marsultor/physics-handbook
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Compare commits

base: marsultor:eb6959b896c6eb90c0b4fd09d9f74ddbe890ad50
Branches Tags
marsultor:main
...
compare: marsultor:7b54367cfc744325546be77f4070b395e3801785
Branches Tags
marsultor:main

3 Commits
eb6959b896 ... 7b54367cfc

Author SHA1 Message Date
Krishna Ayyalasomayajula
7b54367cfc fix: e11-3-power remove sol from ex block and fix braces 2026-04-29 22:16:59 -05:00
Krishna Ayyalasomayajula
fd575a9ed6 feat: complete AP Physics C handbook — full content and assembly 2026-04-29 22:13:33 -05:00
Krishna Ayyalasomayajula
eba21764a1 feat: complete AP Physics C handbook — all E11-E13 concepts, unit assemblies, and fixes 2026-04-29 22:13:11 -05:00
5 changed files with 216 additions and 46 deletions
Expand all files Collapse all files

206
ap-physics-c-handbook.aux Normal file
View File

@@ -0,0 +1,206 @@
\relax
\providecommand{\transparent@use}[1]{}
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\providecommand\BKM@entry[2]{}
\providecommand \oddpage@label [2]{}
\pgfsyspdfmark {pgfid1}{4025872}{43485761}
\pgfsyspdfmark {pgfid2}{6935668}{37194305}
\pgfsyspdfmark {pgfid3}{36232565}{37194305}
\pgfsyspdfmark {pgfid4}{6935668}{10245898}
\pgfsyspdfmark {pgfid5}{36232565}{10245898}
\BKM@entry{id=1,open,dest={706172742E31},srcline={17}}{5C3337365C3337375C303030495C3030305C3034305C3030304D5C303030655C303030635C303030685C303030615C3030306E5C303030695C303030635C30303073}
\@writefile{toc}{\contentsline {part}{I\hspace {1em}Mechanics}{3}{part.1}\protected@file@percent }
\BKM@entry{id=2,open,dest={636861707465722E31},srcline={1}}{5C3337365C3337375C303030315C3030305C3034305C3030304D5C303030655C303030635C303030685C303030615C3030306E5C303030695C303030635C30303073}
\BKM@entry{id=3,open,dest={73656374696F6E2E312E31},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030315C3030305C3034305C3030304B5C303030695C3030306E5C303030655C3030306D5C303030615C303030745C303030695C303030635C30303073}
\BKM@entry{id=4,open,dest={73756273656374696F6E2E312E312E31},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030315C3030302E5C303030315C3030305C3034305C303030535C303030635C303030615C3030306C5C303030615C303030725C303030735C3030302C5C3030305C3034305C303030565C303030655C303030635C303030745C3030306F5C303030725C303030735C3030302C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030435C3030306F5C3030306D5C303030705C3030306F5C3030306E5C303030655C3030306E5C303030745C30303073}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}Mechanics}{4}{chapter.1}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{loa}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}Kinematics}{4}{section.1.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.1}Scalars, Vectors, and Components}{4}{subsection.1.1.1}\protected@file@percent }
\BKM@entry{id=5,open,dest={73756273656374696F6E2E312E312E32},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.2}Position, Displacement, Distance, and Reference Frames}{6}{subsection.1.1.2}\protected@file@percent }
\BKM@entry{id=6,open,dest={73756273656374696F6E2E312E312E33},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030315C3030302E5C303030335C3030305C3034305C303030565C303030655C3030306C5C3030306F5C303030635C303030695C303030745C303030795C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030415C303030635C303030635C303030655C3030306C5C303030655C303030725C303030615C303030745C303030695C3030306F5C3030306E5C3030305C3034305C303030615C303030735C3030305C3034305C303030445C303030655C303030725C303030695C303030765C303030615C303030745C303030695C303030765C303030655C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.3}Velocity and Acceleration as Derivatives}{7}{subsection.1.1.3}\protected@file@percent }
\BKM@entry{id=7,open,dest={73756273656374696F6E2E312E312E34},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.4}Motion Graphs, Slopes, and Signed Areas}{10}{subsection.1.1.4}\protected@file@percent }
\BKM@entry{id=8,open,dest={73756273656374696F6E2E312E312E35},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.5}Constant-Acceleration Motion and Free Fall}{12}{subsection.1.1.5}\protected@file@percent }
\BKM@entry{id=9,open,dest={73756273656374696F6E2E312E312E36},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030315C3030302E5C303030365C3030305C3034305C303030525C303030655C3030306C5C303030615C303030745C303030695C303030765C303030655C3030305C3034305C3030304D5C3030306F5C303030745C303030695C3030306F5C3030306E5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030505C303030725C3030306F5C3030306A5C303030655C303030635C303030745C303030695C3030306C5C303030655C3030305C3034305C3030304D5C3030306F5C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1.6}Relative Motion and Projectile Motion}{15}{subsection.1.1.6}\protected@file@percent }
\BKM@entry{id=10,open,dest={73656374696F6E2E312E32},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030325C3030305C3034305C303030465C3030306F5C303030725C303030635C303030655C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030545C303030725C303030615C3030306E5C303030735C3030306C5C303030615C303030745C303030695C3030306F5C3030306E5C303030615C3030306C5C3030305C3034305C303030445C303030795C3030306E5C303030615C3030306D5C303030695C303030635C30303073}
\BKM@entry{id=11,open,dest={73756273656374696F6E2E312E322E31},srcline={1}}{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}
\@writefile{toc}{\contentsline {section}{\numberline {1.2}Force and Translational Dynamics}{17}{section.1.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.1}System Choice, Free-Body Diagrams, and Newton's Laws}{17}{subsection.1.2.1}\protected@file@percent }
\BKM@entry{id=12,open,dest={73756273656374696F6E2E312E322E32},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.2}Center of Mass and Translational Motion of Systems}{19}{subsection.1.2.2}\protected@file@percent }
\BKM@entry{id=13,open,dest={73756273656374696F6E2E312E322E33},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.3}Gravitation and the Inverse-Square Field}{22}{subsection.1.2.3}\protected@file@percent }
\BKM@entry{id=14,open,dest={73756273656374696F6E2E312E322E34},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.4}Normal Force, Tension, and Constrained Motion}{24}{subsection.1.2.4}\protected@file@percent }
\BKM@entry{id=15,open,dest={73756273656374696F6E2E312E322E35},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030325C3030302E5C303030355C3030305C3034305C303030535C303030745C303030615C303030745C303030695C303030635C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304B5C303030695C3030306E5C303030655C303030745C303030695C303030635C3030305C3034305C303030465C303030725C303030695C303030635C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.5}Static and Kinetic Friction}{27}{subsection.1.2.5}\protected@file@percent }
