On 16-Jun-11 14:17:18, Allan Reese (Cefas) wrote:
> Confusion seems to be entirely generated within the exchanges.
> You posed the question:
> On 16-Jun-11 10:15:56, Gavin and Rosemary Ross wrote:
>> "A circle of radius 1cm rolls round the outside a circle of 3cm.
>> The point A is the initial point of contact of the two circles.
>> How many revolutions does the smaller circle make before it returns to
>> point A?
>
> Hence you specified "outside" and the number of "revolutions" of the
> smaller circle. While you did not write "circle of [radius] 3cm", any
> other parsing would be perverse and arbitrary.
>
> The circle "revolves" when a point on the circumference rotates 360
> degrees relative to the centre. If the small circle slides round the
> large one with the marked point maintaining a fixed orientation, it has
> not revolved. The large circle has circumference 3X that of the small
> circle. In rolling round, whether inside or outside the large circle,
> the small circle revolves three times and arrives back at its start
> point. Starting at the top, after 1 revolution (360) the contact point
> is 4 o'clock and the mark points down, after 2 revolutions it's at 8
> o'clock and after 3 revolutions it's back where it started.
Err, Allan, as before, mark on the small circle the point B where it
was initially in contact with the large circle (marked A on the large
circle). Then, starting at the top, the point B is at the bottom of
the small circle. After one revolution (360 deg) of the small circle
relative to fixed space the small circle has its point of contact at
3 o'clock and the point B is once more at the bottom of the small circle.
Only 3/4 of the circumference of the small circle has passed along the
circumference of the large circle (i.e. the part from B, anticlockwise,
to the point of contact). This is because the direction of the large
circle has changed from horizontal to vertical.
Then after one more revolution the point of contact will be at the
bottom of the large circle, B again at the bottom of the small circle,
and 3/2 of the circumfrenece will have passed along the circumference
of the large circle. And so on!
Ted.
PS: I like the Dalai Lame story!
> If you want word games, the following was related on the Today
> programme. Dalai Lama goes to buy a pizza.
> Pizza man: How do you want your pizza?
> DL: I want "one with everything".
> PM: Yessir. That will be 2-50.
> DL hands over 5, and waits ...
> DL: Where's my change?
> PM: Change must come from within.
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E-Mail: (Ted Harding) <[log in to unmask]>
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Date: 16-Jun-11 Time: 15:43:13
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