{"id":3284,"date":"2019-03-27T17:08:54","date_gmt":"2019-03-27T17:08:54","guid":{"rendered":"https:\/\/physicscatalyst.com\/graduation\/?p=3284"},"modified":"2021-06-05T13:45:27","modified_gmt":"2021-06-05T13:45:27","slug":"degrees-of-freedom-mechanics","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/graduation\/degrees-of-freedom-mechanics\/","title":{"rendered":"degrees of freedom mechanics with examples"},"content":{"rendered":"

Degree of freedom<\/h2>\n

Definition: –<\/strong> The minimum number of independent variables or coordinates required for specifying the position of a dynamical system consisting of one or more particle is called Degree of freedom<\/b>.<\/p>\n

For the $N$ number of particles moving freely in $d$ dimensional space degrees of freedom is represented by the following equation.<\/p>\n

$f=Nd$<\/p>\n

Where $N$ is the number of particles and $d$ denote the dimensions of the particle.<\/p>\n

If there are constraints then<\/p>\n

$f=Nd-k$<\/p>\n

where $k$ is the number of constraints<\/a>.<\/p>\n

Degrees of freedom Examples<\/h2>\n

Example 1 :-<\/h3>\n

Consider a particle moving along x-direction in three dimensional space then in this case<\/span><\/p>\n

$d = 3$, $N = 1$ and $k = 2$<\/p>\n

Constraint $k = 2$ means that particle cannot move in y and z directions. So in this case degrees of freedom would be $f=1$.<\/p>\n

Again the degree of freedom would be $f=1$ when the particle is moving in the x-direction in one-dimensional space.<\/p>\n

Example 2:-<\/h3>\n

Let us consider another case where two particles are moving freely in XY plane. Here in this case<\/p>\n

$\\begin{gathered}
\nd = 2 \\hfill \\\\
\nN = 2 \\hfill \\\\
\nk = 0 \\hfill \\\\
\n\\end{gathered} $<\/p>\n

here $k=0$ because particles are not constrained to move in XY-plane.<\/p>\n

Now degrees of freedom is defined as $f=Nd-k$ which gives us $f=4$<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Degree of freedom Definition: – The minimum number of independent variables or coordinates required for specifying the position of a dynamical system consisting of one or more particle is called Degree of freedom. For the $N$ number of particles moving freely in $d$ dimensional space degrees of freedom is represented by the following equation. $f=Nd$ […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[18],"tags":[],"class_list":["post-3284","post","type-post","status-publish","format-standard","hentry","category-classical-mechanics"],"yoast_head":"\ndegrees of freedom mechanics with examples - Learn about education and B.Sc. 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