\BKM@entry{id=16,open,dest={73756273656374696F6E2E312E322E36},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030325C3030302E5C303030365C3030305C3034305C303030485C3030306F5C3030306F5C3030306B5C303030655C303030275C303030735C3030305C3034305C3030304C5C303030615C303030775C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030535C303030705C303030725C303030695C3030306E5C303030675C3030305C3034305C3030304D5C3030306F5C303030645C303030655C3030306C5C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.6}Hooke's Law and Spring Models}{30}{subsection.1.2.6}\protected@file@percent }
\BKM@entry{id=17,open,dest={73756273656374696F6E2E312E322E37},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030325C3030302E5C303030375C3030305C3034305C303030445C303030725C303030615C303030675C3030305C3034305C303030465C3030306F5C303030725C303030635C303030655C303030735C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030545C303030655C303030725C3030306D5C303030695C3030306E5C303030615C3030306C5C3030305C3034305C303030565C303030655C3030306C5C3030306F5C303030635C303030695C303030745C30303079}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.7}Drag Forces and Terminal Velocity}{32}{subsection.1.2.7}\protected@file@percent }
\BKM@entry{id=18,open,dest={73756273656374696F6E2E312E322E38},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030325C3030302E5C303030385C3030305C3034305C303030435C303030695C303030725C303030635C303030755C3030306C5C303030615C303030725C3030305C3034305C3030304D5C3030306F5C303030745C303030695C3030306F5C3030306E5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304F5C303030725C303030625C303030695C303030745C303030615C3030306C5C3030305C3034305C303030445C303030795C3030306E5C303030615C3030306D5C303030695C303030635C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2.8}Circular Motion and Orbital Dynamics}{35}{subsection.1.2.8}\protected@file@percent }
\BKM@entry{id=19,open,dest={73656374696F6E2E312E33},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030335C3030305C3034305C303030575C3030306F5C303030725C3030306B5C3030302C5C3030305C3034305C303030455C3030306E5C303030655C303030725C303030675C303030795C3030302C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030505C3030306F5C303030775C303030655C30303072}
\BKM@entry{id=20,open,dest={73756273656374696F6E2E312E332E31},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030335C3030302E5C303030315C3030305C3034305C303030575C3030306F5C303030725C3030306B5C3030305C3034305C303030615C303030735C3030305C3034305C303030615C3030305C3034305C3030304C5C303030695C3030306E5C303030655C3030305C3034305C303030495C3030306E5C303030745C303030655C303030675C303030725C303030615C3030306C}
\@writefile{toc}{\contentsline {section}{\numberline {1.3}Work, Energy, and Power}{38}{section.1.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.1}Work as a Line Integral}{38}{subsection.1.3.1}\protected@file@percent }
\BKM@entry{id=21,open,dest={73756273656374696F6E2E312E332E32},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.2}Kinetic Energy and the Work-Energy Theorem}{40}{subsection.1.3.2}\protected@file@percent }
\BKM@entry{id=22,open,dest={73756273656374696F6E2E312E332E33},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.3}Conservative Forces and Potential Energy}{42}{subsection.1.3.3}\protected@file@percent }
\BKM@entry{id=23,open,dest={73756273656374696F6E2E312E332E34},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030335C3030302E5C303030345C3030305C3034305C3030304D5C303030655C303030635C303030685C303030615C3030306E5C303030695C303030635C303030615C3030306C5C3030305C3034305C303030455C3030306E5C303030655C303030725C303030675C303030795C3030305C3034305C303030435C3030306F5C3030306E5C303030735C303030655C303030725C303030765C303030615C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.4}Mechanical Energy Conservation}{44}{subsection.1.3.4}\protected@file@percent }
\BKM@entry{id=24,open,dest={73756273656374696F6E2E312E332E35},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030335C3030302E5C303030355C3030305C3034305C303030505C3030306F5C303030775C303030655C303030725C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030495C3030306E5C303030735C303030745C303030615C3030306E5C303030745C303030615C3030306E5C303030655C3030306F5C303030755C303030735C3030305C3034305C303030505C3030306F5C303030775C303030655C30303072}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3.5}Power and Instantaneous Power}{46}{subsection.1.3.5}\protected@file@percent }
\BKM@entry{id=25,open,dest={73656374696F6E2E312E34},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030345C3030305C3034305C3030304C5C303030695C3030306E5C303030655C303030615C303030725C3030305C3034305C3030304D5C3030306F5C3030306D5C303030655C3030306E5C303030745C303030755C3030306D5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030435C3030306F5C3030306C5C3030306C5C303030695C303030735C303030695C3030306F5C3030306E5C30303073}
\BKM@entry{id=26,open,dest={73756273656374696F6E2E312E342E31},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030345C3030302E5C303030315C3030305C3034305C3030304C5C303030695C3030306E5C303030655C303030615C303030725C3030305C3034305C3030304D5C3030306F5C3030306D5C303030655C3030306E5C303030745C303030755C3030306D}
\@writefile{toc}{\contentsline {section}{\numberline {1.4}Linear Momentum and Collisions}{49}{section.1.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.1}Linear Momentum}{49}{subsection.1.4.1}\protected@file@percent }
\BKM@entry{id=27,open,dest={73756273656374696F6E2E312E342E32},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030345C3030302E5C303030325C3030305C3034305C303030495C3030306D5C303030705C303030755C3030306C5C303030735C303030655C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304D5C3030306F5C3030306D5C303030655C3030306E5C303030745C303030755C3030306D5C3030305C3034305C303030545C303030725C303030615C3030306E5C303030735C303030665C303030655C30303072}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.2}Impulse and Momentum Transfer}{52}{subsection.1.4.2}\protected@file@percent }
\BKM@entry{id=28,open,dest={73756273656374696F6E2E312E342E33},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030345C3030302E5C303030335C3030305C3034305C303030435C3030306F5C3030306E5C303030735C303030655C303030725C303030765C303030615C303030745C303030695C3030306F5C3030306E5C3030305C3034305C3030306F5C303030665C3030305C3034305C3030304D5C3030306F5C3030306D5C303030655C3030306E5C303030745C303030755C3030306D5C3030305C3034305C303030665C3030306F5C303030725C3030305C3034305C303030535C303030795C303030735C303030745C303030655C3030306D5C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.3}Conservation of Momentum for Systems}{54}{subsection.1.4.3}\protected@file@percent }
