ru.wikipedia.org website review
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ru.wikipedia.org is 51% geoptimaliseerd!
SEO Keyword summary for ru.wikipedia.org/wiki/%d0%9c%d0%be%d0%bc%d0%b5%d0%bd%d1%82_%d0%b8%d0%bd%d0%b5%d1%80%d1%86%d0%b8%d0%b8
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle frac rho |
long Tail Keywords (2 words) r m 12pi rho 2 3 1 2 bdisplaystyle b |
long Tail Keywords (3 words) 12pi rho leftfrac 1 2 3 dmrho dvrho cdot h bdisplaystyle b hdisplaystyle h bdisplaystyle 12mcdot l2 l r21 over 12mcdot |
ru.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a ru.wikipedia.org/wiki/%d0%9c%d0%be%d0%bc%d0%b5%d0%bd%d1%82_%d0%b8%d0%bd%d0%b5%d1%80%d1%86%d0%b8%d0%b8 page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
mdash
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
No headings were found !
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
displaystyle jint limits mathrm jasum nmiri jaint dmint vrho jarho int jjcmd frac mleftfrac right mfrac over mcdot left cos nright imleftfrac jsum djisum dmqquad dmr sum dmmr dmrho dvrho cdot rhdrqquad djr rho rdj hint hleftfrac rightr rfrac hleftr rightfrac rightleftr vpi leftr righthqquad mrho righth jfrac mleftr rhh djfrac dmfrac dhfrac leftfrac rhhright beginalignedjint hdjfrac rhright hfrac hleftrho hrightfrac endaligned rsqrt rightdh rrdj rdjpi rleftr rightdhpi leftleftr rightright rpi rightcdot beginalignedjfrac drdrfrac ddrleftfrac rightdrfrac drleftrho drrightfrac mdrlqquad drl mlint drfrac mlleftfrac mlfrac jxyint mxydmint vxyrho jxzint mxzdmint vxzrho jyzint myzdmint vyzrho jvaint dim jvamathrm jsaint jsamathrm wfrac jsarmax jyfrac jzfrac jyjzfrac xyz xoy yoz zox jxoysum nmizi jyozsum nmixi jzoxsum nmiyi jofrac leftjxjyjzright jojxoyjyozjxoz vec sleftvert sxsyszrightvert tleftvert srightvert isvec stcdot hat jcdot sqquad times jleftvert beginarraycccjxxjxyjxzjyxjyyjyzjzxjzyjzzendarrayrightvert jxyjyxquad jxzjzxquad jzyjyzquad jxxint dmquad jyyint jzzint jdhat qtcdot jdleftvert beginarraycccjx jzendarrayrightvert jxjyjz isjxcdot jycdot jzcdot leftsx sqrt isright jxleftsy jyleftsz iseta iszeta eta zeta jxeta jyzeta leftsy leftsz external links wikimedia foundation powered mediawiki
Mobile SEO ru.wikipedia.org/wiki/%d0%9c%d0%be%d0%bc%d0%b5%d0%bd%d1%82_%d0%b8%d0%bd%d0%b5%d1%80%d1%86%d0%b8%d0%b8
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for ru.wikipedia.org/wiki/%d0%9c%d0%be%d0%bc%d0%b5%d0%bd%d1%82_%d0%b8%d0%bd%d0%b5%d1%80%d1%86%d0%b8%d0%b8
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
No contextual keywords found in path
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
creativecommons.org creative commons cc bysa
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ru.m.wikipedia.org |
w journal of geophysical research
httpsruwikipediaorgwindexphptitleoldid133363041
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wiki 1
doi
pmid
wayback machine
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wikimediafoundation.org wikimedia foundation inc
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Links to external pages
Outloing links
nssdc.gsfc.nasa.gov
www.archive.today
www.ncbi.nlm.nih.gov
web.archive.org
dx.doi.org
web.archive.org
web.archive.org
genphys.phys.msu.ru
mathworld.wolfram.com
www.ncatlab.org
wikidata-externalid-url.toolforge.org
www.snl.no
old.bigenc.ru
ru.wikisource.org
www.britannica.com
encyklopedia.pwn.pl
www.d-nb.info
olduli.nli.org.il
aleph.nkp.cz
www.wikidata.org
commons.wikimedia.org
af.wikipedia.org
ar.wikipedia.org
be.wikipedia.org
ca.wikipedia.org
cs.wikipedia.org
cv.wikipedia.org
de.wikipedia.org
el.wikipedia.org
eo.wikipedia.org
es.wikipedia.org
et.wikipedia.org
eu.wikipedia.org
fa.wikipedia.org
fi.wikipedia.org
fr.wikipedia.org
ga.wikipedia.org
gl.wikipedia.org
he.wikipedia.org
hi.wikipedia.org
ht.wikipedia.org
hu.wikipedia.org
hy.wikipedia.org
is.wikipedia.org
it.wikipedia.org
ja.wikipedia.org
ka.wikipedia.org
kk.wikipedia.org
lt.wikipedia.org
lv.wikipedia.org
mk.wikipedia.org
nl.wikipedia.org
nn.wikipedia.org
no.wikipedia.org
pl.wikipedia.org
pt.wikipedia.org
ro.wikipedia.org
sh.wikipedia.org
simple.wikipedia.org
sk.wikipedia.org
sl.wikipedia.org
sq.wikipedia.org
sr.wikipedia.org
ta.wikipedia.org
tg.wikipedia.org
tr.wikipedia.org
tt.wikipedia.org
uk.wikipedia.org
vi.wikipedia.org
wuu.wikipedia.org
zh.wikipedia.org
