{"id":4756,"date":"2021-06-27T16:27:45","date_gmt":"2021-06-27T23:27:45","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=4756"},"modified":"2021-06-27T16:27:45","modified_gmt":"2021-06-27T23:27:45","slug":"moment-of-force","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/moment-of-force.htm","title":{"rendered":"Moment of force","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

Article about Moment of force<\/h3>\n

1. Lever arm<\/span><\/span><\/h4>\n

Review an object that rotates, such as the door of a room. When the door is opened or closed, the door rotates. The hinges that connect the door to the wall act as the axis of rotation.<\/span><\/span><\/p>\n

\"MomentThe door image is seen from above. Review an example where the door is pushed in the same two forces that have the same magnitude and direction, where the direction of the force is perpendicular to the door. At first, the door is pushed with a force of F<\/span>1<\/span><\/sub>, r<\/span>1<\/span><\/sub> from the axis of rotation. Subsequently, the door is pushed with the force of F<\/span>2<\/span><\/sub>, r<\/span>2<\/span><\/sub> away from the axis of rotation. Although the magnitude and direction of the force F<\/span>1 <\/span><\/sub>= F<\/span>2<\/span><\/sub>, the force of F<\/span>2<\/span><\/sub> causes the door to rotate faster than the force of F<\/span>1<\/span><\/sub>. In other words, the force of F<\/span>2 <\/span><\/sub>causes a greater angular acceleration compared to the force of F<\/span>1<\/span><\/sub>. You can prove this.<\/span><\/span><\/p>\n

The magnitude of the angular velocity of the moving object is not only influenced by force but is also influenced by the distance between the working points of the force and the rotary axis (r). If the direction of the force is perpendicular to the surface of the object as in the example above, then the lever arm (l) is equal to the distance between the points of work with the axis of rotation (r). What if the direction of the force is not perpendicular to the surface of the object?<\/span><\/span><\/p>\n

\"MomentReview two other examples, as shown in the figure on the side. Although the magnitude of the force is the same, the direction of the force is different, so the lever arm (l) is also different. In Figure 3, the direction of the work line of force coincides with the axis of rotation so that the lever arm is zero. The lever arm is known by describing the line from the axis of rotation to the line of the workforce. Where the line of the axis of rotation must be perpendicular or form an angle of 90o with a line of force.<\/span><\/span><\/p>\n

\"MomentObserve figure 2 so that you better understand the equation of the lever arm.<\/span><\/span><\/p>\n

Sin <\/span>\u03b8<\/span> = l \/ r<\/span><\/span><\/p>\n

l = r sin <\/span>\u03b8<\/span><\/span><\/p>\n

l = lever arm, r = distance of the point of the workforce with the axis of rotation.<\/i><\/span><\/span><\/p>\n

The equation above is used to calculate the lever arm. If F is perpendicular to r, then the angle formed is 90<\/span>o<\/span><\/sup>.<\/span><\/span><\/p>\n

l = r sin 90<\/span>o <\/span><\/sup>= r (1)<\/span><\/span><\/p>\n

l = r<\/span><\/span><\/p>\n

If F coincides with r, then the angle formed is 0<\/span>o<\/span><\/sup>.<\/span><\/span><\/p>\n

l = r sin 0<\/span>o <\/span><\/sup>= r (0)<\/span><\/span><\/p>\n

l = 0<\/span><\/span><\/p>\n

2.2 Moment of force (<\/span>torque<\/span>)<\/span><\/span><\/span><\/h4>\n

2.2.1 Magnitude of the moment of force<\/a><\/span><\/span><\/p>\n

Mathematically, the magnitude of the moment force is the result of the multiplication of the force (F) and the lever arm (l).<\/span><\/span><\/p>\n

\u03c4<\/span> = F l<\/span><\/span><\/p>\n

\u03c4 = moment of force (Newton meter), F = force (Newton<\/a>), l = lever arm (meter)<\/i><\/span><\/span><\/p>\n

Equation 2 is used to calculate the magnitude of the moment of force. The international system of torque is the same as work, but torque is not energy, so the unit does not need to be replaced with Joule. Physicists often use the term torque, while engineers use the term the moment of force.<\/span><\/span><\/p>\n

2.2.2 Direction of the moment of force<\/span><\/span><\/p>\n

\"MomentThe moment of force is a vector quantity because, in addition to having a magnitude, the moment of force also has a direction. The direction of the moment of force is known easily using the right-hand rule. Rotate the four fingers of your right hand, while the thumb of the right hand is upheld. The direction of the four fingers is the direction of rotation of the object, while the direction shown by the thumb is the direction of the moment of force.<\/span><\/span><\/p>\n

