Euler force

<h2 id="intuitive-example">Intuitive example</h2>
<p>The Euler force will be felt by a person riding a <a href="/facts/Merry-go-round/FSs5Nz0H">merry-go-round</a>. As the ride starts, the Euler force will be the apparent force pushing the person to the back of the horse; and as the ride comes to a stop, it will be the apparent force pushing the person towards the front of the horse. A person on a horse close to the perimeter of the merry-go-round will perceive a greater apparent force than a person on a horse closer to the axis of rotation.
</p>
<h2 id="mathematical-description">Mathematical description</h2>
<p class="note">Main article: <a href="/facts/Rotating_reference_frame/X4ngwkz5">Rotating reference frame</a></p>
<p>The direction and magnitude of the Euler acceleration is given, in the rotating reference frame, by:
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    {\displaystyle \mathbf {a} _{\mathrm {Euler} }=-{\frac {d{\boldsymbol {\omega }}}{dt}}\times \mathbf {r} ,}

<p>where ω is the angular velocity of rotation of the reference frame and r is the vector position of the point in the reference frame. The Euler force on an object of mass <i>m</i> in the rotating reference frame is then
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    {\displaystyle \mathbf {F} _{\mathrm {Euler} }=m\mathbf {a} _{\mathrm {Euler} }=-m{\frac {d{\boldsymbol {\omega }}}{dt}}\times \mathbf {r} .}

<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Fictitious_force/nJp96HPc">Fictitious force</a></li>
<li><a href="/facts/Coriolis_effect/SqCyUY6d">Coriolis effect</a></li>
<li><a href="/facts/Centrifugal_force/CWgvMw6w">Centrifugal force</a></li>
<li><a href="/facts/Rotating_reference_frame/X4ngwkz5">Rotating reference frame</a></li>
<li><a href="/facts/Angular_acceleration/jDv9uzAS">Angular acceleration</a></li></ul>
<h2 id="notes-and-references">Notes and references</h2>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Jerrold E. Marsden, Tudor S. Ratiu (1999). Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems. Springer. p. 251. ISBN 0-387-98643-X. <a href="0-387-98643-X" target="_blank">0-387-98643-X</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>David Morin (2008). Introduction to classical mechanics: with problems and solutions. Cambridge University Press. p. 469. ISBN 978-0-521-87622-3. acceleration azimuthal Morin. <a href="978-0-521-87622-3" target="_blank">978-0-521-87622-3</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Grant R. Fowles and George L. Cassiday (1999). Analytical Mechanics, 6th ed. Harcourt College Publishers. p. 178. <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Richard H Battin (1999). An introduction to the mathematics and methods of astrodynamics. Reston, VA: American Institute of Aeronautics and Astronautics. p. 102. ISBN 1-56347-342-9. <a href="1-56347-342-9" target="_blank">1-56347-342-9</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
</ol>

Euler force open-in-new

Euler force