zh-yue.wikipedia.org
www.wikidata.org
foundation.wikimedia.org
developer.wikimedia.org
foundation.wikimedia.org
www.wikimediafoundation.org
SEO Advice for ru.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 0% | A title should reflect the contents of a site. This site has a 0 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 55 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 85% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 133 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 5 level 1 folders and 8 folders above or in the first level of navigation. | |
Headings | 0% | Headers should reflect the contents of a site. This site has a 0 % match | |
Links | 8% | Link anchors should to some degree reflect the contents of a site. This site has a 4 % match | |
Image alt tags | 31% | Image alt tags should to some degree reflect the contents of a site. This site has a 11 % match | |
Bold and italic | 51% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 17 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 87% | 87.301587301587 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 1735 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 53.75% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 20% | There are no important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 268 inline style declarations ( <a style="color:green">) with a size of 8485 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (4) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 100% | Perfect, we found a correct use of normalized headings ! |
How would you like to have SEO advice for all your pages ?? Start your SEO Dashboard and optimize your website!
ru.wikipedia.org images and descriptions
118 images found at ru.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
https://upload.wikimedia.org/wikipedia/commons/thumb/a/ae/crystal_clear_action_bookmark_silver_approved.svg/14px-crystal_clear_action_bookmark_silver_approved.svg.png height: 14 width: 14 description: Эта статья входит в число добротных статей |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3f926e149297b2f0be756e0d9e91a31393ce526a height: height attribute not set width: width attribute not set description: {\displaystyle j=\int \limits _{(m)}r^{2}\mathrm {d} m} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/moment_of_inertia_examples.gif/250px-moment_of_inertia_examples.gif height: 188 width: 250 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/42a5cda356ec2135363e94cf4b9e5795f1a4f5ca height: height attribute not set width: width attribute not set description: {\displaystyle j_{a}=\sum _{i=1}^{n}m_{i}r_{i}^{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b85fa18ee04919589ff73e4e6eaa762052de9274 height: height attribute not set width: width attribute not set description: {\displaystyle j_{a}=\int \limits _{(m)}r^{2}dm=\int \limits _{(v)}\rho r^{2}dv,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b099549a1d6f1e125b168fd37e405b4b55079951 height: height attribute not set width: width attribute not set description: {\displaystyle j_{a}=\rho \int \limits _{(v)}r^{2}dv.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/88468cc892faa0b0a9608c38ab33fd7cb4c5edfd height: height attribute not set width: width attribute not set description: {\displaystyle j=j_{c}+md^{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0978781b31dc2b9552ba3f4c565535cd032ba308 height: height attribute not set width: width attribute not set description: {\displaystyle j=j_{c}+md^{2}={\frac {1}{12}}ml^{2}+m\left({\frac {l}{2}}\right)^{2}={\frac {1}{3}}ml^{2}.} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/b/b3/traegheit_a_punktmasse.png/100px-traegheit_a_punktmasse.png height: 47 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ddd9d0ea2911509b014b72a7b536acb7376cb455 height: height attribute not set width: width attribute not set description: {\displaystyle mr^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/traegheit_b_zylindermantel.png/100px-traegheit_b_zylindermantel.png height: 62 width: 100 description: no alt description found |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/traegheit_c_vollzylinder.png/100px-traegheit_c_vollzylinder.png height: 62 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2c01af9efcc9bfd0b28bdfb1a2e347b475c5eada