{"id":6252,"date":"2020-10-13T15:23:28","date_gmt":"2020-10-13T09:53:28","guid":{"rendered":"http:\/\/astan.lk\/al_virtualclassroom\/?p=6252"},"modified":"2020-10-13T15:23:44","modified_gmt":"2020-10-13T09:53:44","slug":"circular-motion","status":"publish","type":"post","link":"https:\/\/astan.lk\/al_virtualclassroom\/circular-motion\/","title":{"rendered":"Circular motion"},"content":{"rendered":"<p>When an object moves in a path where the distance from a fixed to that object is constant.Then its path is a circle and and its motion is called circular motion.<\/p>\n<p><strong>Angular displacement<\/strong><br \/>\n<a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/download-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7553\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/download-2.png\" alt=\"download\" width=\"190\" height=\"158\" \/><\/a><\/p>\n<p><strong>Angular velocity<\/strong><\/p>\n<p>In a circular motion ,with time distance changes.At the same time angle also changes.So there is a need to define angular velocity.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cm.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7723\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cm.png\" alt=\"cm\" width=\"170\" height=\"165\" \/><\/a>Rate of change of angular displacement is called angular velocity<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cmt.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7724\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cmt.png\" alt=\"cmt\" width=\"58\" height=\"61\" \/><\/a><\/p>\n<p>[\u03c9]=T<sup>-1<\/sup><\/p>\n<p>unit &#8211; rads<sup>-1<\/sup><\/p>\n<p>In uniform circular motion velocity is not uniform because in every point direction changes<\/p>\n<p>In time t, distance traveled= S<br \/>\n<a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cmv.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7725\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cmv.png\" alt=\"cmv\" width=\"139\" height=\"103\" \/><\/a><\/p>\n<p><strong>Time period(T)-<\/strong>Time taken for one complete revolution.<\/p>\n<p><strong>Frequency-<\/strong>In unit time number of revolutions take place.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cmv-1.png\"><br \/>\n<\/a> <a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/t.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7728\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/t.png\" alt=\"t\" width=\"282\" height=\"124\" \/><\/a><\/p>\n<p><strong>In 1s number of revolutions=f<\/strong><\/p>\n<p><strong>In 1s angle it makes=2\u03c0f<\/strong><\/p>\n<p><strong>Angular velocity\u00a0\u03c9=2\u03c0f<\/strong><\/p>\n<p><strong>Centripetal acceleration<\/strong><\/p>\n<p>In a uniform circular motion acceleration is always directed towards the center.So it is called centripetal acceleration.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/catr.gif\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7556\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/catr.gif\" alt=\"catr\" width=\"432\" height=\"232\" \/><\/a><\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/can.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7757\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/can.png\" alt=\"can\" width=\"188\" height=\"145\" \/><\/a><\/p>\n<p><strong>Centripetal force<\/strong><\/p>\n<p>Centripetal force is a force which acts on a body moving in a circular path and is directed towards the center around which the body is moving.<\/p>\n<p><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cfmag.gif\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-7560 alignleft\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/cfmag.gif\" alt=\"cfmag\" width=\"189\" height=\"69\" \/><\/a><\/p>\n<h3><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/download-1-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7561\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/download-1-1.png\" alt=\"download (1)\" width=\"226\" height=\"110\" \/><\/a><strong>\u00a0 F<sub>centripetal<\/sub> = mr\u03c9\u00b2<\/strong><\/h3>\n<p><strong>Banked curve<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/5b\/Banked_turn.svg\/220px-Banked_turn.svg.png\" \/><\/p>\n<p>The above image \u00a0shows a ball in circular motion on a banked curve. The curve is banked at an angle <i>\u03b8<\/i> from the horizontal, and the surface of the road is considered to be slippery. The objective is to find what angle the bank must have so the ball does not slide off the road.Intuition tells us that, on a flat curve with no banking at all, the ball will simply slide off the road; while with a very steep banking, the ball will slide to the center unless it travels the curve rapidly.