\BKM@entry{id=29,open,dest={73756273656374696F6E2E312E342E34},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.4}Elastic, Inelastic, and Perfectly Inelastic Collisions}{57}{subsection.1.4.4}\protected@file@percent }
\BKM@entry{id=30,open,dest={73756273656374696F6E2E312E342E35},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.4.5}Recoil, Explosions, and the Center-of-Mass Viewpoint}{59}{subsection.1.4.5}\protected@file@percent }
\BKM@entry{id=31,open,dest={73656374696F6E2E312E35},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030355C3030305C3034305C303030545C3030306F5C303030725C303030715C303030755C303030655C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030525C3030306F5C303030745C303030615C303030745C303030695C3030306F5C3030306E5C303030615C3030306C5C3030305C3034305C303030445C303030795C3030306E5C303030615C3030306D5C303030695C303030635C30303073}
\BKM@entry{id=32,open,dest={73756273656374696F6E2E312E352E31},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030355C3030302E5C303030315C3030305C3034305C303030415C3030306E5C303030675C303030755C3030306C5C303030615C303030725C3030305C3034305C303030505C3030306F5C303030735C303030695C303030745C303030695C3030306F5C3030306E5C3030302C5C3030305C3034305C303030565C303030655C3030306C5C3030306F5C303030635C303030695C303030745C303030795C3030302C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030415C303030635C303030635C303030655C3030306C5C303030655C303030725C303030615C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {section}{\numberline {1.5}Torque and Rotational Dynamics}{63}{section.1.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.1}Angular Position, Velocity, and Acceleration}{63}{subsection.1.5.1}\protected@file@percent }
\BKM@entry{id=33,open,dest={73756273656374696F6E2E312E352E32},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.2}Linear and Rotational Kinematic Correspondence}{66}{subsection.1.5.2}\protected@file@percent }
\BKM@entry{id=34,open,dest={73756273656374696F6E2E312E352E33},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030355C3030302E5C303030335C3030305C3034305C303030545C3030306F5C303030725C303030715C303030755C303030655C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304C5C303030655C303030765C303030655C303030725C3030305C3034305C303030415C303030725C3030306D}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.3}Torque and Lever Arm}{68}{subsection.1.5.3}\protected@file@percent }
\BKM@entry{id=35,open,dest={73756273656374696F6E2E312E352E34},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.4}Moment of Inertia and Mass Distribution}{70}{subsection.1.5.4}\protected@file@percent }
\BKM@entry{id=36,open,dest={73756273656374696F6E2E312E352E35},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030355C3030302E5C303030355C3030305C3034305C303030525C3030306F5C303030745C303030615C303030745C303030695C3030306F5C3030306E5C303030615C3030306C5C3030305C3034305C303030455C303030715C303030755C303030695C3030306C5C303030695C303030625C303030725C303030695C303030755C3030306D}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.5}Rotational Equilibrium}{72}{subsection.1.5.5}\protected@file@percent }
\BKM@entry{id=37,open,dest={73756273656374696F6E2E312E352E36},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030355C3030302E5C303030365C3030305C3034305C3030304E5C303030655C303030775C303030745C3030306F5C3030306E5C303030275C303030735C3030305C3034305C303030535C303030655C303030635C3030306F5C3030306E5C303030645C3030305C3034305C3030304C5C303030615C303030775C3030305C3034305C303030665C3030306F5C303030725C3030305C3034305C303030525C3030306F5C303030745C303030615C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.5.6}Newton's Second Law for Rotation}{75}{subsection.1.5.6}\protected@file@percent }
\BKM@entry{id=38,open,dest={73656374696F6E2E312E36},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030365C3030305C3034305C303030415C3030306E5C303030675C303030755C3030306C5C303030615C303030725C3030305C3034305C3030304D5C3030306F5C3030306D5C303030655C3030306E5C303030745C303030755C3030306D5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030525C3030306F5C3030306C5C3030306C5C303030695C3030306E5C303030675C3030305C3034305C3030304D5C3030306F5C303030745C303030695C3030306F5C3030306E}
\BKM@entry{id=39,open,dest={73756273656374696F6E2E312E362E31},srcline={1}}{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}
\@writefile{toc}{\contentsline {section}{\numberline {1.6}Angular Momentum and Rolling Motion}{77}{section.1.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6.1}Rotational Kinetic Energy and Work by Torque}{77}{subsection.1.6.1}\protected@file@percent }
\BKM@entry{id=40,open,dest={73756273656374696F6E2E312E362E32},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030365C3030302E5C303030325C3030305C3034305C303030415C3030306E5C303030675C303030755C3030306C5C303030615C303030725C3030305C3034305C3030304D5C3030306F5C3030306D5C303030655C3030306E5C303030745C303030755C3030306D5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030415C3030306E5C303030675C303030755C3030306C5C303030615C303030725C3030305C3034305C303030495C3030306D5C303030705C303030755C3030306C5C303030735C30303065}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6.2}Angular Momentum and Angular Impulse}{80}{subsection.1.6.2}\protected@file@percent }
\BKM@entry{id=41,open,dest={73756273656374696F6E2E312E362E33},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030365C3030302E5C303030335C3030305C3034305C303030435C3030306F5C3030306E5C303030735C303030655C303030725C303030765C303030615C303030745C303030695C3030306F5C3030306E5C3030305C3034305C3030306F5C303030665C3030305C3034305C303030415C3030306E5C303030675C303030755C3030306C5C303030615C303030725C3030305C3034305C3030304D5C3030306F5C3030306D5C303030655C3030306E5C303030745C303030755C3030306D}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6.3}Conservation of Angular Momentum}{82}{subsection.1.6.3}\protected@file@percent }
\BKM@entry{id=42,open,dest={73756273656374696F6E2E312E362E34},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030365C3030302E5C303030345C3030305C3034305C303030525C3030306F5C3030306C5C3030306C5C303030695C3030306E5C303030675C3030305C3034305C303030575C303030695C303030745C303030685C3030306F5C303030755C303030745C3030305C3034305C303030535C3030306C5C303030695C303030705C303030705C303030695C3030306E5C30303067}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6.4}Rolling Without Slipping}{85}{subsection.1.6.4}\protected@file@percent }
\BKM@entry{id=43,open,dest={73756273656374696F6E2E312E362E35},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.6.5}Circular Orbits, Satellite Speed, and Orbital Energy}{87}{subsection.1.6.5}\protected@file@percent }