height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{2}}mr^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/traegheit_d_hohlzylinder2.png/100px-traegheit_d_hohlzylinder2.png height: 62 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b82536c1d1606def8976c8bc6897cc9775229967 height: height attribute not set width: width attribute not set description: {\displaystyle m{\frac {r_{2}^{2}+r_{1}^{2}}{2}}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/2/29/traegheit_e_vollzylinder_2.png/100px-traegheit_e_vollzylinder_2.png height: 92 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e47edc2fdbcb0bbb72ddf9846a501bc6392858e height: height attribute not set width: width attribute not set description: {\displaystyle {1 \over 4}m\cdot r^{2}+{1 \over 12}m\cdot l^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/traegheit_f_zylindermantel_2.png/100px-traegheit_f_zylindermantel_2.png height: 92 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/27941d7223e3319d7a3558eb623fed1bdbbfb5dc height: height attribute not set width: width attribute not set description: {\displaystyle {1 \over 2}m\cdot r^{2}+{1 \over 12}m\cdot l^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/traegheit_g_stab1.png/100px-traegheit_g_stab1.png height: 58 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3b91b477ad64a0fc60f47254f935a6571b9783b1 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{12}}ml^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/7/7f/traegheit_h_stab2.png/100px-traegheit_h_stab2.png height: 58 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/68a814fe2246c36a1761123e861e2679bb7d4de7 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{3}}ml^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/traegheit_i_kugel1.png/100px-traegheit_i_kugel1.png height: 92 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c46d75f1ef69303419520ce124fa9019a916bf08 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {2}{3}}mr^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/f/f5/traegheit_j_kugel1.png/100px-traegheit_j_kugel1.png height: 92 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d775d25aafeee69fa5b1c97a53ec658164e31e00 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {2}{5}}mr^{2}} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/7/75/cone_%28geometry%29.svg/50px-cone_%28geometry%29.svg.png height: 90 width: 50 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a698ce99572daeeadc4a884c4c99479ec74653bd height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {3}{10}}mr^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d889093b8234cd96098c5e8084ad12116ed7e76a height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{24}}m(a^{2}+12h^{2})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f61f11ff87fbadc7bda6481c78f7f4753be5da8 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{12}}ma^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dbe766aab94d79406d469866676cc5c51eb2242c height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{6}}ma^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/41d84e0f4fbde06fec2644a0ed0091270689a9de height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {1}{12}}m(a^{2}+b^{2})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/66f8e082bfcfa76ec17978bb90ad38c5e3be5e56 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {mr^{2}}{6}}\left[1+2\cos ^{2}(\pi /n)\right]} |
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https://upload.wikimedia.org/wikipedia/commons/thumb/6/63/torus_3d.png/100px-torus_3d.png height: 75 width: 100 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e66b1815d347eb6e5296de4ea2529db29ff00f3 height: height attribute not set width: width attribute not set description: {\displaystyle i=m\left({\frac {3}{4}}\,r^{2}+r^{2}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c65eea12611c2e5ac614c46eb5845829b7eeb2fd height: height attribute not set width: width attribute not set description: {\displaystyle j=\sum dj_{i}=\sum r_{i}^{2}dm.\qquad (1).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f93682080abb497f9dd2b00561abf6dc78681117 height: height attribute not set width: width attribute not set description: {\displaystyle j=\sum r^{2}dm=r^{2}\sum dm=mr^{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f743d9c5015a0cbf5adfd02ba0328d6aac761886 height: height attribute not set width: width attribute not set description: {\displaystyle dm=\rho dv=\rho \cdot 2\pi rhdr;\qquad dj=r^{2}dm=2\pi \rho hr^{3}dr.