\section{Bicycle pedals}

%
%
%Fluff.  PGD, January 2006
%
% It is fairly commonly known, at least among bicyclists, that there is
There is
something funny about the way that the pedals of a bicycle screw into
the cranks.  One of the pedals has a normal `right-hand thread', so that
you screw it in clockwise---the usual way---like a normal screw or lightbulb,
and you unscrew it counter-clockwise.  The other pedal has a `left-hand thread',
so that it works exactly backwards:
You screw it in counter-clockwise, and you unscrew it clockwise.

This `asymmetry' between the two pedals---actually it's a surfeit of
symmetry we have here, rather than a dearth---is not
just some whimsical notion on the
part of bike manufacturers.
If the pedals both had normal threads, one of them would fall out before
you got to the end of the block.

%
%Fluff.  PGD, January 2006
%If you're assembling a new bike out of the box,
%the fact that one of the pedals screws in the wrong way may
%cause some momentary confusion,
%but you can easily figure out what to do by looking at the
%threads.
%The real confusion comes when for one reason or another you need to unscrew
%one of your pedals, and you can't remember whether this  pedal is the
%normal one or the screwy one,
%and the pedal is on so tightly that a modest torque in either
%direction fails to budge it.
%You get set to give it a major twist,
%only which way do you turn it?
%You worry that if you to turn
%it the wrong way you'll get it on so tight that you'll never get it off.

If you try to figure out which pedal is the normal one using common sense,
the chances are overwhelming that you will figure it out exactly wrong.
If you remember this, then you're all set:
Just figure it out by common sense, and then go for the opposite answer.
Another good strategy is to remember that `right is right; left is wrong.'

%
%Defluffing.  PGD, January 2006
%
\begin{problems}
\item
Take a screw or a bolt (what's the difference?) or a candy cane,
and sight along it, observing the twist.
Compare this with what you see when you sight along it the other way.
\item
Take two identical bolts or screws or candy canes
(or lightbulbs or barber poles), and place them tip to tip.
Describe how the two spirals meet.
Now take one of them and hold it
perpendicular to a mirror so that its tip appears to touch the tip
of its mirror image.
Describe how the two spirals meet.
\item
Why is a right-hand thread called a `right-hand thread'?
What is the `right-hand rule'?
\item
Use common sense to
figure out which pedal on a bike has the normal, right-hand thread.
Did you come up with the correct answer that
`right is right; left is wrong'?
\item
You can simulate what is going on here by curling your fingers loosely around
the eraser end of a nice long pencil (a long thin stick works even better),
so that there's a little extra room for the pencil to roll around inside your
grip.
%
%Do it yourself!  PGD, January 2006
%
%Get someone else to
Press down gently on the business end of the pencil,
to simulate the weight of the rider's foot on the pedal, and see what happens
when you rotate your arm like the crank of a bicycle.
\item
The best thing is to make a wooden model.  Drill a block through a block of
wood to represent the hole in the crank that the pedal screws into,
and use a dowel just a little smaller in diameter than the hole to represent
the pedal.
%
%Fluff.  PGD, January 2006
%
%\item
%If your pedal is on really, really tight, you might be tempted to
%use a `cheater', which is a pipe that you slip over the end of a wrench
%to increase the effective length of the handle.
%If it takes a force of 150 pounds on the end of a 9-inch long
%adjustable wrench to loosen the pedal, how much force will be required on
%the end of an 18-inch long cheater?
%\item
%Wrench manufacturers, pipe manufacturers, bicycle manufacturers,
%your insurance underwriter, your family doctor, and your geometry teacher
%all maintain that using a cheater
%is a bad idea.  Do you understand why?
%Discuss some of the dangers to which you might expose yourself by using
%a cheater.
%If despite all this well-meaning advice you should
%go ahead and use a cheater, and some harm should come to you, 
%who will be to blame?
\item
Do all candy canes spiral the same way?
What about barber poles?
What other things spiral?
Do they always spiral the same way?
\item
Which way do tornados and hurricanes rotate in the northern hemisphere?
Why?
\item
Which way does water spiral down the drain in the southern hemisphere,
and how do you know?
\item
When you hold something up to an ordinary mirror you
can't quite get it to appear to touch its mirror image.
Why not?
How close can you come?
What if you use a different kind of mirror?
\end{problems}
