%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EA%20flywhe
ID: 3899844 • Letter: #
Question
%3Cp%3E%3Cbr%20%2F%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EA%20flywheel%20with%20a%20radius%20of%0A0.310%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767051490_12%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-1-Frame%22%3E%3Cspan%20class%3D%22c5%22%3E%3Cspan%20class%3D%0A%22c4%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-2%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-3%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-4%22%3E%3Cspan%20class%3D%22texatom%20c3%22%20id%3D%0A%22MathJax-Span-5%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-6%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-7%22%3Em%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%20starts%0Afrom%20rest%20and%20accelerates%20with%20a%20constant%20angular%20acceleration%20of%0A0.660%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767051490_22%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-2-Frame%22%3E%3Cspan%20class%3D%22c13%22%3E%3Cspan%20class%3D%0A%22c12%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-9%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-10%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-11%22%3E%3Cspan%20class%3D%22texatom%20c3%22%20id%3D%0A%22MathJax-Span-12%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-13%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-14%22%3Er%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-15%22%3Ea%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-16%22%3Ed%3C%2Fspan%3E%3Cspan%20class%3D%22texatom%20c3%22%20id%3D%0A%22MathJax-Span-17%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-18%22%3E%3Cspan%20class%3D%22mo%20c2%22%20id%3D%0A%22MathJax-Span-19%22%3E%2F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22msubsup%20c3%22%0Aid%3D%22MathJax-Span-20%22%3E%3Cspan%20class%3D%22c11%22%3E%3Cspan%20class%3D%0A%22c8%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-21%22%3Es%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c10%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-22%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-23%22%3E%3Cspan%20class%3D%22mn%20c9%22%20id%3D%0A%22MathJax-Span-24%22%3E2%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3B.%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EPart%20A.%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c14%22%3ECompute%0Athe%20magnitude%20of%20the%20tangential%20acceleration%2C%20the%20radial%0Aacceleration%2C%20and%20the%20resultant%20acceleration%20of%20a%20point%20on%20its%20rim%0Aat%20the%20start.%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c14%22%3EPart%20B.%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c14%22%3ECompute%0Athe%20magnitude%20of%20the%20tangential%20acceleration%2C%20the%20radial%0Aacceleration%2C%20and%20the%20resultant%20acceleration%20of%20a%20point%20on%20its%20rim%0Aafter%20it%20has%20turned%20through%2060.0%20degrees.%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c14%22%3EPart%20C.%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c14%22%3ECompute%0Athe%20magnitude%20of%20the%20tangential%20acceleration%2C%20the%20radial%0Aacceleration%2C%20and%20the%20resultant%20acceleration%20of%20a%20point%20on%20its%20rim%0Aafter%20it%20has%20turned%20through%20120%20degrees.%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%0A%22c14%22%3E_______________________________________________________________________________________________________%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c14%22%3E%3Cbr%20%2F%3E%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EA%20vacuum%20cleaner%20belt%20is%20looped%20over%20a%20shaft%20of%0Aradius%200.46%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767168520_12%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-1-Frame%22%3E%3Cspan%20class%3D%22c15%22%3E%3Cspan%20class%3D%0A%22c8%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-2%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-3%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-4%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-5%22%3Ec%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-6%22%3Em%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3Band%0Aa%20wheel%20of%20radius%201.60%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%0Aid%3D%22yui_3_11_0_24_1395767168520_22%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-2-Frame%22%3E%3Cspan%20class%3D%22c15%22%3E%3Cspan%20class%3D%0A%22c8%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-8%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-9%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-10%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-11%22%3Ec%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-12%22%3Em%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3B.%0AThe%20arrangement%20of%20the%20belt%2C%20shaft%2C%20and%20wheel%20is%20similar%20to%20that%20of%0Athe%20chain%20and%20sprockets%3C%2Fspan%3E%3Cspan%20id%3D%0A%22yui_3_11_0_24_1395767168520_25%22%20class%3D%0A%22c1%22%3E%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E.