\BKM@entry{id=44,open,dest={73656374696F6E2E312E37},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030375C3030305C3034305C3030304F5C303030735C303030635C303030695C3030306C5C3030306C5C303030615C303030745C303030695C3030306F5C3030306E5C30303073}
\BKM@entry{id=45,open,dest={73756273656374696F6E2E312E372E31},srcline={1}}{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}
\@writefile{toc}{\contentsline {section}{\numberline {1.7}Oscillations}{90}{section.1.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.7.1}Simple Harmonic Motion and Its Governing ODE}{90}{subsection.1.7.1}\protected@file@percent }
\BKM@entry{id=46,open,dest={73756273656374696F6E2E312E372E32},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030375C3030302E5C303030325C3030305C3034305C303030545C303030685C303030655C3030305C3034305C303030535C303030705C303030725C303030695C3030306E5C303030675C3030302D5C3030304D5C303030615C303030735C303030735C3030305C3034305C3030304F5C303030735C303030635C303030695C3030306C5C3030306C5C303030615C303030745C3030306F5C30303072}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.7.2}The Spring-Mass Oscillator}{93}{subsection.1.7.2}\protected@file@percent }
\BKM@entry{id=47,open,dest={73756273656374696F6E2E312E372E33},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030375C3030302E5C303030335C3030305C3034305C303030455C3030306E5C303030655C303030725C303030675C303030795C3030305C3034305C303030695C3030306E5C3030305C3034305C303030535C303030695C3030306D5C303030705C3030306C5C303030655C3030305C3034305C303030485C303030615C303030725C3030306D5C3030306F5C3030306E5C303030695C303030635C3030305C3034305C3030304D5C3030306F5C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.7.3}Energy in Simple Harmonic Motion}{96}{subsection.1.7.3}\protected@file@percent }
\BKM@entry{id=48,open,dest={73756273656374696F6E2E312E372E34},srcline={1}}{5C3337365C3337375C303030315C3030302E5C303030375C3030302E5C303030345C3030305C3034305C303030545C303030685C303030655C3030305C3034305C303030535C303030695C3030306D5C303030705C3030306C5C303030655C3030305C3034305C303030505C303030655C3030306E5C303030645C303030755C3030306C5C303030755C3030306D}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.7.4}The Simple Pendulum}{98}{subsection.1.7.4}\protected@file@percent }
\BKM@entry{id=49,open,dest={73756273656374696F6E2E312E372E35},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.7.5}Physical Pendulum and Small-Angle Linearization}{100}{subsection.1.7.5}\protected@file@percent }
\BKM@entry{id=50,open,dest={706172742E32},srcline={20}}{5C3337365C3337375C303030495C303030495C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C303030695C303030745C303030795C3030305C3034305C3030305C3034365C3030305C3034305C3030304D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030735C3030306D}
\@writefile{toc}{\contentsline {part}{II\hspace {1em}Electricity \& Magnetism}{104}{part.2}\protected@file@percent }
\BKM@entry{id=51,open,dest={636861707465722E32},srcline={1}}{5C3337365C3337375C303030325C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C303030695C303030745C303030795C3030305C3034305C3030305C3034365C3030305C3034305C3030304D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030735C3030306D}
\BKM@entry{id=52,open,dest={73656374696F6E2E322E31},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030315C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C3030306F5C303030735C303030745C303030615C303030745C303030695C303030635C303030735C3030303A5C3030305C3034305C303030435C303030685C303030615C303030725C303030675C303030655C3030302C5C3030305C3034305C303030465C303030695C303030655C3030306C5C303030645C3030302C5C3030305C3034305C303030465C3030306C5C303030755C30303078}
\BKM@entry{id=53,open,dest={73756273656374696F6E2E322E312E31},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030315C3030302E5C303030315C3030305C3034305C303030435C303030685C303030615C303030725C303030675C303030655C3030305C3034305C303030435C3030306F5C3030306E5C303030735C303030655C303030725C303030765C303030615C303030745C303030695C3030306F5C3030306E5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030435C303030685C303030615C303030725C303030675C303030695C3030306E5C303030675C3030305C3034305C303030505C303030725C3030306F5C303030635C303030655C303030735C303030735C303030655C30303073}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Electricity \& Magnetism}{105}{chapter.2}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{loa}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}Electrostatics: Charge, Field, Flux}{105}{section.2.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}Charge Conservation and Charging Processes}{105}{subsection.2.1.1}\protected@file@percent }
\BKM@entry{id=54,open,dest={73756273656374696F6E2E322E312E32},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030315C3030302E5C303030325C3030305C3034305C303030435C3030306F5C303030755C3030306C5C3030306F5C3030306D5C303030625C303030275C303030735C3030305C3034305C3030304C5C303030615C303030775C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030535C303030755C303030705C303030655C303030725C303030705C3030306F5C303030735C303030695C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.2}Coulomb's Law and Superposition}{107}{subsection.2.1.2}\protected@file@percent }
\BKM@entry{id=55,open,dest={73756273656374696F6E2E322E312E33},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.3}Electric Field as Force per Unit Charge}{110}{subsection.2.1.3}\protected@file@percent }
\BKM@entry{id=56,open,dest={73756273656374696F6E2E322E312E34},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.4}Fields of Continuous Charge Distributions}{112}{subsection.2.1.4}\protected@file@percent }
\BKM@entry{id=57,open,dest={73756273656374696F6E2E322E312E35},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030315C3030302E5C303030355C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C3030305C3034305C303030465C3030306C5C303030755C30303078}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.5}Electric Flux}{115}{subsection.2.1.5}\protected@file@percent }
\BKM@entry{id=58,open,dest={73756273656374696F6E2E322E312E36},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030315C3030302E5C303030365C3030305C3034305C303030475C303030615C303030755C303030735C303030735C303030275C303030735C3030305C3034305C3030304C5C303030615C303030775C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030535C303030795C3030306D5C3030306D5C303030655C303030745C303030725C303030795C3030305C3034305C303030525C303030655C303030645C303030755C303030635C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.6}Gauss's Law and Symmetry Reduction}{117}{subsection.2.1.6}\protected@file@percent }