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1442e4188e3df4206977b08eff904b984e696334 height: height attribute not set width: width attribute not set description: {\displaystyle j=\int _{r_{1}}^{r}dj=2\pi \rho h\int _{r_{1}}^{r}r^{3}dr=} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/79504a5cee06ea51637c5319c714c7042b150a6b height: height attribute not set width: width attribute not set description: {\displaystyle =2\pi \rho h\left.{\frac {r^{4}}{4}}\right|_{r_{1}}^{r}={\frac {1}{2}}\pi \rho h\left(r^{4}-r_{1}^{4}\right)={\frac {1}{2}}\pi \rho h\left(r^{2}-r_{1}^{2}\right)\left(r^{2}+r_{1}^{2}\right).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6d0c61d5985dbe5c39b74bb7c967b718fd3f72b2 height: height attribute not set width: width attribute not set description: {\displaystyle v=\pi \left(r^{2}-r_{1}^{2}\right)h;\qquad m=\rho v=\pi \rho \left(r^{2}-r_{1}^{2}\right)h,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/700929343d1e3eb7f82945ddf1c6df8d3ca5ce60 height: height attribute not set width: width attribute not set description: {\displaystyle j={\frac {1}{2}}m\left(r^{2}+r_{1}^{2}\right).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6df541c00f30427ffb3e7286f16fd9a8e49ea89f height: height attribute not set width: width attribute not set description: {\displaystyle j={\frac {1}{2}}mr^{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/50dedab87196fa4c9e457d091392bb116de1784f height: height attribute not set width: width attribute not set description: {\displaystyle r={\frac {rh}{h}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/88c8933a86629b84181be78081bd25a67c5eb3b2 height: height attribute not set width: width attribute not set description: {\displaystyle dm=\rho dv=\rho \cdot \pi r^{2}dh;} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/31bdef0ad971f38118e274d855efcc37155ffa13 height: height attribute not set width: width attribute not set description: {\displaystyle dj={\frac {1}{2}}r^{2}dm={\frac {1}{2}}\pi \rho r^{4}dh={\frac {1}{2}}\pi \rho \left({\frac {rh}{h}}\right)^{4}dh;} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d315864751a4202f74efc0b8f18183d01901999a height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}j=\int _{0}^{h}dj={\frac {1}{2}}\pi \rho \left({\frac {r}{h}}\right)^{4}\int _{0}^{h}h^{4}dh={\frac {1}{2}}\pi \rho \left({\frac {r}{h}}\right)^{4}\left.{\frac {h^{5}}{5}}\right|_{0}^{h}=={\frac {1}{10}}\pi \rho r^{4}h=\left(\rho \cdot {\frac {1}{3}}\pi r^{2}h\right){\frac {3}{10}}r^{2}={\frac {3}{10}}mr^{2}.\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/afc247a9c918020647c968d8c42b673c96fa7e5b height: height attribute not set width: width attribute not set description: {\displaystyle r={\sqrt {r^{2}-h^{2}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/278777dd09471dc94a48ba6ca0a035eda0cc1732 height: height attribute not set width: width attribute not set description: {\displaystyle dj={\frac {1}{2}}r^{2}dm={\frac {1}{2}}\pi \rho r^{4}dh={\frac {1}{2}}\pi \rho \left(r^{2}-h^{2}\right)^{2}dh={\frac {1}{2}}\pi \rho \left(r^{4}-2r^{2}h^{2}+h^{4}\right)dh.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/be2056d0a70e60e97757fa82cd4f5e18d4197ac0 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}j&=\int _{-r}^{r}dj=2\int _{0}^{r}dj=\pi \rho \int _{0}^{r}\left(r^{4}-2r^{2}h^{2}+h^{4}\right)dh=\\&=\pi \rho \left.\left(r^{4}h-{\frac {2}{3}}r^{2}h^{3}+{\frac {1}{5}}h^{5}\right)\right|_{0}^{r}=\pi \rho \left(r^{5}-{\frac {2}{3}}r^{5}+{\frac {1}{5}}r^{5}\right)={\frac {8}{15}}\pi \rho r^{5}=\\&=\left({\frac {4}{3}}\pi r^{3}\rho \right)\cdot {\frac {2}{5}}r^{2}={\frac {2}{5}}mr^{2}.\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e89a43019c59bea96cff0a9b31d0a1124f540995 height: height attribute not set width: width attribute not set description: {\displaystyle j_{0}={\frac {2}{5}}mr^{2}={\frac {8}{15}}\pi \rho r^{5}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9166010c1fafa10eb161333628f83018b12f122a height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}j&={\frac {dj_{0}}{dr}}dr={\frac {d}{dr}}\left({\frac {8}{15}}\pi \rho r^{5}\right)dr=\\&={\frac {8}{3}}\pi \rho r^{4}dr=\left(\rho \cdot 4\pi r^{2}dr\right){\frac {2}{3}}r^{2}={\frac {2}{3}}mr^{2}.