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List of moments of inertia and Talk:Henri Pieck: Difference between pages

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{{WPBiography|class=stub}}
The following is a list of [[moment of inertia|moments of inertia]].
 
== disagree with edit ==
==Moments of inertia==
 
<blockquote>
Moments of inertia have [[physical unit|units]] of dimension mass &times; length<sup>2</sup>. The following moments of inertia are derived from the fact that the moment of inertia of a point object is <math>mr^2 \,</math>.
Arrested on 9 June 1941 for resistance activities, he spent the rest of World War II in German custody, first in the “Oranjehotel,” '''a prison set up by the Germans''', after which he was deported to Buchenwald via the Nazi transit camp Amersfoort. </blockquote>
 
I disagree with the modification" a prison set up by the Germans" which was added to the sentence.
<table border="1" cellspacing = "0" cellpadding="2" align="center">
<tr>
<th>Description</th>
<th>Figure</th>
<th>Moment(s) of inertia</th>
<th>Comment</th>
</tr>
<tr>
<td>Thin [[cylinder (geometry)|cylindrical]] shell with open ends, of radius <math>r</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_thin_cylinder.png]]</td><td><math>I = m r^2 \,</math></td><td>&mdash;</td>
</tr>
<tr>
<td>Thick cylinder with open ends, of inner radius <math>r_1</math>, outer radius <math>r_2</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_thick_cylinder.png]]</td><td><math>I_z = \frac{1}{2} m({r_1}^2 + {r_2}^2)</math><br><math>I_x = I_y = \frac{1}{12} m[3({r_1}^2 + {r_2}^2)+h^2]</math><br>or if we let <math>t_n</math> be the normalized thickness <math>\frac{t}{r}</math> and <math>r = r_2</math><br>then <math>I_z = mr^2(1-t_n+\frac{1}{2}t_n^2) </math></td><td>&mdash;</td>
</tr>
<tr>
<td>Solid cylinder of radius <math>r</math>, height <math>h</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_solid_cylinder.png]]</td><td><math>I_z = \frac{1}{2} mr^2</math><br><math>I_x = I_y = \frac{1}{12} m(3r^2+h^2)</math></td><td>&mdash;</td>
</tr>
<tr>
<td>Thin, solid [[disk (mathematics)|disk]] of radius <math>r</math> and mass <math>m</math></td><td>[[Image:moment of inertia disc.png]]</td><td><math>I_z = \frac{1}{2} mr^2</math><br><math>I_x = I_y = \frac{1}{4} mr^2</math></td><td>&mdash;</td>
</tr>
<tr>
<td>Solid [[sphere]] of radius <math>r</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_solid_sphere.png]]</td><td><math>I = \frac{2}{5} mr^2</math></td><td>&mdash;</td>
</tr>
<tr>
<td>Hollow sphere of radius <math>r</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_solid_sphere.png]]</td><td><math>I = \frac{2}{3} mr^2</math></td><td>&mdash;</td>
</tr>
<tr>
<td>[[right angle|Right]] circular [[cone (solid)|cone]] with radius <math>r</math>, height <math>h</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_cone.png]]</td>
<td><math>I_z = (3/10)mr^2 \,\!</math><br>
<math>I_x = I_y = (3/5)m(r^2/4+h^2) \,\!</math></td><td>&mdash;</td>
</tr>
<tr>
<td>Solid [[cuboid]] of height <math>h</math>, width <math>w</math>, and depth <math>d</math>, and mass <math>m</math></td><td>[[Image:moment_of_inertia_solid_rectangular_prism.png]]</td><td><math>I_h = \frac{1}{12} m(w^2+d^2)</math><br><math>I_w = \frac{1}{12} m(h^2+d^2)</math><br><math>I_d = \frac{1}{12} m(h^2+w^2)</math></td><td>For a similarly oriented [[cube (geometry)|cube]] with sides of length <math>s</math> and mass <math>M</math>, <math>I_{CM} = \frac{1}{6} ms^2</math>.</td>
</tr>
<tr>
<td>Rod of length <math>L</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_rod_center.png]]</td><td><math>I_{center} = \frac{1}{12} mL^2</math></td><td>This expression is an approximation, and assumes that the mass of the rod is distributed in the form of an infinitely thin (but rigid) wire.</td>
</tr>
<tr>
<td>Rod of length <math>L</math> and mass <math>m</math></td><td>[[Image:moment_of_inertia_rod_end.png]]</td><td><math>I_{end} = \frac{1}{3} mL^2</math></td><td>This expression is an approximation, and assumes that the mass of the rod is distributed in the form of an infinitely thin (but rigid) wire.</td>
</tr>
<tr>
<td>[[Torus]] of tube radius <math>a</math>, cross-sectional radius <math>b</math> and mass <math>m</math>.</td>
<td>[[Image:torus_cycles.png|122px]]</td>
<td>
About a diameter:<math>\frac{1}{8}(4a^2 + 5b^2)m</math>
 