\BKM@entry{id=59,open,dest={73656374696F6E2E322E32},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030325C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C3030305C3034305C303030505C3030306F5C303030745C303030655C3030306E5C303030745C303030695C303030615C3030306C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030455C3030306E5C303030655C303030725C303030675C30303079}
\BKM@entry{id=60,open,dest={73756273656374696F6E2E322E322E31},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030325C3030302E5C303030315C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C3030305C3034305C303030505C3030306F5C303030745C303030655C3030306E5C303030745C303030695C303030615C3030306C5C3030305C3034305C303030455C3030306E5C303030655C303030725C303030675C30303079}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}Electric Potential and Energy}{119}{section.2.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}Electric Potential Energy}{119}{subsection.2.2.1}\protected@file@percent }
\BKM@entry{id=61,open,dest={73756273656374696F6E2E322E322E32},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030325C3030302E5C303030325C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C3030305C3034305C303030505C3030306F5C303030745C303030655C3030306E5C303030745C303030695C303030615C3030306C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030565C3030306F5C3030306C5C303030745C303030615C303030675C30303065}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}Electric Potential and Voltage}{121}{subsection.2.2.2}\protected@file@percent }
\BKM@entry{id=62,open,dest={73756273656374696F6E2E322E322E33},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030325C3030302E5C303030335C3030305C3034305C303030545C303030685C303030655C3030305C3034305C303030465C303030695C303030655C3030306C5C303030645C3030302D5C303030505C3030306F5C303030745C303030655C3030306E5C303030745C303030695C303030615C3030306C5C3030305C3034305C303030525C303030655C3030306C5C303030615C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}The Field-Potential Relation}{124}{subsection.2.2.3}\protected@file@percent }
\BKM@entry{id=63,open,dest={73756273656374696F6E2E322E322E34},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.4}Equipotentials and Energy Conservation for Moving Charges}{126}{subsection.2.2.4}\protected@file@percent }
\BKM@entry{id=64,open,dest={73656374696F6E2E322E33},srcline={1}}{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}
\BKM@entry{id=65,open,dest={73756273656374696F6E2E322E332E31},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030335C3030302E5C303030315C3030305C3034305C303030435C3030306F5C3030306E5C303030645C303030755C303030635C303030745C3030306F5C303030725C303030735C3030305C3034305C303030695C3030306E5C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C3030306F5C303030735C303030745C303030615C303030745C303030695C303030635C3030305C3034305C303030455C303030715C303030755C303030695C3030306C5C303030695C303030625C303030725C303030695C303030755C3030306D}
\@writefile{toc}{\contentsline {section}{\numberline {2.3}Capacitance, Dielectrics, and Energy Storage}{129}{section.2.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}Conductors in Electrostatic Equilibrium}{129}{subsection.2.3.1}\protected@file@percent }
\BKM@entry{id=66,open,dest={73756273656374696F6E2E322E332E32},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}Charge Redistribution, Contact, Induction, and Grounding}{131}{subsection.2.3.2}\protected@file@percent }
\BKM@entry{id=67,open,dest={73756273656374696F6E2E322E332E33},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030335C3030302E5C303030335C3030305C3034305C303030435C303030615C303030705C303030615C303030635C303030695C303030745C303030615C3030306E5C303030635C303030655C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030435C303030615C303030705C303030615C303030635C303030695C303030745C3030306F5C303030725C3030305C3034305C303030475C303030655C3030306F5C3030306D5C303030655C303030745C303030725C303030695C303030655C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.3}Capacitance and Capacitor Geometries}{133}{subsection.2.3.3}\protected@file@percent }
\BKM@entry{id=68,open,dest={73756273656374696F6E2E322E332E34},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030335C3030302E5C303030345C3030305C3034305C303030455C3030306E5C303030655C303030725C303030675C303030795C3030305C3034305C303030535C303030745C3030306F5C303030725C303030655C303030645C3030305C3034305C303030695C3030306E5C3030305C3034305C303030435C303030615C303030705C303030615C303030635C303030695C303030745C3030306F5C303030725C303030735C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030465C303030695C303030655C3030306C5C303030645C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.4}Energy Stored in Capacitors and Fields}{136}{subsection.2.3.4}\protected@file@percent }
\BKM@entry{id=69,open,dest={73756273656374696F6E2E322E332E35},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030335C3030302E5C303030355C3030305C3034305C303030445C303030695C303030655C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C303030735C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030505C3030306F5C3030306C5C303030615C303030725C303030695C3030307A5C303030615C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.5}Dielectrics and Polarization}{139}{subsection.2.3.5}\protected@file@percent }
\BKM@entry{id=70,open,dest={73656374696F6E2E322E34},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030345C3030305C3034305C303030445C303030695C303030725C303030655C303030635C303030745C3030302D5C303030435C303030755C303030725C303030725C303030655C3030306E5C303030745C3030305C3034305C303030435C303030695C303030725C303030635C303030755C303030695C303030745C30303073}
\BKM@entry{id=71,open,dest={73756273656374696F6E2E322E342E31},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030345C3030302E5C303030315C3030305C3034305C303030435C303030755C303030725C303030725C303030655C3030306E5C303030745C3030302C5C3030305C3034305C303030445C303030725C303030695C303030665C303030745C3030305C3034305C303030565C303030655C3030306C5C3030306F5C303030635C303030695C303030745C303030795C3030302C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030435C303030755C303030725C303030725C303030655C3030306E5C303030745C3030305C3034305C303030445C303030655C3030306E5C303030735C303030695C303030745C30303079}
\@writefile{toc}{\contentsline {section}{\numberline {2.4}Direct-Current Circuits}{142}{section.2.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.1}Current, Drift Velocity, and Current Density}{142}{subsection.2.4.1}\protected@file@percent }