\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/96a57cbb5722a2cc8eafdf14b9f4fe50055a9213 height: height attribute not set width: width attribute not set description: {\displaystyle dm={\frac {mdr}{l}};\qquad dj=r^{2}dm={\frac {mr^{2}dr}{l}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/08fb33c168707ff3c964d4ae4e2c0860c659c306 height: height attribute not set width: width attribute not set description: {\displaystyle j=\int _{-l/2}^{l/2}dj=2\int _{0}^{l/2}dj={\frac {2m}{l}}\int _{0}^{l/2}r^{2}dr={\frac {2m}{l}}\left.{\frac {r^{3}}{3}}\right|_{0}^{l/2}={\frac {2m}{l}}{\frac {l^{3}}{24}}={\frac {1}{12}}ml^{2}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9805c1f942002317c93c68a05b7fc0338a68bd7c height: height attribute not set width: width attribute not set description: {\displaystyle j=j_{0}+mr^{2}=j_{0}+m\left({\frac {l}{2}}\right)^{2}={\frac {1}{12}}ml^{2}+{\frac {1}{4}}ml^{2}={\frac {1}{3}}ml^{2}.} |
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https://upload.wikimedia.org/wikipedia/ru/timeline/gxlyfst71tx9p3b4kv1doekbumuox30.png height: height attribute not set width: width attribute not set description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9ea9538c8f486b74578769ee9c3dd3f2d48ed4bb height: height attribute not set width: width attribute not set description: {\displaystyle j_{xy}=\int \limits _{(m)}xydm=\int \limits _{(v)}xy\rho dv,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e7f0b017157856101eb1603c2a73f8212633598f height: height attribute not set width: width attribute not set description: {\displaystyle j_{xz}=\int \limits _{(m)}xzdm=\int \limits _{(v)}xz\rho dv,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a7e67b2e62ae82045e410cabc461a8b114002c5d height: height attribute not set width: width attribute not set description: {\displaystyle j_{yz}=\int \limits _{(m)}yzdm=\int \limits _{(v)}yz\rho dv,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/941e8b3ae5e88498d204ebd1960ce086e8c07d3e height: height attribute not set width: width attribute not set description: {\displaystyle j_{va}=\int \limits _{(v)}r^{2}dv,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9f4df2dd538545a07d9f89419ba71b66a0922d02 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {dim} j_{va}=\mathrm {l^{5}} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f4208880e71cf112ca7a721f98f001606fc0a0eb height: height attribute not set width: width attribute not set description: {\displaystyle j_{sa}=\int \limits _{(s)}r^{2}ds,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5d17430bd28b32761530815fb358e1a26ed7f3e3 height: height attribute not set width: width attribute not set description: {\displaystyle \mathrm {dim} j_{sa}=\mathrm {l^{4}} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/40af8415a74da96e1b346d9990ffbf189ded820a height: height attribute not set width: width attribute not set description: {\displaystyle w={\frac {j_{sa}}{r_{max}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a height: height attribute not set width: width attribute not set description: {\displaystyle h} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3 height: height attribute not set width: width attribute not set description: {\displaystyle b} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f3c86c8a7ddc180e2a7f7fb2274a4f3c46971ac height: height attribute not set width: width attribute not set description: {\displaystyle j_{y}={\frac {bh^{3}}{12}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ceba8932181b45970477cbaf043c506b75bbe52e height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}={\frac {hb^{3}}{12}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b height: height attribute not set width: width attribute not set description: {\displaystyle h} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a height: height attribute not set width: width attribute not set description: {\displaystyle b} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2ad43a86d57936ce294911bbe5814c8d1eb1a43a height: height attribute not set width: width attribute not set description: {\displaystyle j_{z}={\frac {bh^{3}}{12}}-{\frac {bh^{3}}{12}}={\frac {1}{12}}(bh^{3}-bh^{3})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fca357a451b2b0f63c9f3be3e27cf86461a5955c height: height attribute not set width: