=&#034;\color[RGB]{2,112,20}{\bm{d= v_0\cdot t + \frac{a}{2}\cdot t^2}}&#034; title=&#034;\color[RGB]{2,112,20}{\bm{d= v_0\cdot t + \frac{a}{2}\cdot t^2}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Using the data in the problem statement: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/40d10dde567195268cfdf4dad4ae2a6d.png' style=&#034;vertical-align:middle;&#034; width=&#034;364&#034; height=&#034;50&#034; alt=&#034;d= 1\ \frac{m}{\cancel{s}}\cdot 5\ \cancel{s} + \frac{2.5}{2}\ \frac{m}{\cancel{s^2}}\cdot 5^2\ \cancel{s^2} = \fbox{\color[RGB]{192,0,0}{\bf 36\ m}}&#034; title=&#034;d= 1\ \frac{m}{\cancel{s}}\cdot 5\ \cancel{s} + \frac{2.5}{2}\ \frac{m}{\cancel{s^2}}\cdot 5^2\ \cancel{s^2} = \fbox{\color[RGB]{192,0,0}{\bf 36\ m}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; b) You must relate the distance covered to the radius of the wheel: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/ee69a671765cfeddd0b72e12907af2e5.png' style=&#034;vertical-align:middle;&#034; width=&#034;360&#034; height=&#034;49&#034; alt=&#034;d= \varphi\cdot R\ \to\ R = \frac{d}{\varphi} = \frac{36\ m}{60} = \color[RGB]{0,112,192}{\bf 0.6\ m}&#034; title=&#034;d= \varphi\cdot R\ \to\ R = \frac{d}{\varphi} = \frac{36\ m}{60} = \color[RGB]{0,112,192}{\bf 0.6\ m}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Diameter is two times the radius: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/75215b9ef5bbbc0c16a98726f667802f.png' style=&#034;vertical-align:middle;&#034; width=&#034;280&#034; height=&#034;27&#034; alt=&#034;D= 2R = 2\cdot 0.6\ m = \fbox{\color[RGB]{192,0,0}{\bf 1.2\ m}}&#034; title=&#034;D= 2R = 2\cdot 0.6\ m = \fbox{\color[RGB]{192,0,0}{\bf 1.2\ m}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; c) The final angular velocity is: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/913cf07ea0899fa18d7833250496b91c.png' style=&#034;vertical-align:middle;&#034; width=&#034;388&#034; height=&#034;52&#034; alt=&#034;v = \omega\cdot R\ \to\ \omega =\frac{v}{R} = \frac{14\ \frac{\cancel{m}}{s}}{0.6\ \cancel{m}} = \fbox{\color[RGB]{192,0,0}{\bm{23\ s^{-1}}}}&#034; title=&#034;v = \omega\cdot R\ \to\ \omega =\frac{v}{R} = \frac{14\ \frac{\cancel{m}}{s}}{0.6\ \cancel{m}} = \fbox{\color[RGB]{192,0,0}{\bm{23\ s^{-1}}}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; The angular acceleration is: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/ca3eb66e459803142a99a2d77c73ce5d.png' style=&#034;vertical-align:middle;&#034; width=&#034;395&#034; height=&#034;52&#034; alt=&#034;a = \alpha\cdot R\ \to\ \alpha = \frac{a}{R}= \frac{2.5\ \frac{\cancel{m}}{s^2}}{0.6\ \cancel{m}} = \fbox{\color[RGB]{192,0,0}{\bm{4.2\ s^{-2}}}}&#034; title=&#034;a = \alpha\cdot R\ \to\ \alpha = \frac{a}{R}= \frac{2.5\ \frac{\cancel{m}}{s^2}}{0.6\ \cancel{m}} = \fbox{\color[RGB]{192,0,0}{\bm{4.2\ s^{-2}}}}&#034; /&gt;&lt;/p&gt;
&lt;/math&gt;&lt;/p&gt;
&lt;p&gt; &lt;br/&gt;&lt;/p&gt;
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		<title>Angular position and velocity of a wheel (7424)</title>
		<link>https://ejercicios-fyq.com/Angular-position-and-velocity-of-a-wheel-7424</link>