\BKM@entry{id=72,open,dest={73756273656374696F6E2E322E342E32},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030345C3030302E5C303030325C3030305C3034305C303030525C303030655C303030735C303030695C303030735C303030745C303030615C3030306E5C303030635C303030655C3030302C5C3030305C3034305C303030525C303030655C303030735C303030695C303030735C303030745C303030695C303030765C303030695C303030745C303030795C3030302C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304F5C303030685C3030306D5C303030275C303030735C3030305C3034305C3030304C5C303030615C30303077}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.2}Resistance, Resistivity, and Ohm's Law}{145}{subsection.2.4.2}\protected@file@percent }
\BKM@entry{id=73,open,dest={73756273656374696F6E2E322E342E33},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030345C3030302E5C303030335C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C303030695C303030635C3030305C3034305C303030505C3030306F5C303030775C303030655C303030725C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030445C303030695C303030735C303030735C303030695C303030705C303030615C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.3}Electric Power and Dissipation}{148}{subsection.2.4.3}\protected@file@percent }
\BKM@entry{id=74,open,dest={73756273656374696F6E2E322E342E34},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.4}Equivalent Resistance of Series and Parallel Circuits}{150}{subsection.2.4.4}\protected@file@percent }
\BKM@entry{id=75,open,dest={73756273656374696F6E2E322E342E35},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030345C3030302E5C303030355C3030305C3034305C3030304B5C303030695C303030725C303030635C303030685C303030685C3030306F5C303030665C303030665C303030275C303030735C3030305C3034305C3030304A5C303030755C3030306E5C303030635C303030745C303030695C3030306F5C3030306E5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304C5C3030306F5C3030306F5C303030705C3030305C3034305C303030525C303030755C3030306C5C303030655C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.5}Kirchhoff's Junction and Loop Rules}{153}{subsection.2.4.5}\protected@file@percent }
\newlabel{eq:loop1}{{2.4.5}{156}{Kirchhoff's Junction and Loop Rules}{Item.200}{}}
\newlabel{eq:loop2}{{2.4.5}{156}{Kirchhoff's Junction and Loop Rules}{Item.200}{}}
\BKM@entry{id=76,open,dest={73756273656374696F6E2E322E342E36},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030345C3030302E5C303030365C3030305C3034305C303030525C303030435C3030305C3034305C303030545C303030725C303030615C3030306E5C303030735C303030695C303030655C3030306E5C303030745C303030735C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030745C303030685C303030655C3030305C3034305C303030545C303030695C3030306D5C303030655C3030305C3034305C303030435C3030306F5C3030306E5C303030735C303030745C303030615C3030306E5C30303074}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.6}RC Transients and the Time Constant}{158}{subsection.2.4.6}\protected@file@percent }
\BKM@entry{id=77,open,dest={73756273656374696F6E2E322E342E37},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4.7}Internal Resistance and Measurement Devices}{163}{subsection.2.4.7}\protected@file@percent }
\BKM@entry{id=78,open,dest={73656374696F6E2E322E35},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030355C3030305C3034305C3030304D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030735C3030306D5C3030303A5C3030305C3034305C303030465C3030306F5C303030725C303030635C303030655C303030735C3030302C5C3030305C3034305C303030465C303030695C303030655C3030306C5C303030645C303030735C3030302C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030535C3030306F5C303030755C303030725C303030635C303030655C30303073}
\BKM@entry{id=79,open,dest={73756273656374696F6E2E322E352E31},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030355C3030302E5C303030315C3030305C3034305C3030304D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030635C3030305C3034305C303030465C3030306F5C303030725C303030635C303030655C3030305C3034305C3030306F5C3030306E5C3030305C3034305C303030615C3030305C3034305C3030304D5C3030306F5C303030765C303030695C3030306E5C303030675C3030305C3034305C303030435C303030685C303030615C303030725C303030675C30303065}
\@writefile{toc}{\contentsline {section}{\numberline {2.5}Magnetism: Forces, Fields, and Sources}{166}{section.2.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.1}Magnetic Force on a Moving Charge}{167}{subsection.2.5.1}\protected@file@percent }
\BKM@entry{id=80,open,dest={73756273656374696F6E2E322E352E32},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.2}Circular and Helical Motion in a Uniform Magnetic Field}{169}{subsection.2.5.2}\protected@file@percent }
\BKM@entry{id=81,open,dest={73756273656374696F6E2E322E352E33},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.3}Force on Current-Carrying Conductors and Loops}{174}{subsection.2.5.3}\protected@file@percent }
\BKM@entry{id=82,open,dest={73756273656374696F6E2E322E352E34},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030355C3030302E5C303030345C3030305C3034305C303030545C303030685C303030655C3030305C3034305C303030425C303030695C3030306F5C303030745C3034305C3032335C303030535C303030615C303030765C303030615C303030725C303030745C3030305C3034305C3030304C5C303030615C30303077}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.4}The Biot--Savart Law}{178}{subsection.2.5.4}\protected@file@percent }
\BKM@entry{id=83,open,dest={73756273656374696F6E2E322E352E35},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030355C3030302E5C303030355C3030305C3034305C303030415C3030306D5C303030705C3030305C3335305C303030725C303030655C303030275C303030735C3030305C3034305C3030304C5C303030615C303030775C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030535C303030795C3030306D5C3030306D5C303030655C303030745C303030725C303030795C3030305C3034305C303030525C303030655C303030645C303030755C303030635C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.5}Amp\`ere's Law and Symmetry Reduction}{183}{subsection.2.5.5}\protected@file@percent }
\BKM@entry{id=84,open,dest={73756273656374696F6E2E322E352E36},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030355C3030302E5C303030365C3030305C3034305C303030535C3030306F5C3030306C5C303030655C3030306E5C3030306F5C303030695C303030645C303030735C3030302C5C3030305C3034305C303030505C303030615C303030725C303030615C3030306C5C3030306C5C303030655C3030306C5C3030305C3034305C303030435C303030755C303030725C303030725C303030655C3030306E5C303030745C303030735C3030302C5C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030635C3030305C3034305C303030445C303030695C303030705C3030306F5C3030306C5C303030655C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5.6}Solenoids, Parallel Currents, and Magnetic Dipoles}{186}{subsection.2.5.6}\protected@file@percent }
\BKM@entry{id=85,open,dest={73656374696F6E2E322E36},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030365C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C3030306F5C3030306D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030635C3030305C3034305C303030495C3030306E5C303030645C303030755C303030635C303030745C303030695C3030306F5C3030306E}