width attribute not set description: {\displaystyle j_{y}={\frac {hb^{3}}{12}}-{\frac {hb^{3}}{12}}={\frac {1}{12}}(hb^{3}-hb^{3})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e85ff03cbe0c7341af6b982e47e9f90d235c66ab height: height attribute not set width: width attribute not set description: {\displaystyle d} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6f34309c60393ebc00d7ac1891e22e5d3a0e09cb height: height attribute not set width: width attribute not set description: {\displaystyle j_{y}=j_{z}={\frac {\pi d^{4}}{64}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc height: height attribute not set width: width attribute not set description: {\displaystyle o} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bbeca34b28f569a407ef74a955d041df9f360268 height: height attribute not set width: width attribute not set description: {\displaystyle x,y,z} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/71b1bb75b9334ed1e4b00f5e7c20e9368b580b13 height: height attribute not set width: width attribute not set description: {\displaystyle xoy} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/415a63a82ee31c543a74f30679fe6832d3d3c5de height: height attribute not set width: width attribute not set description: {\displaystyle yoz} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de6fba8542f766988576394c2939ef6113e4d953 height: height attribute not set width: width attribute not set description: {\displaystyle zox} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c32ecd673c4dd652566e9e3497bb500cdc4d9485 height: height attribute not set width: width attribute not set description: {\displaystyle j_{xoy}=\sum _{i=1}^{n}m_{i}z_{i}^{2}\ ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8266748c6f55912368e6c5b8e1d50eddadca1dc height: height attribute not set width: width attribute not set description: {\displaystyle j_{yoz}=\sum _{i=1}^{n}m_{i}x_{i}^{2}\ ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5da213dbb01283ee8fc39045bccfa60b90f6488d height: height attribute not set width: width attribute not set description: {\displaystyle j_{zox}=\sum _{i=1}^{n}m_{i}y_{i}^{2}\ .} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f1bc26d4fd760386f2f2e811679afe2a30bcbdbf height: height attribute not set width: width attribute not set description: {\displaystyle j_{o}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7b17d7d89155e6cc1af7415aa80aba8baec7352b height: height attribute not set width: width attribute not set description: {\displaystyle dm=\rho dv} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/21c3a0961325e164fddf3f56b30add5bce2f37f0 height: height attribute not set width: width attribute not set description: {\displaystyle dv} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64 height: height attribute not set width: width attribute not set description: {\displaystyle \rho } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538 height: height attribute not set width: width attribute not set description: {\displaystyle r} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fe3e49f8dfd034bad71060cc51cb77903496d9f6 height: height attribute not set width: width attribute not set description: {\displaystyle j_{o}={\frac {1}{2}}\left(j_{x}+j_{y}+j_{z}\right),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5609e1ec87fed7f97e6c2a4d1135f847ce9fb51c height: height attribute not set width: width attribute not set description: {\displaystyle j_{o}=j_{xoy}+j_{yoz}+j_{xoz}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d1e16b1a730122f71a69b4380ce523e55c379e20 height: height attribute not set width: width attribute not set description: {\displaystyle {\vec {s}}=\left\vert s_{x},s_{y},s_{z}\right\vert ^{t},\left\vert {\vec {s}}\right\vert =1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b7f2c67928606b46540b715fba66706949bda04d height: height attribute not set width: width attribute not set description: {\displaystyle i_{s}={\vec {s}}^{t}\cdot {\hat {j}}\cdot {\vec {s}},\qquad } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b58109952c904943886cc08e0a385b42cd5ae8b6 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {j}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc0d4d6106875f8006be1d898512ca5843bad8e height: height attribute not set width: width attribute not set description: {\displaystyle 3\times 3} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f1220a1ba8d0f22712e3efece99472fd810fb275 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {j}}=\left\vert {\begin{array}{ccc}j_{xx}&-j_{xy}&-j_{xz}\\-j_{yx}&j_{yy}&-j_{yz}\\-j_{zx}&-j_{zy}&j_{zz}\end{array}}\right\vert ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/09c210157194adc9f1ab63b796423db159df8073 height: height attribute not set width: width attribute not set description: {\displaystyle j_{xy}=j_{yx},\quad j_{xz}=j_{zx},\quad j_{zy}=j_{yz},\quad } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99f9c4e4decec97061104d72958e8704fed3391c height: height attribute not set width: width attribute not set description: {\displaystyle j_{xx}=\int \limits _{(m)}(y^{2}+z^{2})dm,\quad j_{yy}=\int \limits _{(m)}(x^{2}+z^{2})dm,\quad j_{zz}=\int \limits _{(m)}(x^{2}+y^{2})dm.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9fc70e16eee6e5eac45c23e3964a9ab7c6f2c2aa height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {j}}_{d}={\hat {q}}^{t}\cdot {\hat {j}}\cdot {\hat {q}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3a45ccddc8a7457bbcb1570f87298a5fee177d67 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {j}}_{d}=\left\vert {\begin{array}{ccc}j_{x}&0&0\\0&j_{y}&0\\0&0&j_{z}\end{array}}\right\vert ,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2837cadd52889967c6393c6497f52f49de808c19 height: height attribute not set width: width attribute not set description: {\displaystyle {\hat {q}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ca766d0a2b2293b77e6f297c9f78455096ea54a6 height: height attribute not set width: width attribute not set description: {\displaystyle j_{x},j_{y},j_{z}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/059264c4c5006b09700b6513343bc2311cbe1141 height: height attribute not set width: width attribute not set description: {\displaystyle i_{s}=j_{x}\cdot s_{x}^{2}+j_{y}\cdot s_{y}^{2}+j_{z}\cdot s_{z}^{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/da7c52cd07d12dbec808d9b0c5a17ccd346054f3 height: height attribute not set width: width attribute not set description: {\displaystyle i_{s}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fa93f8dc0a461a55a7cf8ca77bba3246d621ce8e height: height attribute not set width: width attribute not set description: {\displaystyle \left({s_{x} \over {\sqrt {i_{s}}}}\right)^{2}\cdot j_{x}+\left({s_{y} \over {\sqrt {i_{s}}}}\right)^{2}\cdot j_{y}+\left({s_{z} \over {\sqrt {i_{s}}}}\right)^{2}\cdot j_{z}=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/582f24cfce81c69975efb4e731d22944b33ede71 height: height attribute not set width: width attribute not set description: {\displaystyle \xi ={s_{x} \over {\sqrt {i_{s}}}},\eta ={s_{y} \over {\sqrt {i_{s}}}},\zeta ={s_{z} \over {\sqrt {i_{s}}}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/506c6f84f95cf918a56632206c297f1ba73abbfd height: height attribute not set width: width attribute not set description: {\displaystyle \xi \eta \zeta } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/64e245ac2a8a47a8c563e0e4911a1d52c971d9f8 height: height attribute not set width: width attribute not set description: {\displaystyle \xi ^{2}\cdot j_{x}+\eta ^{2}\cdot j_{y}+\zeta ^{2}\cdot j_{z}=1.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4abfaa1a2120ff857a617187464fc49859ef2d28 height: height attribute not set width: width attribute not set description: {\displaystyle r^{2}=\xi ^{2}+\eta ^{2}+\zeta ^{2}=\left({s_{x} \over {\sqrt {i_{s}}}}\right)^{2}+\left({s_{y} \over {\sqrt {i_{s}}}}\right)^{2}+\left({s_{z} \over {\sqrt {i_{s}}}}\right)^{2}={1 \over i_{s}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b35c10fc1a69a55965de085cea12149c79fefc0f height: height attribute not set width: width attribute not set description: {\displaystyle m_{2}-m_{1}=m} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/23ba4e2f3ed20d4bbe002ad33bb8541150a06273 height: height attribute not set width: width attribute not set description: {\displaystyle m_{1}=m{\frac {r_{1}^{2}}{r_{2}^{2}-r_{1}^{2}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9d2700a2fa50ad2e86cff6a8e1368312a5b3c95d height: height attribute not set width: width attribute not set description: {\displaystyle m_{2}=m{\frac {r_{2}^{2}}{r_{2}^{2}-r_{1}^{2}}}} |
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