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Re: rolling

I agree, as I stated in my original post, that the board moves a distance L with respect to the ground. The question asks, "What length of board has rolled over the top of the drum?" If the drum moves L/2 and the board L then the board moves L/2 w.r.t. the drum. I am still confused about how the length "rolling over the top of the drum" could be L.

In a message dated 2/3/2004 6:08:16 PM Eastern Standard Time, dcrowe@SOTC.ORG writes:

The board is always in contact with the top of the drum.
If the drum rolls without slipping, then the velocity
of the top of the drum is twice the velocity of the
center of the drum. Therefore, the board moves twice
the distance covered by the center of the drum. Note
that the board is in contact with different points on
the circumference of the drum as the drum rolls.

Daniel Crowe
Oklahoma School of Science and Mathematics
Ardmore Regional Center

-----Original Message-----
=46rom: Justin Parke [mailto:FIZIX29@AOL.COM]
Sent: Tuesday, February 03, 2004 11:03 AM
Subject: rolling

I need some help with the following question from Halliday et al (6th=
ch. 12 question 5:

"A woman rolls a cylindrical drum, by means of a board on top, throug=
h the
distance L/2, which is half the board's length. The drum rolls smoot=
hly, 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 =
moved with respect to the ground then I agree it is L.

Answers in algebraic form (plus verbal explanations) are
preferable t=
strictly verbal arguments.


Justin Parke
Oakland Mills High School
Columbia, MD