{"id":230646,"date":"2025-06-09T19:05:57","date_gmt":"2025-06-09T19:05:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230646"},"modified":"2025-06-09T19:05:59","modified_gmt":"2025-06-09T19:05:59","slug":"a-uniform-rigid-rod-rests-on-a-level-frictionless-surface","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/09\/a-uniform-rigid-rod-rests-on-a-level-frictionless-surface\/","title":{"rendered":"A uniform rigid rod rests on a level, frictionless surface."},"content":{"rendered":"\n

A uniform rigid rod rests on a level, frictionless surface. The diagram below indicates four different combinations of (1) net force on the rod,
, and (2) net torque on the rod about its center of mass,
. In each box, draw vectors that represent one or two forces that achieve the given combination of net force and net torque. If any combination is not possible, state so explicitly. For example: In the second case, indicate one or two forces that could be exerted on the rod so that at the instant shown the net force on it is zero, but the net torque on it is not zero. Top view<\/p>\n\n\n\n

A uniform rigid rod rests on a level, frictionless surface. The diagram below indicates four different combinations of (1) net force on the rod, F\u20d7net, and (2) net torque on the rod about its center of mass, \u03c4\u20d7net. In each box, draw vectors that represent one or two forces that achieve the given combination of net force and net torque. If any combination is not possible, state so explicitly.<\/p>\n\n\n\n

For example: In the second case, indicate one or two forces that could be exerted on the rod so that at the instant shown the net force on it is zero, but the net torque on it is not zero.
Top view
|F\u20d7net| = 0, |\u03c4\u20d7net| = 0 |F\u20d7net| = 0, |\u03c4\u20d7net| \u2260 0 |F\u20d7net| \u2260 0, |\u03c4\u20d7net| = 0 |F\u20d7net| \u2260 0, |\u03c4\u20d7net| \u2260 0
Added by<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To solve this, we’ll consider the physics of rigid body motion<\/strong> on a frictionless surface<\/strong>, focusing on combinations of net force<\/strong> and net torque<\/strong>. We assume the rod lies horizontally and we view it from the top.<\/p>\n\n\n\n

\n\n\n\n

The Four Cases:<\/strong><\/h3>\n\n\n\n

Let\u2019s consider each combination of net force (F)<\/strong> and net torque (\u03c4)<\/strong> on the rod:<\/p>\n\n\n\n

\n\n\n\n

Case 1: Net Force \u2260 0, Net Torque = 0<\/strong><\/h4>\n\n\n\n

\u2705 Possible<\/strong><\/p>\n\n\n\n

Explanation<\/strong>: Apply two equal and parallel forces<\/strong> at opposite ends of the rod, both pointing in the same direction<\/strong>, along the axis of the rod. For example, if both are pushing to the right, they sum to a net force but since they are equal, opposite in position, and aligned, their torques cancel.<\/p>\n\n\n\n

Diagram<\/strong>:
\u2192 \u2014\u2014\u2192
(Forces on both ends pointing right)<\/p>\n\n\n\n

\n\n\n\n

Case 2: Net Force = 0, Net Torque \u2260 0<\/strong><\/h4>\n\n\n\n

\u2705 Possible<\/strong><\/p>\n\n\n\n

Explanation<\/strong>: Apply a force pair (a couple)<\/strong> \u2014 equal in magnitude, opposite in direction, but not collinear. For example, apply one force up on one end of the rod, and an equal force down on the opposite end. Their linear effects cancel, but they create a pure torque<\/strong>.<\/p>\n\n\n\n

Diagram<\/strong>:
\u2191 \u2014\u2014 \u2193
(One up, one down on opposite ends)<\/p>\n\n\n\n

\n\n\n\n

Case 3: Net Force \u2260 0, Net Torque \u2260 0<\/strong><\/h4>\n\n\n\n

\u2705 Possible<\/strong><\/p>\n\n\n\n

Explanation<\/strong>: Apply a single force<\/strong> not at the center of mass. This will both translate<\/strong> (net force) and rotate<\/strong> (net torque) the rod. The farther from the center, the greater the torque.<\/p>\n\n\n\n

Diagram<\/strong>:
\u2192
(One force off-center, pointing right)<\/p>\n\n\n\n

\n\n\n\n

Case 4: Net Force = 0, Net Torque = 0<\/strong><\/h4>\n\n\n\n

\u2705 Possible<\/strong><\/p>\n\n\n\n

Explanation<\/strong>: Apply equal and opposite forces directly through the center of mass<\/strong>. They cancel out both in force and torque, or apply no forces at all<\/strong>.<\/p>\n\n\n\n

Diagram<\/strong>:
(No arrows, or opposing equal arrows through center)<\/p>\n\n\n\n

\n\n\n\n

Conclusion (Summary Table):<\/strong><\/h3>\n\n\n\n
Case<\/th>Net Force<\/th>Net Torque<\/th>Possible?<\/th>How to Achieve<\/th><\/tr><\/thead>
1<\/td>Yes<\/td>No<\/td>Yes<\/td>Two equal forces in same direction<\/td><\/tr>
2<\/td>No<\/td>Yes<\/td>Yes<\/td>Force couple (equal\/opposite, off-axis)<\/td><\/tr>
3<\/td>Yes<\/td>Yes<\/td>Yes<\/td>One off-center force<\/td><\/tr>
4<\/td>No<\/td>No<\/td>Yes<\/td>No force or equal\/opposite through center<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

All combinations are physically possible<\/strong>. The key lies in understanding the placement and direction<\/strong> of forces relative to the center of mass<\/strong>.<\/p>\n\n\n\n

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

A uniform rigid rod rests on a level, frictionless surface. The diagram below indicates four different combinations of (1) net force on the rod,, and (2) net torque on the rod about its center of mass,. In each box, draw vectors that represent one or two forces that achieve the given combination of net force […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","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":"","ast-disable-related-posts":"","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":[25],"tags":[],"class_list":["post-230646","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230646","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=230646"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230646\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230646"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230646"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230646"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}