%20The%20motor%20turns%20the%20shaft%20at%0Arotational%20velocity%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%0A%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767168520_35%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-3-Frame%22%3E%3Cspan%20class%3D%22c19%22%3E%3Cspan%20class%3D%0A%22c18%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-14%22%3E%3Cspan%20class%3D%0A%22maction%20c3%22%20id%3D%22MathJax-Span-15%22%3E%3Cspan%20class%3D%22MathJax_HitBox%20c16%22%0Aid%3D%22MathJax-HitBox-15%22%20title%3D%22omega%22%3E%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c17%22%0Aid%3D%22MathJax-Span-16%22%20title%3D%0A%22omega%22%3E%3F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%3D%0A58.0%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767168520_38%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-4-Frame%22%3E%3Cspan%20class%3D%22c21%22%3E%3Cspan%20class%3D%0A%22c20%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-18%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-19%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-20%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-21%22%3Er%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-22%22%3Ee%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-23%22%3Ev%3C%2Fspan%3E%3Cspan%20class%3D%22texatom%20c3%22%20id%3D%0A%22MathJax-Span-24%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-25%22%3E%3Cspan%20class%3D%22mo%20c2%22%20id%3D%0A%22MathJax-Span-26%22%3E%2F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-27%22%3Es%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3Band%0Athe%20moving%20belt%20turns%20the%20wheel%2C%20that%20in%20turn%20is%20connected%20by%0Aanother%20shaft%20to%20the%20roller%20that%20beats%20the%20dirt%20out%20of%20the%20rug%0Abeing%20vacuumed.%20Assume%20that%20the%20belt%20doesn't%20slip%20on%20either%20the%0Ashaft%20or%20the%20wheel.%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EPart%20A.%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c14%22%3EWhat%20is%0Athe%20angular%20velocity%20of%20the%20wheel%20in%20rad%2Fs%3F%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%0A%22c14%22%3E_______________________________________________________________________________________________________%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c14%22%3E%3Cbr%20%2F%3E%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EA%20solid%2C%20uniform%20ball%20rolls%20without%20slipping%20up%0Aa%20hill%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E.%20At%20the%20top%20of%20the%20hill%2C%20it%20is%0Amoving%20horizontally%3B%20then%20it%20goes%20over%20the%20vertical%20cliff.%0ATake%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767215528_29%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-1-Frame%22%3E%3Cspan%20class%3D%22c24%22%3E%3Cspan%20class%3D%0A%22c23%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-2%22%3E%3Cspan%20class%3D%0A%22maction%20c3%22%20id%3D%22MathJax-Span-3%22%3E%3Cspan%20class%3D%22MathJax_HitBox%20c22%22%0Aid%3D%22MathJax-HitBox-3%22%20title%3D%22V%22%3E%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c17%22%20id%3D%0A%22MathJax-Span-4%22%20title%3D%0A%22V%22%3EV%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3B%3D%0A27.0%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767215528_32%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-2-Frame%22%3E%3Cspan%20class%3D%22c26%22%3E%3Cspan%20class%3D%0A%22c25%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-6%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-7%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-8%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-9%22%3Em%3C%2Fspan%3E%3Cspan%20class%3D%22texatom%20c3%22%20id%3D%0A%22MathJax-Span-10%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-11%22%3E%3Cspan%20class%3D%22mo%20c2%22%20id%3D%0A%22MathJax-Span-12%22%3E%2F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-13%22%3Es%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3Band%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%0Aid%3D%22yui_3_11_0_24_1395767215528_35%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-3-Frame%22%3E%3Cspan%20class%3D%22c29%22%3E%3Cspan%20class%3D%0A%22c28%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-15%22%3E%3Cspan%20class%3D%0A%22maction%20c3%22%20id%3D%22MathJax-Span-16%22%3E%3Cspan%20class%3D%22MathJax_HitBox%20c27%22%0Aid%3D%22MathJax-HitBox-16%22%20title%3D%22H%22%3E%3C%2Fspan%3E%3Cspan%20class%3D%22mi%20c17%22%20id%3D%0A%22MathJax-Span-17%22%20title%3D%0A%22H%22%3EH%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3B%3D%0A25.0%3C%2Fspan%3E%3Cspan%20class%3D%22replace-insert%20done%20c1%22%20id%3D%0A%22yui_3_11_0_24_1395767215528_38%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-4-Frame%22%3E%3Cspan%20class%3D%22c5%22%3E%3Cspan%20class%3D%0A%22c4%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-19%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-20%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-21%22%3E%3Cspan%20class%3D%22mi%20c2%22%20id%3D%0A%22MathJax-Span-22%22%3Em%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3B.