Nice Easy Puzzle For Ya ............

[Gizmonster]

In the figure below, the radius of circle A is 2 units, the radius of circle B is 3 units.
Starting from the position shown in the figure, circle A rolls around circle B (circle B remains stationary).
At the end of how many revolutions of circle A, will the centre of circle A be back at its starting point ??

Link to image:

http://i264.photobucket.com/albums/ii200/Burnleymoonbeam/circles2_zpsa7f10d41.gif

[rockyracoon]

One and a half?

[Gizmonster]

Nope - that's what lots of people think :P

[mallyh]

3

[jim360]

3

[Gizmonster]

Still wrong - not as easy as it first appears lol ;P

[mallyh]

9

[jim360]

Oh. Interesting.

My thinking was that the time the starting point coincides would be the lowest common multiple of two and three, which is six, which corresponds to three full revolutions. I'm not instantly sure why this isn't right.

[grasscarp]

4

[Prudie]

Also made it 3, the time it took for 4pi to be an exact multiple of 6pi which I made 12 ie 3 revolutions. Obviously missing something

[Gizmonster]

Just so you fully understand the question, circle A rotates around circle B, until it ends up back in its original position.
How many revolutions has circle A made ??

[Gizmonster]

Still all wrong by the way.

[grasscarp]

The motion of the small circle is not in a straight line, but rather around a large circle. This revolving action around the large circle contributes an extra revolution as circle A rolls around circle B - so 4 not 3

[Gizmonster]

Still wrong - but you're getting there :)

[jim360]

Ah -- changes the way I was looking at the question, which was in trying to get the lines aligned again (I think then 3 is still wrong, of course, by grasscarps' logic).

So 1.5 + 1 = 2.5?

[Gizmonster]

..... and we have a winner :)

[bhg481]

2 1/2

[Gizmonster]

Jim just beat you to it :(

Just to fully explain the answer:
If you take the circumference of circle B and flatten it out into a straight line and let circle A roll over it, circle A will make 1.5 revolutions to cross it. However, when it rotates around circle B, it's also rotating around its axis and therefore makes 1 more revolution, so the answer is 2.5 and not 1.5 as most people think.

[bhg481]

Beat me to it Jim - my excuse is that my wife was talking to me while I tried to work it out.

I worked it out by saying that the centre of circle a travels 2pi*(3+2) units, so makes 2pi(3+2) / 2pi/2 revolutions = 2 1/2.

[bhg481]

I must learn to type more quickly

[jim360]

That's a lovely solution, bhg.