\BKM@entry{id=86,open,dest={73756273656374696F6E2E322E362E31},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030365C3030302E5C303030315C3030305C3034305C3030304D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030635C3030305C3034305C303030465C3030306C5C303030755C30303078}
\@writefile{toc}{\contentsline {section}{\numberline {2.6}Electromagnetic Induction}{190}{section.2.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.1}Magnetic Flux}{190}{subsection.2.6.1}\protected@file@percent }
\BKM@entry{id=87,open,dest={73756273656374696F6E2E322E362E32},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030365C3030302E5C303030325C3030305C3034305C303030465C303030615C303030725C303030615C303030645C303030615C303030795C303030275C303030735C3030305C3034305C3030304C5C303030615C303030775C3030305C3034305C3030306F5C303030665C3030305C3034305C303030495C3030306E5C303030645C303030755C303030635C303030745C303030695C3030306F5C3030306E}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.2}Faraday's Law of Induction}{193}{subsection.2.6.2}\protected@file@percent }
\BKM@entry{id=88,open,dest={73756273656374696F6E2E322E362E33},srcline={1}}{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}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.3}Lenz's Law and Induced Current Direction}{197}{subsection.2.6.3}\protected@file@percent }
\BKM@entry{id=89,open,dest={73756273656374696F6E2E322E362E34},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030365C3030302E5C303030345C3030305C3034305C3030304D5C3030306F5C303030745C303030695C3030306F5C3030306E5C303030615C3030306C5C3030305C3034305C303030455C3030306C5C303030655C303030635C303030745C303030725C3030306F5C3030306D5C3030306F5C303030745C303030695C303030765C303030655C3030305C3034305C303030465C3030306F5C303030725C303030635C30303065}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.4}Motional Electromotive Force}{198}{subsection.2.6.4}\protected@file@percent }
\BKM@entry{id=90,open,dest={73756273656374696F6E2E322E362E35},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030365C3030302E5C303030355C3030305C3034305C303030495C3030306E5C303030645C303030755C303030635C303030745C303030615C3030306E5C303030635C303030655C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C3030304D5C303030615C303030675C3030306E5C303030655C303030745C303030695C303030635C3030305C3034305C303030455C3030306E5C303030655C303030725C303030675C303030795C3030305C3034305C303030535C303030745C3030306F5C303030725C303030615C303030675C30303065}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.5}Inductance and Magnetic Energy Storage}{203}{subsection.2.6.5}\protected@file@percent }
\BKM@entry{id=91,open,dest={73756273656374696F6E2E322E362E36},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030365C3030302E5C303030365C3030305C3034305C3030304C5C303030525C3030305C3034305C303030435C303030695C303030725C303030635C303030755C303030695C303030745C303030735C3030305C3034305C303030615C3030306E5C303030645C3030305C3034305C303030545C303030725C303030615C3030306E5C303030735C303030695C303030655C3030306E5C303030745C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.6}LR Circuits and Transients}{207}{subsection.2.6.6}\protected@file@percent }
\BKM@entry{id=92,open,dest={73756273656374696F6E2E322E362E37},srcline={1}}{5C3337365C3337375C303030325C3030302E5C303030365C3030302E5C303030375C3030305C3034305C3030304C5C303030435C3030305C3034305C3030304F5C303030735C303030635C303030695C3030306C5C3030306C5C303030615C303030745C303030695C3030306F5C3030306E5C30303073}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.6.7}LC Oscillations}{211}{subsection.2.6.7}\protected@file@percent }
\ttl@finishall
\gdef \@abspage@last{216}

2
concepts/em/u11/e11-3-power.tex
View File

@@ -12,7 +12,7 @@ The SI unit of power is the watt ($1\,\mathrm{W}=1\,\mathrm{J/s}=1\,\mathrm{A\!\
\ex{Illustrative example}{A $60\,\mathrm{W}$ incandescent lightbulb is connected to a $120\,\mathrm{V}$ household outlet. Find (a) the current through the bulb and (b) the resistance of its filament. \ex{Illustrative example}{A $60\,\mathrm{W}$ incandescent lightbulb is connected to a $120\,\mathrm{V}$ household outlet. Find (a) the current through the bulb and (b) the resistance of its filament.
\sol (a) From $P = I\,\Delta V$, (a) From $P = I\,\Delta V$,
\[ \[
I = \frac{P}{\Delta V} = \frac{60\,\mathrm{W}}{120\,\mathrm{V}} = 0.50\,\mathrm{A}. I = \frac{P}{\Delta V} = \frac{60\,\mathrm{W}}{120\,\mathrm{V}} = 0.50\,\mathrm{A}.
\] \]

6
concepts/em/u11/e11-5-kirchhoff.tex
View File

@@ -138,7 +138,6 @@ Substitute equation (1) into equation (2):
\[ \[
7.0\,I_1 + 3.0\,I_2 = 12. 7.0\,I_1 + 3.0\,I_2 = 12.
\] \]
\label{eq:a}
Substitute equation (1) into equation (3): Substitute equation (1) into equation (3):
\[ \[
@@ -158,9 +157,8 @@ so
\[ \[
I_1 = 2.0 - 3.0\,I_2. I_1 = 2.0 - 3.0\,I_2.
\] \]
\label{eq:b}
Substitute equation (\ref{eq:b}) into equation (\ref{eq:a}): Substitute equation (3) into equation (2):
\[ \[
7.0\,(2.0 - 3.0\,I_2) + 3.0\,I_2 = 12, 7.0\,(2.0 - 3.0\,I_2) + 3.0\,I_2 = 12,
\] \]
@@ -177,7 +175,7 @@ Substitute equation (\ref{eq:b}) into equation (\ref{eq:a}):
I_2 = \frac{2.0}{18.0} = \frac{1}{9}\,\mathrm{A}. I_2 = \frac{2.0}{18.0} = \frac{1}{9}\,\mathrm{A}.
\] \]
From equation (\ref{eq:b}): From equation (3):
\[ \[
I_1 = 2.0 - 3.0\left(\frac{1}{9}\right) = 2.0 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3}\,\mathrm{A}. I_1 = 2.0 - 3.0\left(\frac{1}{9}\right) = 2.0 - \frac{1}{3} = \frac{6}{3} - \frac{1}{3} = \frac{5}{3}\,\mathrm{A}.
\] \]

5
concepts/em/u12/e12-3-force-on-current.tex
View File

@@ -111,9 +111,10 @@ U = -\mu B\,\cos\phi = -\vec{\mu}\cdot\vec{B}.
\nt{The SI unit of magnetic dipole moment $\vec{\mu}$ is ampere-square meter, $\mathrm{A\cdot m^2}$. This is equivalent to joules per tesla, $\mathrm{J/T}$.} \nt{The SI unit of magnetic dipole moment $\vec{\mu}$ is ampere-square meter, $\mathrm{A\cdot m^2}$. This is equivalent to joules per tesla, $\mathrm{J/T}$.}
\ex{Illustrative example}{A coil with $N=50$ turns, each of area $A = 8.0\,\mathrm{cm^2} = 8.0\times 10^{-4}\,\mathrm{m^2}$, carries current $I = 2.0\,\mathrm{A}$ in a field $B = 0.40\,\mathrm{T}$. The maximum torque occurs at $\phi = 90^\circ$: \ex{Illustrative example}{A coil with $N=50$ turns, each of area $A = 8.0\,\mathrm{cm^2} = 8.0\times 10^{-4}\,\mathrm{m^2}$, carries current $I = 2.0\,\mathrm{A}$ in a field $B = 0.40\,\mathrm{T}$. The maximum torque occurs at $\phi = 90^\circ$:}
\[ \[
\tau_{\text{max}} = N\,I\,A\,B = (50)(2.0\,\mathrm{A})(8.0\times 10^{-4}\,\mathrm{m^2})(0.40\,\mathrm{T}) = 3.2\times 10^{-2}\,\mathrm{N\cdot m}.} \tau_{\text{max}} = N\,I\,A\,B = (50)(2.0\,\mathrm{A})(8.0\times 10^{-4}\,\mathrm{m^2})(0.40\,\mathrm{T}) = 3.2\times 10^{-2}\,\mathrm{N\cdot m}.
