\relax 
\citation{Frautschi}
\citation{Neher62}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces A spinning toy top.}}{1}}
\newlabel{fig:top}{{1}{1}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces A ``dynamic'' sculpture whose center of mass sits below its support, or pivot point.}}{1}}
\newlabel{fig:tightrope_walker}{{2}{1}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Another example of a dynamic sculpture, this time with a single balance point.}}{2}}
\newlabel{fig:balancing_sculpture}{{3}{2}}
\@writefile{toc}{\contentsline {section}{\numberline {1}Dynamics of a spinning top}{2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Gyroscopic motion}{2}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces The top you will be using in this lab. Its pivot point is a smooth ball inside a cup, floated on an air bearing to reduce friction. The pivot point is located at the center of the ball and is labeled ``O'' in this drawing. Most of the mass of the top is in a heavy, steel ``skirt'' that hangs below the pivot point, but there is a sliding mass that you can raise or lower to move the center of mass above or below the pivot point. Drive jets tap air from the bearing, diverting it out in such a way as to spin the top up and keep it going.}}{3}}
\newlabel{fig:MaxwellTopCartoon1}{{4}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Symmetric top subject to an external force $\mathaccentV {vec}17E{F}$ which produces a torque $\mathaccentV {vec}17E{\tau } = r F \mathaccentV {hat}05E{z}$.}}{4}}
\newlabel{fig:Top1}{{5}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Precession of the top. In this sketch $\mathaccentV {vec}17E{\tau }$ is parallel to the $y$ axis and is pointing to the negative direction of the $y$ axis. The vector $\mathaccentV {vec}17E{h_{CM}}$ is in the plane $Oxz$}}{5}}
\newlabel{fig:TopPrecession}{{6}{5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Quantitative prediction of precession}{6}}
\newlabel{eq:torque}{{1}{6}}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces Projection and variation of the angular momentum in the horizontal plane.}}{6}}
\newlabel{fig:TopPrecessionProjection}{{7}{6}}
\newlabel{eq:Omega}{{2}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Experimental setup}{7}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Safety}{7}}
\@writefile{toc}{\contentsline {section}{\numberline {3}First laboratory week}{8}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}The obvious method: acceleration in response to a known, constant torque}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Direct measurement of the torque applied by the air jets by balancing it out with a hanging weight of known mass.}}{9}}
\newlabel{fig:MaxwellTopConstAcc}{{8}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}The not-so-obvious method: the loaded torsional pendulum}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Unloaded (left) and loaded torsional-pendulum setups for measuring the moment of inertia of the top.}}{12}}
\newlabel{fig:MaxwellTopSuspended}{{9}{12}}
\newlabel{eq:I}{{3}{13}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Second laboratory week}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Dependence on center-of-mass position $h_{CM}$}{14}}
\newlabel{eq:Omega3}{{4}{14}}
\citation{Neher62}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2}Dependence on $\phi $, null experiments}{16}}
\newlabel{eq:string_theory_Omega}{{5}{16}}
\bibcite{Frautschi}{1}
\bibcite{Neher62}{2}