Re: rolling

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

If I may be forgiven for saying so, it seems to me that there has
been considerably more than the usual amount of confusion generated
in this thread.  Justin's question was simple and reasonable and it
seems to me that it has not yet been answered.

He wrote:

> "A woman rolls a cylindrical drum, by means of a board on top,
> through the distance L/2, which is half the board's length.  The
> drum rolls smoothly, and the board does not slide over the drum.
> a)  What length of board has rolled over the top of the drum?
> b)  How far has the woman walked?"
>
> The answers in the book are L and 1.5 L.  I am not sure I understand
> what is meant by "what length of board has rolled over the top of
> the drum."  It seems to me that it should be L/2.  If the questions
> means how far has the board moved with respect to the ground then I
> agree it is L.
>
> Answers in algebraic form (plus verbal explanations) are preferable to
> strictly verbal arguments.

It seems to me that Justin is right to wonder a little about what is
meant by the problem statement, that he nevertheless interprets it in
the most reasonable manner, that he is right, and that the book is
wrong.

If the cylinder rolls a distance L/2 along the ground, then a length
L/2 (not L) of the board has rolled over the top, and the woman
(along with the board) has moved a distance L (not 1.5 L) along the
ground.  Moreover, I'd point out that none of this fundamentally
depends on how long the board is.

--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm