{"id":1462,"date":"2018-02-06T17:16:35","date_gmt":"2018-02-06T17:16:35","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/?post_type=chapter&p=1462"},"modified":"2018-02-06T17:16:35","modified_gmt":"2018-02-06T17:16:35","slug":"11-chapter-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/chapter\/11-chapter-review\/","title":{"raw":"11 Chapter Review","rendered":"11 Chapter Review"},"content":{"raw":"
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Key Terms<\/span><\/h3>\r\n
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angular momentum<\/strong><\/dt>\r\n \t
rotational analog of linear momentum, found by taking the product of moment of inertia and angular velocity<\/dd>\r\n<\/dl>\r\n
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law of conservation of angular momentum<\/strong><\/dt>\r\n \t
angular momentum is conserved, that is, the initial angular momentum is equal to the final angular momentum when no external torque is applied to the system<\/dd>\r\n<\/dl>\r\n
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precession<\/strong><\/dt>\r\n \t
circular motion of the pole of the axis of a spinning object around another axis due to a torque<\/dd>\r\n<\/dl>\r\n
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rolling motion<\/strong><\/dt>\r\n \t
combination of rotational and translational motion with or without slipping<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<\/div>\r\n
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Key Equations<\/span><\/h3>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Velocity of center of mass of rolling object<\/td>\r\nv<\/span>CM<\/span><\/span><\/span>=<\/span>R<\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span>vCM=R\u03c9<\/span><\/span><\/td>\r\n<\/tr>\r\n
Acceleration of center of mass of rolling object<\/td>\r\na<\/span>CM<\/span><\/span><\/span>=<\/span>R<\/span>\u03b1<\/span><\/span><\/span><\/span><\/span><\/span>aCM=R\u03b1<\/span><\/span><\/td>\r\n<\/tr>\r\n
Displacement of center of mass of rolling object<\/td>\r\nd<\/span>CM<\/span><\/span><\/span>=<\/span>R<\/span>\u03b8<\/span><\/span><\/span><\/span><\/span><\/span>dCM=R\u03b8<\/span><\/span><\/td>\r\n<\/tr>\r\n
Acceleration of an object rolling without slipping<\/td>\r\na<\/span>CM<\/span><\/span><\/span>=<\/span>m<\/span>g<\/span><\/span>sin<\/span><\/span>\u03b8<\/span><\/span>m<\/span>+<\/span>(<\/span>I<\/span>CM<\/span><\/span><\/span><\/span>\/<\/span>r<\/span>2<\/span><\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>aCM=mgsin\u03b8m+(ICM\/r2)<\/span><\/span><\/td>\r\n<\/tr>\r\n
Angular momentum<\/td>\r\nl<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>=<\/span>r<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>p<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>l\u2192=r\u2192\u00d7p\u2192<\/span><\/span><\/td>\r\n<\/tr>\r\n
Derivative of angular momentum equals torque<\/td>\r\nd<\/span>l<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span>=<\/span>\u2211<\/span>\u03c4<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>dl\u2192dt=\u2211\u03c4\u2192<\/span><\/span><\/td>\r\n<\/tr>\r\n
Angular momentum of a system of particles<\/td>\r\nL<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>=<\/span>l<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span>l<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>2<\/span><\/span>+<\/span>\u22ef<\/span>+<\/span>l<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>N<\/span><\/span><\/span><\/span><\/span><\/span><\/span>L\u2192=l\u21921+l\u21922+\u22ef+l\u2192N<\/span><\/span><\/td>\r\n<\/tr>\r\n
For a system of particles, derivative of angular\r\n
<\/div>\r\nmomentum equals torque<\/td>\r\n
d<\/span>L<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span>=<\/span>\u2211<\/span>\u03c4<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>dL\u2192dt=\u2211\u03c4\u2192<\/span><\/span><\/td>\r\n<\/tr>\r\n
Angular momentum of a rotating rigid body<\/td>\r\nL<\/span>=<\/span>I<\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span>L=I\u03c9<\/span><\/span><\/td>\r\n<\/tr>\r\n
Conservation of angular momentum<\/td>\r\nd<\/span>L<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span><\/span>d<\/span>t<\/span><\/span><\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span><\/span>dL\u2192dt=0<\/span><\/span><\/td>\r\n<\/tr>\r\n
Conservation of angular momentum<\/td>\r\nL<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>=<\/span>l<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>1<\/span><\/span>+<\/span>l<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>2<\/span><\/span>+<\/span>\u22ef<\/span>+<\/span>l<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>N<\/span><\/span>=<\/span>constant<\/span><\/span><\/span><\/span><\/span><\/span>L\u2192=l\u21921+l\u21922+\u22ef+l\u2192N=constant<\/span><\/span><\/td>\r\n<\/tr>\r\n
Precessional angular velocity<\/td>\r\n\u03c9<\/span>P<\/span><\/span>=<\/span>r<\/span>M<\/span>g<\/span><\/span>I<\/span>\u03c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03c9P=rMgI\u03c9<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><\/div>\r\n<\/div>\r\n
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Summary<\/span><\/h3>\r\n
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11.1<\/span>\u00a0<\/span>Rolling Motion<\/span><\/h4>\r\n