{"id":87507,"date":"2025-06-01T06:45:40","date_gmt":"2025-06-01T06:45:40","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=87507"},"modified":"2025-06-01T06:45:40","modified_gmt":"2025-06-01T06:45:40","slug":"which-one-of-the-following-is-the-correct-relation-between-frequency","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-correct-relation-between-frequency\/","title":{"rendered":"Which one of the following is the correct relation between frequency $"},"content":{"rendered":"

Which one of the following is the correct relation between frequency $f$ and angular frequency $\\omega$?<\/p>\n

[amp_mcq option1=”$f = \\pi\\omega$” option2=”$\\omega = 2\\pi f$” option3=”$f = 2\\omega\/\\pi$” option4=”$f = 2\\pi\\omega$” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC NDA-1 – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe question asks for the correct relation between frequency ($f$) and angular frequency ($\\omega$).
\n<\/section>\n
\nFrequency ($f$) represents the number of cycles or revolutions per unit of time (usually per second), measured in Hertz (Hz).
\nAngular frequency ($\\omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad\/s.
\nOne complete cycle or revolution corresponds to an angle of $2\\pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f \\times (2\\pi)$ radians.
\nTherefore, the angular frequency $\\omega$ is related to the frequency $f$ by the equation:
\n$\\omega = 2\\pi f$
\n<\/section>\n
\nAngular frequency is commonly used in physics and engineering, particularly when dealing with circular motion, oscillations (like simple harmonic motion), and waves. It simplifies many equations compared to using frequency directly, especially in the context of derivatives and integrals involving sinusoidal functions. The unit of angular frequency is radians per second (rad\/s), whereas the unit of frequency is Hertz (Hz) or cycles per second.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one of the following is the correct relation between frequency $f$ and angular frequency $\\omega$? [amp_mcq option1=”$f = \\pi\\omega$” option2=”$\\omega = 2\\pi f$” option3=”$f = 2\\omega\/\\pi$” option4=”$f = 2\\pi\\omega$” correct=”option2″] This question was previously asked in UPSC NDA-1 – 2017 Download PDFAttempt Online The question asks for the correct relation between frequency ($f$) and … <\/p>\n

Detailed SolutionWhich one of the following is the correct relation between frequency $<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1093],"tags":[1101,1128,1274],"class_list":["post-87507","post","type-post","status-publish","format-standard","hentry","category-upsc-nda-1","tag-1101","tag-physics","tag-wave-motion","no-featured-image-padding"],"yoast_head":"\nWhich one of the following is the correct relation between frequency $<\/title>\n<meta name=\"description\" content=\"The question asks for the correct relation between frequency ($f$) and angular frequency ($omega$). Frequency ($f$) represents the number of cycles or revolutions per unit of time (usually per second), measured in Hertz (Hz). Angular frequency ($omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad\/s. One complete cycle or revolution corresponds to an angle of $2pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f times (2pi)$ radians. Therefore, the angular frequency $omega$ is related to the frequency $f$ by the equation: $omega = 2pi f$\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-correct-relation-between-frequency\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which one of the following is the correct relation between frequency $\" \/>\n<meta property=\"og:description\" content=\"The question asks for the correct relation between frequency ($f$) and angular frequency ($omega$). Frequency ($f$) represents the number of cycles or revolutions per unit of time (usually per second), measured in Hertz (Hz). Angular frequency ($omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad\/s. One complete cycle or revolution corresponds to an angle of $2pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f times (2pi)$ radians. Therefore, the angular frequency $omega$ is related to the frequency $f$ by the equation: $omega = 2pi f$\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-correct-relation-between-frequency\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T06:45:40+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Which one of the following is the correct relation between frequency $","description":"The question asks for the correct relation between frequency ($f$) and angular frequency ($omega$). Frequency ($f$) represents the number of cycles or revolutions per unit of time (usually per second), measured in Hertz (Hz). Angular frequency ($omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad\/s. One complete cycle or revolution corresponds to an angle of $2pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f times (2pi)$ radians. Therefore, the angular frequency $omega$ is related to the frequency $f$ by the equation: $omega = 2pi f$","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-correct-relation-between-frequency\/","og_locale":"en_US","og_type":"article","og_title":"Which one of the following is the correct relation between frequency $","og_description":"The question asks for the correct relation between frequency ($f$) and angular frequency ($omega$). Frequency ($f$) represents the number of cycles or revolutions per unit of time (usually per second), measured in Hertz (Hz). Angular frequency ($omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad\/s. One complete cycle or revolution corresponds to an angle of $2pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f times (2pi)$ radians. Therefore, the angular frequency $omega$ is related to the frequency $f$ by the equation: $omega = 2pi f$","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-correct-relation-between-frequency\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T06:45:40+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-correct-relation-between-frequency\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-correct-relation-between-frequency\/","name":"Which one of the following is the correct relation between frequency $","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T06:45:40+00:00","dateModified":"2025-06-01T06:45:40+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The question asks for the correct relation between frequency ($f$) and angular frequency ($\\omega$). Frequency ($f$) represents the number of cycles or revolutions per unit of time (usually per second), measured in Hertz (Hz). Angular frequency ($\\omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad\/s. One complete cycle or revolution corresponds to an angle of $2\\pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f \\times (2\\pi)$ radians. 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