%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3EPart%20A.%26nbsp%3B%3Cspan%20class%3D%22c14%22%3EHow%20fast%20is%20it%20moving%20just%20before%0Ait%20lands%3F%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cdiv%20class%3D%22answer%20c32%22%20id%3D%22yui_3_11_0_20_1395767215528_83%22%3E%0A%3Cdiv%20class%3D%22work%20c31%22%20id%3D%22yui_3_11_0_24_1395767215528_60%22%3E%0A%3Cdiv%20id%3D%22solutionSymbolic_1_area%22%20class%3D%0A%22gadget%20solutionSymbolic%20genericFlash%20c30%22%3E%3C%2Fdiv%3E%0A%3C%2Fdiv%3E%0A%3C%2Fdiv%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3EPart%20B.%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c14%22%3ENotice%0Athat%20when%20the%20ball%20lands%2C%20it%20has%20a%20larger%20translational%20speed%20than%0Ait%20had%20at%20the%20bottom%20of%20the%20hill.%20Does%20this%20mean%20that%20the%20ball%0Asomehow%26nbsp%3B%3C%2Fspan%3E%3Ci%20class%3D%22c33%22%3Egained%3C%2Fi%3E%3Cspan%20class%3D%0A%22c14%22%3E%26nbsp%3Benergy%20by%20going%20up%20the%20hill%3F%20Explain!%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%0A%22c14%22%3E_______________________________________________________________________________________________________%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22replace-insert%20done%20c39%22%20id%3D%0A%22yui_3_11_0_24_1395767051490_59%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-8-Frame%22%3E%3Cspan%20class%3D%22math%20c3%22%20id%3D%0A%22MathJax-Span-112%22%3E%3Cspan%20class%3D%22c38%22%3E%3Cspan%20class%3D%22c37%22%3E%3Cspan%20class%3D%0A%22mrow%20c3%22%20id%3D%22MathJax-Span-113%22%3E%3Cspan%20class%3D%22texatom%20c3%22%20id%3D%0A%22MathJax-Span-114%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-115%22%3E%3Cspan%20class%3D%22msubsup%20c3%22%20id%3D%0A%22MathJax-Span-116%22%3E%3Cspan%20class%3D%22c36%22%3E%3Cspan%20class%3D%22c34%22%3E%3Cspan%20class%3D%0A%22mi%20c3%22%20id%3D%22MathJax-Span-117%22%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c35%22%3E%3Cspan%20class%3D%22mo%20c9%22%20id%3D%0A%22MathJax-Span-118%22%3E%3F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22replace-insert%20done%20c39%22%20id%3D%0A%22yui_3_11_0_24_1395767051490_39%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-5-Frame%22%3E%3Cspan%20class%3D%22c38%22%3E%3Cspan%20class%3D%0A%22c37%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%22MathJax-Span-66%22%3E%3Cspan%20class%3D%0A%22texatom%20c3%22%20id%3D%22MathJax-Span-67%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-68%22%3E%3Cspan%20class%3D%22msubsup%20c3%22%20id%3D%0A%22MathJax-Span-69%22%3E%3Cspan%20class%3D%22c36%22%3E%3Cspan%20class%3D%22c34%22%3E%3Cbr%20class%3D%0A%22Apple-interchange-newline%22%20%2F%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c35%22%3E%3Cspan%20class%3D%0A%22mo%20c9%22%20id%3D%0A%22MathJax-Span-71%22%3E%3F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c40%22%3E%0A%5D%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22replace-insert%20done%20c39%22%20id%3D%0A%22yui_3_11_0_24_1395767051490_39%22%3E%3Cspan%20class%3D%0A%22type-specific%22%3E%3Cspan%20class%3D%22MathJax%20c7%22%20id%3D%0A%22MathJax-Element-5-Frame%22%3E%3Cspan%20class%3D%22math%20c3%22%20id%3D%0A%22MathJax-Span-65%22%3E%3Cspan%20class%3D%22c38%22%3E%3Cspan%20class%3D%22c37%22%3E%3Cspan%20class%3D%0A%22mrow%20c3%22%20id%3D%22MathJax-Span-66%22%3E%3Cspan%20class%3D%22texatom%20c3%22%20id%3D%0A%22MathJax-Span-67%22%3E%3Cspan%20class%3D%22mrow%20c3%22%20id%3D%0A%22MathJax-Span-68%22%3E%3Cspan%20class%3D%22msubsup%20c3%22%20id%3D%0A%22MathJax-Span-69%22%3E%3Cspan%20class%3D%22c36%22%3E%3Cspan%20class%3D%22c34%22%3E%3Cspan%20class%3D%0A%22mi%20c3%22%20id%3D%22MathJax-Span-70%22%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c35%22%3E%3Cspan%20class%3D%22mo%20c9%22%20id%3D%0A%22MathJax-Span-71%22%3E%3F%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3Cspan%20class%3D%22c40%22%3E%0A%3Cbr%20%2F%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fspan%3E%3C%2Fp%3E%0AExplanation / Answer
The formulae for components of acceleration of a particle moving in a curve with polar co-ordinates (r, t) are:
Normal: r''- r(t')^2
Tangential: rt''+ 2r't'
For circular motion r' and r'' are zero, yielding:
Normal: - r(t')^2
Tangential: rt''
For the flywheel, the normal acceleration of a particle on the rim at the start is:
0, as t' is initially 0.
The tangential acceleration is:
0.300 * 0.600
= 0.18 m/s^2.
The resultant acceleration is the same as the tangential.
When the flywheel has rotated through pi/3 (= 60 deg):
(t')^2 = 2 * 0.600 * pi/3
t = 1.12 rad/s.
The normal acceleration is:
- 0.300 * 2 * 0.6 * pi / 3
= - 0.38 m/s^2.
The tangential acceleration is still 0.18 m/s^2, as it is constant.
The resultant accleration is of magnitude:
sqrt(0.38^2 + 0.18^2)
= 0.42 m/s^2.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.