<\/p>\n<p>Apart from any acceleration that might occur in the direction of the path, the lower part of the image above indicates the forces on the ball. There are <i>two<\/i> forces; one is the force of gravity vertically downward through the center of mass of the ball <i>m<\/i><b>g<\/b>, where <i>m<\/i> is the mass of the ball and <b>g<\/b> is the gravitational acceleration ; the second is the upward normal force \u00a0exerted by the road perpendicular to the road surface <i>m<\/i><b>a<\/b><sub>n<\/sub>. The centripetal force demanded by the curved motion is also shown above. This centripetal force is not a third force applied to the ball, but rather must be provided by the net force\u00a0on the ball resulting from vector addition\u00a0of the normal force and the force of gravity. The resultant or net force on the ball found by vector addition of the normal force exerted by the road and vertical force due to gravity must equal the centripetal force dictated by the need to travel a circular path. The curved motion is maintained so long as this net force provides the centripetal force requisite to the motion.<\/p>\n<p>The horizontal net force on the ball is the horizontal component of the force from the road, which has magnitude <b>F<\/b><sub>h<\/sub>\u00a0= <i>m<\/i><b>a<\/b><sub>n<\/sub>sin<i>\u03b8<\/i>. The vertical component of the force from the road must counteract the gravitational force: <b>F<\/b><sub>v<\/sub>\u00a0= <i>m<\/i><b>a<\/b><sub>n<\/sub>cos<i>\u03b8<\/i> = <i>m<\/i><b>g<\/b>, which implies <b>a<\/b><sub>n<\/sub>=<b>g<\/b>\u00a0\/ cos<i>\u03b8<\/i>. Substituting into the above formula for <b>F<\/b><sub>h<\/sub>\u00a0yields a horizontal force to be:<\/p>\n<dl>\n<dd><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/f6f729a660dcc4e5947c42112db6541d451c6cd0\" alt=\" |\\mathbf{F}_\\mathrm{h}| = m |\\mathbf{g}| \\frac { \\mathrm{sin}\\ \\theta}{ \\mathrm {cos}\\ \\theta} = m|\\mathbf{g}| \\mathrm{tan}\\ \\theta \\ . \" \/><\/span><\/dd>\n<\/dl>\n<p>On the other hand, at velocity <b>v<\/b>\u00a0on a circular path of radius <i>r<\/i>, kinematics says that the force needed to turn the ball continuously into the turn is the radially inward centripetal force <b>F<\/b><sub>c<\/sub> of magnitude:<\/p>\n<dl>\n<dd><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d2723fb42d5dc62af57d1f5d5a994c7a5466a305\" alt=\"|\\mathbf{F}_\\mathrm{c}| = m |\\mathbf{a}_\\mathrm{c}| = \\frac{m|\\mathbf{v}|^2}{r} \\ . \" \/><\/span><\/dd>\n<\/dl>\n<p>Consequently, the ball is in a stable path when the angle of the road is set to satisfy the condition:<\/p>\n<dl>\n<dd><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2f49bb73602503361085d2466169cdff0ddb5381\" alt=\"m |\\mathbf{g}| \\mathrm{tan}\\ \\theta = \\frac{m|\\mathbf{v}|^2}{r} \\ ,\" \/><\/span><\/dd>\n<\/dl>\n<p>or,<\/p>\n<dl>\n<dd><span class=\"mwe-math-element\"><img decoding=\"async\" class=\"mwe-math-fallback-image-inline\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/bc74a45beb50c8d0cc4dc3285e98624ccce96d9e\" alt=\" \\mathrm{tan}\\ \\theta = \\frac {|\\mathbf{v}|^2} {|\\mathbf{g}|r} \\ .\" \/><\/span><\/dd>\n<\/dl>\n<p>As the angle of bank <i>\u03b8<\/i> approaches 90\u00b0, the tangent function\u00a0approaches infinity, allowing larger values for <b>v<\/b><sup>2<\/sup>\/<i>r<\/i>. In words, this equation states that for faster speeds\u00a0the road must be banked more steeply (a larger value for <i>\u03b8<\/i>), and for sharper turns (smaller <i>r<\/i>) the road also must be banked more steeply. When the angle <i>\u03b8<\/i> does not satisfy the above condition, the horizontal component of force exerted by the road does not provide the correct centripetal force, and an additional frictional force tangential to the road surface is called upon to provide the difference. If friction cannot do this , the ball slides to a different radius where the balance can be realized.<\/p>\n<p><strong>In vertical circular motion<\/strong><\/p>\n<p><strong><a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/Untitled-3-2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-7774\" src=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/Untitled-3-2.png\" alt=\"Untitled-3\" width=\"590\" height=\"352\" \/><\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<a href=\"http:\/\/astan.lk\/al_virtualclassroom\/wp-content\/uploads\/2017\/01\/Untitled.png\"><br \/>\n<\/a><\/strong><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When an object moves in a path where the distance from a fixed to that object is constant.Then its path is a circle and and its motion is called circular motion. Angular displacement Angular velocity In a circular motion ,with time distance changes.At the same time angle also changes.So there is a need to define [&hellip;]<\/p>\n","protected":false},"author":842,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[16,1948],"tags":[],"class_list":["post-6252","post","type-post","status-publish","format-standard","hentry","category-physics","category-unit-02-en"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Circular motion - Learning &amp; Education Portal<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/astan.lk\/al_virtualclassroom\/circular-motion\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Circular motion - Learning &amp; Education Portal\" \/>\n<meta property=\"og:description\" content=\"When an object moves in a path where the distance from a fixed to that object is constant.Then its path is a circle and and its motion is called circular motion. 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