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
dcrowe@sotc.org
-----Original Message-----
From: Justin Parke [mailto:FIZIX29@AOL.COM]
Sent: Tuesday, February 03, 2004 11:03 AM
To: PHYS-L@lists.nau.edu
Subject: rolling
I need some help with the following question from Halliday et al (6th ed.),
ch. 12 question 5:
"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.