		<guid isPermaLink="true">https://ejercicios-fyq.com/Angular-position-and-velocity-of-a-wheel-7424</guid>
		<dc:date>2021-12-10T05:42:50Z</dc:date>
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		<dc:language>es</dc:language>
		<dc:creator>F_y_Q</dc:creator>


		<dc:subject>MCUA</dc:subject>
		<dc:subject>EDICO</dc:subject>
		<dc:subject>Kinematics</dc:subject>
		<dc:subject>SOLVED</dc:subject>

		<description>
&lt;p&gt;The angular velocity of a bicycle wheel is , and its angular acceleration is . &lt;br class='autobr' /&gt;
a) What are the angular position and angular velocity at t = 5 s? &lt;br class='autobr' /&gt;
b) What are the angular position and angular velocity at t = 5 s, expressed in revolutions? &lt;br class='autobr' /&gt;
c) What are the final velocity and displacement of the bicycle at t = 5 s if the tire has a diamater of 1 meter?&lt;/p&gt;


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 <content:encoded>&lt;div class='rss_texte'&gt;&lt;p&gt;The angular velocity of a bicycle wheel is &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L93xH20/70124dff8077ee176669f0d84fbb3c19-ce407.png?1732982689' style='vertical-align:middle;' width='93' height='20' alt=&#034;5\ rad\cdot s^{-1}&#034; title=&#034;5\ rad\cdot s^{-1}&#034; /&gt;, and its angular acceleration is &lt;img src='https://ejercicios-fyq.com/local/cache-vignettes/L93xH20/4a2090a2dd7626fb243fc11645b5d620-001f4.png?1732982689' style='vertical-align:middle;' width='93' height='20' alt=&#034;3\ rad\cdot s^{-2}&#034; title=&#034;3\ rad\cdot s^{-2}&#034; /&gt;.&lt;/p&gt;
&lt;p&gt;a) What are the angular position and angular velocity at t = 5 s?&lt;/p&gt;
&lt;p&gt;b) What are the angular position and angular velocity at t = 5 s, expressed in revolutions?&lt;/p&gt;
&lt;p&gt;c) What are the final velocity and displacement of the bicycle at t = 5 s if the tire has a diamater of 1 meter?&lt;/math&gt;&lt;/p&gt;&lt;/div&gt;
		&lt;hr /&gt;
		&lt;div &lt;div class='rss_ps'&gt;&lt;p&gt;a) The equation for angular velocity is: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/105760096e045a63feb51378c3255255.png' style=&#034;vertical-align:middle;&#034; width=&#034;142&#034; height=&#034;19&#034; alt=&#034;\color[RGB]{2,112,20}{\bm{\omega= \omega_0 + \alpha\cdot t}}&#034; title=&#034;\color[RGB]{2,112,20}{\bm{\omega= \omega_0 + \alpha\cdot t}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Using the given values: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/79f59c4ab5bcb60fe436e4f4087645c1.png' style=&#034;vertical-align:middle;&#034; width=&#034;382&#034; height=&#034;49&#034; alt=&#034;\omega = 5\ \frac{rad}{s} + 3\ \frac{rad}{s\cancel{^2}}\cdot 5\ \cancel{s}= \fbox{\color[RGB]{192,0,0}{\bm{20\ rad\cdot s^{-1}}}}&#034; title=&#034;\omega = 5\ \frac{rad}{s} + 3\ \frac{rad}{s\cancel{^2}}\cdot 5\ \cancel{s}= \fbox{\color[RGB]{192,0,0}{\bm{20\ rad\cdot s^{-1}}}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; The equation for angular position is: &lt;br/&gt; &lt;br/&gt; &lt;img