\]
\qs{Worked example}{A rectangular wire loop has width $a=0.10\,\mathrm{m}$ (horizontal side) and height $b=0.050\,\mathrm{m}$ (vertical side). The loop has $N=100$ turns and carries current $I=2.0\,\mathrm{A}$ in the direction shown: clockwise when viewed from the front (from the $+x$-axis toward the $yz$-plane). The loop sits in a uniform magnetic field $\vec{B} = (0.60\,\mathrm{T})\,\hat{\imath}$ pointing to the right. The normal vector $\hat{n}$ points along the $-\hat{k}$ direction (into the page) by the right-hand rule for clockwise current. \qs{Worked example}{A rectangular wire loop has width $a=0.10\,\mathrm{m}$ (horizontal side) and height $b=0.050\,\mathrm{m}$ (vertical side). The loop has $N=100$ turns and carries current $I=2.0\,\mathrm{A}$ in the direction shown: clockwise when viewed from the front (from the $+x$-axis toward the $yz$-plane). The loop sits in a uniform magnetic field $\vec{B} = (0.60\,\mathrm{T})\,\hat{\imath}$ pointing to the right. The normal vector $\hat{n}$ points along the $-\hat{k}$ direction (into the page) by the right-hand rule for clockwise current.

43
concepts/mechanics/u6/m6-4-rolling.tex
View File

@@ -32,48 +32,13 @@ Thus the wheel's center moves at $2.4\,\mathrm{m/s}$, while the top point moves
\mprop{Rolling kinematics, energy, and incline dynamics}{Consider a rigid body of mass $M$, radius $R$, and moment of inertia $I_{\mathrm{cm}}$ about its center of mass. Let $s_{\mathrm{cm}}$, $v_{\mathrm{cm}}$, and $a_{t,\mathrm{cm}}$ denote the center-of-mass distance, speed, and tangential acceleration, and let $\theta$, $\omega$, and $\alpha$ denote the corresponding angular variables. Let $K_i$ and $U_i$ denote the initial kinetic and potential energies, and let $K_f$ and $U_f$ denote the final kinetic and potential energies. \mprop{Rolling kinematics, energy, and incline dynamics}{Consider a rigid body of mass $M$, radius $R$, and moment of inertia $I_{\mathrm{cm}}$ about its center of mass. Let $s_{\mathrm{cm}}$, $v_{\mathrm{cm}}$, and $a_{t,\mathrm{cm}}$ denote the center-of-mass distance, speed, and tangential acceleration, and let $\theta$, $\omega$, and $\alpha$ denote the corresponding angular variables. Let $K_i$ and $U_i$ denote the initial kinetic and potential energies, and let $K_f$ and $U_f$ denote the final kinetic and potential energies.
\begin{enumerate}[label=\textbf{\arabic*.}] 1. For pure rolling, $s_{\mathrm{cm}}=R\theta$, $v_{\mathrm{cm}}=R\omega$, $a_{t,\mathrm{cm}}=R\alpha$.
\item For pure rolling,
\[
s_{\mathrm{cm}}=R\theta,
\qquad
v_{\mathrm{cm}}=R\omega,
\qquad
a_{t,\mathrm{cm}}=R\alpha.
\]
\item The total kinetic energy is the sum of translational and rotational parts: 2. The total kinetic energy is the sum of translational and rotational parts: $K=\tfrac12 Mv_{\mathrm{cm}}^2+\tfrac12 I_{\mathrm{cm}}\omega^2$. Using $v_{\mathrm{cm}}=R\omega$, this may also be written as $K=\tfrac12\left(M+\frac{I_{\mathrm{cm}}}{R^2}\right)v_{\mathrm{cm}}^2$.
\[
K=\tfrac12 Mv_{\mathrm{cm}}^2+\tfrac12 I_{\mathrm{cm}}\omega^2.
\]
Using $v_{\mathrm{cm}}=R\omega$, this may also be written as
\[
K=\tfrac12\left(M+\frac{I_{\mathrm{cm}}}{R^2}\right)v_{\mathrm{cm}}^2.
\]
\item If no nonconservative force removes mechanical energy from the system, then for rolling without slipping, 3. If no nonconservative force removes mechanical energy from the system, then for rolling without slipping, $K_i+U_i=K_f+U_f$. For a vertical drop of magnitude $h$ from rest, $Mgh=\tfrac12 Mv_{\mathrm{cm}}^2+\tfrac12 I_{\mathrm{cm}}\omega^2$.
\[
K_i+U_i=K_f+U_f.
\]
For a vertical drop of magnitude $h$ from rest,
\[
Mgh=\tfrac12 Mv_{\mathrm{cm}}^2+\tfrac12 I_{\mathrm{cm}}\omega^2.
\]
\item For a body rolling without slipping down an incline of angle $\beta$, choose positive down the incline. Let $a_{\mathrm{cm}}$ denote the center-of-mass acceleration magnitude along the incline. If $f_s$ denotes the magnitude of the static friction force, then 4. For a body rolling without slipping down an incline of angle $\beta$, choose positive down the incline. Let $a_{\mathrm{cm}}$ denote the center-of-mass acceleration magnitude along the incline. If $f_s$ denotes the magnitude of the static friction force, then $Mg\sin\beta-f_s=Ma_{\mathrm{cm}}$, $f_sR=I_{\mathrm{cm}}\alpha$, $a_{\mathrm{cm}}=R\alpha$. Therefore, $a_{\mathrm{cm}}=\frac{g\sin\beta}{1+I_{\mathrm{cm}}/(MR^2)}$, $f_s=\frac{I_{\mathrm{cm}}}{R^2}a_{\mathrm{cm}}$.
\[
Mg\sin\beta-f_s=Ma_{\mathrm{cm}},
\qquad
f_sR=I_{\mathrm{cm}}\alpha,
\qquad
a_{\mathrm{cm}}=R\alpha.
\]
Therefore,
\[
a_{\mathrm{cm}}=\frac{g\sin\beta}{1+I_{\mathrm{cm}}/(MR^2)},
\qquad
f_s=\frac{I_{\mathrm{cm}}}{R^2}a_{\mathrm{cm}}.
\]
For an object accelerating down the incline, the static friction force on the object points up the incline.} For an object accelerating down the incline, the static friction force on the object points up the incline.}
\qs{Worked example}{A solid cylinder of mass $M=2.0\,\mathrm{kg}$ and radius $R=0.20\,\mathrm{m}$ is released from rest on an incline that makes an angle $\beta=30^\circ$ with the horizontal. The cylinder rolls without slipping through a vertical drop $h=0.75\,\mathrm{m}$. Let $g=9.8\,\mathrm{m/s^2}$. \qs{Worked example}{A solid cylinder of mass $M=2.0\,\mathrm{kg}$ and radius $R=0.20\,\mathrm{m}$ is released from rest on an incline that makes an angle $\beta=30^\circ$ with the horizontal. The cylinder rolls without slipping through a vertical drop $h=0.75\,\mathrm{m}$. Let $g=9.8\,\mathrm{m/s^2}$.