a little diversion

Hi, gentlemen the answer is in it's ratio, it is a simple equation i.e. 3+1=4

Circle B stationary = 4 revs of circle A around circle B.

Both circles rotating = circle B 1 rev and circle A 3 revs = 4 revs in total of both.

Circle A stationary = 4 revs of circle B around circle A

Although circle B would come back to the same position at 2 / 3 of a rotation, but not with the same letters aligning as in Macolm's sketch.

Regards Nick.

Edited By Nicholas Farr on 11/10/2021 11:36:44

Hi, I have to correct the above highlighted in bold, it should say one and one third rotations.

Regards Nick.

Edited By Nicholas Farr on 11/10/2021 13:07:10

C’mon people . Get sensible. The ration is simply the ratio of the circumferences. Work it out!

Think sensibly. How many times do the same size rotate in this scenario? How many times would the smaller circle rotate if the ratio were 2;1?

How many on here have worked out gear or pulley ratios and come up with complicated calculations?

The answer is three. Nothing complicated, just simple maths where the circumference is proportional to the diameter, the proportionality constant simply being Pi.

Circumference of a circle = Pi x Diameter

NDIY, well I thought it had to be 3, A @ radius 1, circumference = 6.28, B @ radius 3, circumference = 18.85, everyone do the maths 18.85/6.28 = 3?] Just watched the YouTube video, it looks like it could be 4This is ridiculous some guy has modelled it in a CAD program & got 3.

Tony

Edited By Tony Pratt 1 on 11/10/2021 13:58:01

Edited By Tony Pratt 1 on 11/10/2021 14:04:58

People are not taking this seriously! To consolidate the confusion, what if the small circle rolls inside the large one?

Edited By Macolm on 11/10/2021 14:07:49

Macolm, I think people [me] are confused enough as it is.

Tony

Wonderful puzzle.

I think I have convinced myself the answer is 4. Malcolm's diagram is very clear.

The original question asked was "How many times does the circle "A" revolve in total?

and NOT "How many times does the circle "A" rotate about circle "B"?

So, A rotates around its own centre 3 times, and A also rotates once around the centre of B. So, 3+1 =4.

I think the same argument also applies to the situation where A is inside B.

This is one of those situations where one has to concentrate on answering the question as asked. Can't see many at Westminster being able to cope with this.

Rod

Final answer is 3, confused no more, I reckon the videos have been spoofed the maths doesn't lie.

Just seen Rod's answer, it then becomes a question of interpretation which is a whole different argument & poor question setting.

Tony

Edited By Tony Pratt 1 on 11/10/2021 14:49:04

It does seem, as Ron Renshaw suggests, that an O level in any science subject disqualifies anyone seeking election to Parliament. What a state the wonderful traditional public schools and universities have got us into! Sorry, into which they have got us.

Tim

Sorry Tony, you're confused, it's definitely 4, and to answer Malcolm's question, 2.

I'm sorry gentlemen, but it seems obvious to me that the difference between the centres of the the

two circles is 3r + r = 4r. What's the problem?

Yes, 4. If you look at Malcom's diagram the small wheel rotates 120° around from the top to the point where the small wheel's A is next to the large wheel's A the small wheel has rotated 1 + 1/3 turns. When it has gone around another 120° to the point where the two A marks are together the small wheel has now done 2 +2/3 turns. By the time it gets back to the top it has done 3 + 3/3 = 4 turns.

Martin C

This problem gets better or is it worse?

After scrolling down David's link following David's suggestion to Michael, I am beginning to think my earlier answer of 4 might be wrong.

Is there a difference between "Revolve" and "Rotate"? While it true that Circle A rotates 3 times in it's circuit around Circle B, are any of these "turns" actually revolutions? The poster posits that a revolution means going around something else, a fixed point, and by implication turning on one's own axis is not a revolution. I know we often use these words almost interchangeably, but we can be more precise.

The question asks "How may times does Circle A revolve?" Since the only fixed point we have in this line drawing is Circle B, and Circle A only goes around Circle B once, should the answer be !?

Any other answers?

Rod

You've been reading the original thread, haven't you Rod?

Hi Rod, according to my dictionary, both revolve and rotate can be; 1, "to orbit a central point" 2, "to turn on an axis" the term revolution can mean; 1, "orbital motion about a fixed point" 2, "a turning or rotational motion about an axis" so I guess they all mean much the same thing in this context. All three of these words have other definitions as well.

Regards Nick.

Edited By Nicholas Farr on 11/10/2021 19:00:27

If both circles were the same size, would the right answer be 1 or 2? It's a question of definition, surely.

Hi, I don't think anyone is suggesting that the maths are telling lies, and we all know that the circumference of circle B is three times that of circle A and the ratio therefore is three to one, which means there must be four revolutions to a cycle. Circle B is not rotating, but the whole configuration is still a ratio of three to one, and for circle A to complete one cycle, there has to be four revolutions and the only thing revolving is circle A.

Regards Nick.

Hi Gary, I think it's a case of two for the price of one, as one cycle and one rotation would take place in the same time and space.

Regards Nick.

Edited By Nicholas Farr on 11/10/2021 19:27:16

Peter - I was reading the 32 nd poster responding to the original post on the Practical Machinist website, and to which I was signposted by David's suggestion to Michael. Are you saying there was a previous thread on this forum, if so I was not aware of it, I was just trying to keep this "diversion" moving.

Nick - thanks for the definitions. I was more or less quoting the 32 nd poster I referred to above, and who seemed quite precise and authoritative about his understanding that a revolution must be around a fixed point.

As someone has said there may be several answers depending on one's interpretation of the problem and the question. I can't imagine the original question setter could have imagined how much entertainment his/ her question would generate.

Rod

3 rotations and a translation or orbit. Translations are not rotations.

regards Martin