\documentclass[]{book}
\usepackage{epsfig}

\input{iliheader}



\begin{document}




\noindent {\Large  Names: }
\bigskip
 

\bigskip


\centerline{\bf\LARGE Torque Play}

\bigskip

In this lab we will use torque to explain several very odd phenomena.


\section{Review}
Before we begin the experiments, we need to recall the
key equations.
\begin{enumerate}
\item Write down the definition of torque.
\vskip.3in
\item Write down
the relation between torque and change in angular momentum.
\vskip.3in
\item  How do we denote a vector into the page? out of the page?
\vskip.3in
\end{enumerate}



\section{\bf Turning the Wheel Over}
Spin up the bicycle wheel so that $\vec \omega$ is pointing upward. 
 With your right hand on the top handle and left hand on bottom, turn
the wheel over to your right so that you end up with your right hand on
bottom and your left hand on top. (You would have to flip your hands to
be able to turn it to your left.)

 Describe how it feels as you turn it.
\vfill

Now we will find the most efficient way to turn over
the wheel, using the following steps and our understanding of torque. 
We will focus on just the initial phase of turning over, but the same
ideas apply through the whole turn.
\begin{enumerate}
\item  First, based on the sketches below, sketch $\vec 
L_{1}$ and $\vec L_{2}$.  

\centerline{\psfig{figure=wheel.eps,height=2.5in,width=4in}}
\item  Now sketch $\Delta \vec L \equiv \vec L_{2} -
\vec L_{1}$.
\item What direction must the torque be in to induce such a
change in $\vec L$?  (Drawn it on the sketch.)
\item If you apply a force at the end of the top and bottom handle, what
is the moment arm $\vec r$ in each case?.
\item Given $\vec \tau$ and $\vec r$, what direction must $\vec F$ be
in to give the torque we need?
\vfill
\break
\item Now you need to check your prediction.  Spin up the wheel
as before and exert the forces needed that you found in the last
question.  Describe what you feel.
\vfill
\item  Now spin the wheel in just the opposite way (clockwise
as seen from above) and try to
turn it over with the same force as you did before.  Describe what you
feel.
\vfill
\item Explain, using the notion of torque, what you initially
felt when you tried to turn over the wheel. 
\vfill

\end{enumerate}


\section{\bf Dropping the Wheel}
Loop the string over your wrist, then spin up the
wheel. Let the wheel  fall while holding onto the string.

\begin{enumerate}
\item  Describe what you see.  
\vfill
\item What happens if you spin the wheel the other way and then drop it?
\vfill
\clearpage

\item On the diagram below (which should be a good representation
of what you see), sketch the force of gravity, the moment arm for
gravity, the torque due to gravity.  Hint:  you can recognize the axis
of rotation because it is the still point of the motion.

\centerline{\psfig{figure=sidewheel.eps,height=2in,width=2in}}



\item  On the diagram below, I have sketched $\vec L$ for two closely
spaced times. {\bf We have now switched to a top view}. Sketch the
direction of the torque due to gravity based on your sketch above.

\centerline{\psfig{figure=topwheel.eps,height=2.5in,width=5in}}



\item Is your direction of torque consistent with the direction in the
change in angular momentum?
\vfill
\item What direction would torque have to be in to make the wheel
fall over as it does when it is not rotating (it might help to refer back to
the last experiment where you turned the wheel over).  Can gravity
provide such a torque?  
\vfill


\clearpage
\end{enumerate}
\end{document}

\break
\section{Alien Hat}
Place the alien hat on your head.  Once it is balanced, quickly turn
around 180 degrees, making sure that your partner is able to catch the
hat if it falls.  
\begin{enumerate}
\item  Describe what happens.  
\vfill
\item What external torque could make the hat rotate?  Draw a
sketch of $\vec r$ and $\vec F$.  
\vfill
\item Using your sketch, explain the motion of the "hat".

\vfill

\end{enumerate}


\section {Spools}
How can we make the spool move forward, backward, no net movement?
Don't forget friction.
\vskip2truein

\section {Wrenches}
\begin{enumerate}
\item You have a wrench whose shape can be changed.  Predict
which setup will allow you to loosen the nut with the least amount of
force.  Explain your predictions.
\vskip2truein

\item Now try the various combinations and describe what you feel.

\item Reconcile any differences with your predictions.


\end{enumerate}

\vfill
\end{document}