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Re: rolling

It is given that the drum moves distance L/2
It is given that the motivating board is L long.
It is NOT given that the board moves distance L/2

The circumferential movement may be made more concrete
by considering a tape fastened to the drum and the board,
and being wound or unwound appropriately.

It would do no harm to consider that the roll axis of the drum
moves half as fast as the board in the same time.

Brian W

At 11:03 AM 2/3/2004, you wrote:
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.


Brian Whatcott Altus OK Eureka!