src='https://ejercicios-fyq.com/local/cache-TeX/91d0fc5df07d431ce9f3459899968109.png' style=&#034;vertical-align:middle;&#034; width=&#034;179&#034; height=&#034;43&#034; alt=&#034;\color[RGB]{2,112,20}{\bm{\varphi= \omega_0\cdot t + \frac{\alpha}{2}\cdot t^2}}&#034; title=&#034;\color[RGB]{2,112,20}{\bm{\varphi= \omega_0\cdot t + \frac{\alpha}{2}\cdot t^2}}&#034; /&gt; &lt;br/&gt; &lt;br/&gt; Using the given values: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/94c5de21530264256284e01c1f8ee01e.png' style=&#034;vertical-align:middle;&#034; width=&#034;400&#034; height=&#034;50&#034; alt=&#034;\varphi = 5\ \frac{rad}{\cancel{s}}\cdot 5\ \cancel{s} + \frac{3}{2}\ \frac{rad}{\cancel{s^2}}\cdot 5^2\ \cancel{s^2} = \fbox{\color[RGB]{192,0,0}{\bf 63 \ rad}}&#034; title=&#034;\varphi = 5\ \frac{rad}{\cancel{s}}\cdot 5\ \cancel{s} + \frac{3}{2}\ \frac{rad}{\cancel{s^2}}\cdot 5^2\ \cancel{s^2} = \fbox{\color[RGB]{192,0,0}{\bf 63 \ rad}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; b) To convert angular velocity and position to revolutions: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/acadcd1627166f09ec7d78dd18dc60c1.png' style=&#034;vertical-align:middle;&#034; width=&#034;357&#034; height=&#034;49&#034; alt=&#034;\omega = 20\ \frac{\cancel{rad}}{s}\cdot \frac{1\ rev}{2\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bm{3.2\ rev\cdot s^{-1}}}}&#034; title=&#034;\omega = 20\ \frac{\cancel{rad}}{s}\cdot \frac{1\ rev}{2\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bm{3.2\ rev\cdot s^{-1}}}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; For angular position: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/1d82355552c8c4bbcb4041fbff0e8bdf.png' style=&#034;vertical-align:middle;&#034; width=&#034;299&#034; height=&#034;46&#034; alt=&#034;\varphi = 63\ \cancel{rad}\cdot \frac{1\ rev}{2\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bf 10 \ rev}}&#034; title=&#034;\varphi = 63\ \cancel{rad}\cdot \frac{1\ rev}{2\pi\ \cancel{rad}} = \fbox{\color[RGB]{192,0,0}{\bf 10 \ rev}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; c) To convert angular quantities into linear quantities, use the wheel radius: &lt;br/&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/b458b5a7f90b467b8e3233216e6e05a8.png' style=&#034;vertical-align:middle;&#034; width=&#034;371&#034; height=&#034;45&#034; alt=&#034;v = \omega\cdot R = 20\ \frac{1}{s}\cdot 0.5\ m = \fbox{\color[RGB]{192,0,0}{\bm{10\ m\cdot s^{-1}}}}&#034; title=&#034;v = \omega\cdot R = 20\ \frac{1}{s}\cdot 0.5\ m = \fbox{\color[RGB]{192,0,0}{\bm{10\ m\cdot s^{-1}}}}&#034; /&gt;&lt;/p&gt; &lt;br/&gt; &lt;p class=&#034;spip&#034; style=&#034;text-align: center;&#034;&gt;&lt;img src='https://ejercicios-fyq.com/local/cache-TeX/bc6e142592665fbb20550fbac1477088.png' style=&#034;vertical-align:middle;&#034; width=&#034;296&#034; height=&#034;27&#034; alt=&#034;d = \varphi\cdot R = 63\cdot 0.5\ m= \fbox{\color[RGB]{192,0,0}{\bf 32\ m}}&#034; title=&#034;d = \varphi\cdot R = 63\cdot 0.5\ m= \fbox{\color[RGB]{192,0,0}{\bf 32\ m}}&#034; /&gt;&lt;/p&gt;
&lt;/math&gt;&lt;/p&gt;
&lt;p&gt; &lt;br/&gt;&lt;/p&gt;
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