At the start of WWII The Dutch turned it into a prison for prisoners of war, and after the capitulation of The Netherlands the Germans took over the prison. (De Scheveningse gevangenis werd in de eerste dagen van de oorlog nog gebruikt voor Duitse krijgsgevangenen, maar na de capitulatie namen de Duitsers de gevangenis over) See http://www.oranjehotel.org/
About the vertical axis:<math>(a^2 + \frac{3}{4}b^2)m</math>
</td>
<td></td>
</tr>
 
<tr>
<td>Thin, solid, polygon shaped plate with vertices <math>\vec{P}_{1}</math>, <math>\vec{P}_{2}</math>, <math>\vec{P}_{3}</math>, ..., <math>\vec{P}_{N}</math> and mass <math>m</math>.</td>
<td>[[Image:Polygon_moment_of_inertia.png|130px]]</td>
<td>
<math>I=\frac{m}{6}\frac{\sum_{n=1}^{N}||\vec{P}_{n+1}\times\vec{P}_{n}||(\vec{P}^{2}_{n+1}+\vec{P}_{n+1}\cdot\vec{P}_{n}+\vec{P}_{n}^{2})}{\sum_{n=1}^{N}||\vec{P}_{n+1}\times\vec{P}_{n}||}</math>
</td>
<td></td>
</tr>
 
The "Oranjehotel" was as no time a hotel but always a correction facility, and I think this needs to be specified, or the correct name of the institution used which is "Scheveningse Huis van Bewaring".(My fault but I have no idea what the English name would be for Huis van Bewaring, therefore I used it's nickname).
</tr>
A Huis of Bewaring is a place were inmates were kept in cells to await trail and sentencing. It's unclear why the place became more known by it's nickname then official name.
 
</table>
 
==Area moments of inertia==
The ''area moment of inertia'' or [[second moment of area]] has a [[physical unit|unit]] of dimension Length<sup>4</sup>. Each is with respect to a horizontal axis through the [[centroid]] of the given shape, unless otherwise specified.
 
<table border="1" cellspacing = "0" cellpadding="2" align="center">
<tr>
<th>Description</th>
<th>Figure</th>
<th>Area Moment(s) of inertia</th>
<th>Comment</th>
</tr>
 
<tr><td>a filled circular area of radius <math>r \,</math></td><td></td><td><math>I_0 = \pi r^4/4 \,</math></td><td></td></tr>
 
<tr><td>a circular area of inner radius <math>r_1</math> and outer radius <math>r_2</math></td><td></td><td><math>I_0 = \frac{1}{4} \pi({r_2}^4-{r_1}^4)</math></td><td></td></tr>
 
<tr><td>a filled semicircle with radius <math>r \,</math> resting on a horizontal line</td><td></td><td><math>I_0 = \left(\frac{\pi}{8} - \frac{8}{9\pi}\right)r^4 \,</math></td><td></td></tr>
 
<tr><td>a filled semicircle as above but with respect to an axis collinear with the base</td><td></td><td><math>I = \pi r^4/8 \,</math></td><td></td></tr>
 
<tr><td>a filled semicircle as above but with respect to a vertical axis through the centroid</td><td></td><td><math>I_0 = \pi r^4/8 \,</math></td><td></td></tr>
 
<tr><td>a filled quarter circle with radius <math>r \,</math> entirely in the 1st quadrant of the [[Cartesian coordinate system]]</td><td></td><td><math>I_0 = \pi r^4/16 \,</math></td><td></td></tr>
 
<tr><td>a filled [[ellipse]] whose radius along the <math>x</math>-axis is <math>a \,</math> and whose radius along the <math>y</math>-axis is <math>b \,</math></td><td></td><td><math>I_0 = \pi ab^3/4 \,</math></td><td></td></tr>
 
<tr><td>a filled rectangular area with a base width of <math>b \,</math> and height <math>h \,</math></td><td></td><td><math>I_0 = bh^3/12 \,</math></td><td></td></tr>
 
<tr><td>a filled rectangular area as above but with respect to an axis collinear with the base</td><td></td><td><math>I = bh^3/3 \,</math></td><td>This is a trivial result from the [[parallel axes rule]]</td></tr>
 
<tr><td>a filled triangular area with a base width of <math>b \,</math> and height <math>h</math></td><td></td><td><math>I_0 = bh^3/36 \,</math></td><td></td></tr>
 
<tr><td>a filled triangular area as above but with respect to an axis collinear with the base</td><td></td><td><math>I = bh^3/12 \,</math></td><td>This is a consequence of the parallel axes rule and the fact that the distance between these two axes is always <math>h/3 \,</math></td></tr>
 
<tr><td>a filled regular hexagon with a side length of <math>a \,</math></td><td></td><td><math>I_0 = 5\sqrt{3}a^4/16 \,</math></td><td></td></tr>
 
</table>
 
[[Category:Mechanics|Moment of inertia]]
[[Category:Physics lists|Moments of inertia]]
[[Category:Introductory physics]]
 
[[ms:Senarai momen inersia]]
[[pl:Lista_moment%C3%B3w_bezw%C5%82adno%C5%9Bci]]
 
 
{{physics-stub}}
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