When is the rotational momentum of a system constant? A) Only when its total kinetic energy is constant. B) Only when no net external force acts on the system. C) Only when the linear momentum and the energy are constant. D) Only when no net external torque acts on the system. E) Only when the rotational inertia is constant.<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n The correct answer is:<\/p>\n\n\n\n D) Only when no net external torque acts on the system.<\/strong><\/p>\n\n\n\n Rotational momentum, also known as angular momentum<\/strong>, is a fundamental physical quantity in rotational dynamics. It describes the rotational equivalent of linear momentum and is defined for a system as: L=I\u03c9\\mathbf{L} = I \\boldsymbol{\\omega}<\/p>\n\n\n\n where:<\/p>\n\n\n\n Angular momentum of a system is conserved<\/strong> (constant in magnitude and direction) only if no external torque acts on the system<\/strong>. This is a direct consequence of Newton\u2019s second law for rotation, which states: \u03c4net=dLdt\\mathbf{\\tau}_{\\text{net}} = \\frac{d\\mathbf{L}}{dt}<\/p>\n\n\n\n Here, \u03c4net\\mathbf{\\tau}_{\\text{net}} is the net external torque acting on the system. If the net external torque is zero: \u03c4net=0\u2005\u200a\u27f9\u2005\u200adLdt=0\u2005\u200a\u27f9\u2005\u200aL=constant\\mathbf{\\tau}_{\\text{net}} = 0 \\implies \\frac{d\\mathbf{L}}{dt} = 0 \\implies \\mathbf{L} = \\text{constant}<\/p>\n\n\n\n This principle is called the conservation of angular momentum<\/strong>.<\/p>\n\n\n\n Angular momentum remains constant if and only if no external torque acts on the system.<\/strong> This principle is fundamental in physics and underlies phenomena ranging from spinning ice skaters to planetary orbits. External forces affect linear momentum, but only external torques change angular momentum.<\/p>\n","protected":false},"excerpt":{"rendered":" When is the rotational momentum of a system constant? A) Only when its total kinetic energy is constant. B) Only when no net external force acts on the system. C) Only when the linear momentum and the energy are constant. D) Only when no net external torque acts on the system. E) Only when the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-23410","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23410","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=23410"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23410\/revisions"}],"predecessor-version":[{"id":23411,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23410\/revisions\/23411"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=23410"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=23410"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=23410"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nExplanation:<\/h3>\n\n\n\n
\n
\n\n\n\nWhen is angular momentum constant?<\/h4>\n\n\n\n
\n\n\n\nWhy not the other options?<\/h4>\n\n\n\n
\n
Kinetic energy can change without changing angular momentum if internal forces cause redistribution of energy. Energy conservation alone doesn\u2019t guarantee constant angular momentum.<\/li>\n\n\n\n
No net external force means linear momentum is conserved, but angular momentum can still change if external torque acts (e.g., a force applied off-center).<\/li>\n\n\n\n
Neither constant linear momentum nor energy alone ensures angular momentum conservation. External torques specifically affect angular momentum.<\/li>\n\n\n\n
Rotational inertia may change if the system changes shape or mass distribution (like a figure skater pulling in arms), but angular momentum can still be conserved if no external torque acts. In such cases, the angular velocity adjusts to keep angular momentum constant.<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nSummary<\/h3>\n\n\n\n