If the direction of the moment of force is upward (in the direction of the y-axis) or rightward (in the direction of the x-axis) then the moment of force is positive. Conversely, if the direction of the moment of force is downward (in the direction of the y-axis) or to the leftward (in the direction of the \u2013x-axis), the moment of force is negative. In other words, if the direction of rotation of objects is clockwise, then the moment of force is negative. Conversely, if the direction of rotation of objects is opposite to the clockwise rotation, then the moment of force is positive.<\/span><\/span><\/p>\n

2.2.3 Sample problems of the moment of force<\/span><\/span><\/p>\n

\"MomentSample problems 1.<\/span><\/span><\/p>\n

A block has a length of 8 meters. On the beam works three forces, as in the figure. What is the magnitude of the moment of force that causes the beam to rotate about its center?<\/span><\/span><\/p>\n

Solution:<\/span><\/span><\/p>\n

The center of the beam is located in the middle. The long of the beam is 8 meters, therefore the center of the beam is 4 meters from the end of the beam.<\/span><\/span><\/p>\n

Torque 1 = F<\/span>1<\/span><\/sub> l<\/span>1 <\/span><\/sub>= (10 N)(4 m) = 40 N m<\/span><\/span><\/p>\n

Torque 1 is positive because torque 1 causes the beams to rotate opposite clockwise.<\/span><\/span><\/p>\n

Torque 2 = F<\/span>2<\/span><\/sub> l<\/span>2<\/span><\/sub> = (10 N)(2 m) = – 20 N m<\/span><\/span><\/p>\n

Torque 2 is negative because torque 2 causes the beam to rotate clockwise.<\/span><\/span><\/p>\n

Torque 3 = F<\/span>3<\/span><\/sub> l<\/span>3 <\/span><\/sub>= (15 N)(2 m) = – 30 N m<\/span><\/span><\/p>\n

Torque 3 is negative because torque 3 causes the beam to rotate clockwise.<\/span><\/span><\/p>\n

Net torque = 40 N m \u2013 20 N m \u2013 30 N m = – 10 N m<\/span><\/span><\/p>\n

The resultant torque is negative, this indicates that the direction of rotation of the beam is clockwise.<\/span><\/span><\/p>\n

Sample problems 2.<\/span><\/span><\/p>\n

F<\/span>1 <\/span><\/sub>= 10 N, F<\/span>2<\/span><\/sub> = 15 N, F<\/span>3<\/span><\/sub> = 15 N and F<\/span>4 <\/span><\/sub>= 10 N, work on the rod of ABCD as shown in figure. The length of rod ABCD is 20 meters. If the rod mass is ignored, the axis of rotation located at point D determines the magnitude of the moment of force.<\/span><\/span><\/p>\n

\"MomentSolution:<\/span><\/span><\/p>\n

The question of this difficulty is what is the net torque that causes the beam to rotate, where the axis of rotation is located at point D.<\/span><\/span><\/p>\n

Torque 1 = F<\/span>1<\/span><\/sub> l<\/span>1<\/span><\/sub> = (10 N)(15 m) = 150 N m<\/span><\/span><\/p>\n

Torque 1 is positive because torque 1 causes the beam to rotate<\/span><\/span><\/p>\n

opposite to the direction of clockwise.<\/span><\/span><\/p>\n

Torque 2 = F<\/span>2 <\/span><\/sub>l<\/span>2 <\/span><\/sub>= (15 N)(5 m) = -75 N m<\/span><\/span><\/p>\n

Torque 2 is negative because torque 2 causes the beam to rotate in the direction clockwise.<\/span><\/span><\/p>\n

Torque 3 = F<\/span>3<\/span><\/sub> l<\/span>3 <\/span><\/sub>= (15 N)(0 m) = 0 N m<\/span><\/span><\/p>\n

Torque 3 is zero because F<\/span>3<\/span><\/sub> coincides with the axis of rotation.<\/span><\/span><\/p>\n

Torque 4 = F<\/span>4<\/span><\/sub> l<\/span>4 <\/span><\/sub>= (10 N)(5 m) = 50 N m<\/span><\/span><\/p>\n

Torque 4 is positive because torque 4 causes the beam to rotate in opposite directions clockwise.<\/span><\/span><\/p>\n

Net torque = 150 N m \u2013 75 N m + 50 N m = 125 N m<\/span><\/span><\/p>\n

The net torque is positive, therefore the direction of rotation of the beam is opposite to the direction of clockwise.<\/span><\/span><\/p>\n

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Article about Moment of force 1. Lever arm Review an object that rotates, such as the door of a room. When the door is opened or closed, the door rotates. The hinges that connect the door to the wall act as the axis of rotation. The door image is seen from above. Review an example … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Moment of force","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[2],"tags":[],"class_list":["post-4756","post","type-post","status-publish","format-standard","hentry","category-basic-physics-tutorials"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/4756","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=4756"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/4756\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=4756"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=4756"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=4756"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}