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  • #566200
    david bennett 8
    Participant
      @davidbennett8

      I thought this may be of interest.

      https://www.practicalmachinist.com/vb/general/ot-math-question-about-ratio-old-sat-exam-395259/

      Edited By david bennett 8 on 09/10/2021 18:08:15

      Edited By david bennett 8 on 09/10/2021 18:11:49

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      #28386
      david bennett 8
      Participant
        @davidbennett8
        #566202
        Michael Gilligan
        Participant
          @michaelgilligan61133

          Very nicely demonstrated. yes

          MichaelG.

          #566217
          Martin Connelly
          Participant
            @martinconnelly55370

            Its like asking how many times does the earth revolve on its axis in a year if viewed from outside the solar system. The answer is 366 because on earth one rotation around the sun looks like no rotation as it would look if tidally locked, we only see 365 days. This is also why the sidereal day is slightly less than 24 hours.

            Martin C

            #566277
            Macolm
            Participant
              @macolm

              None of the explanations seemed instantly self evident. Here is my attempt.

              circles.jpg

              #566286
              ChrisLH
              Participant
                @chrislh

                Start off by fixing gear axes. Then if large gear is rotated 1 rev clockwise, small gear rotates 3 revs anticlockwise. Then to get the large gear back to the beginning the whole lot must be rotated 1 rev anticlockwise in which case the small gear will have made 4 revs anticlockwise. Is there a fallacy given that 4 is not one of the listed answers ?

                #566287
                Mikelkie
                Participant
                  @mikelkie

                  I like Macolm's explanation (3)

                  #566290
                  Michael Gilligan
                  Participant
                    @michaelgilligan61133
                    Posted by ChrisLH on 10/10/2021 15:44:04:

                    […]

                    Is there a fallacy given that 4 is not one of the listed answers ?

                    .

                    I think “4 is not one of the listed answers” was the point of the original post, wasn’t it ?

                    MichaelG.

                    Edited By Michael Gilligan on 10/10/2021 16:22:00

                    #566291
                    Michael Gilligan
                    Participant
                      @michaelgilligan61133
                      Posted by Macolm on 10/10/2021 14:35:14:

                      None of the explanations seemed instantly self evident. Here is my attempt.

                      .

                      Tidier than the video, but essentially the same information

                      MichaelG.

                      #566292
                      david bennett 8
                      Participant
                        @davidbennett8

                        Michael, how did you like post #32 in the link?

                        Dave8

                        #566294
                        Michael Gilligan
                        Participant
                          @michaelgilligan61133
                          Posted by david bennett 8 on 10/10/2021 16:32:47:

                          Michael, how did you like post #32 in the link?

                          Dave8

                          .

                          Sorry, I have to admit I didn’t read that far … but I have now done so

                          star

                          MichaelG.

                          #566300
                          Nicholas Farr
                          Participant
                            @nicholasfarr14254

                            Hi, as can be seen in Macolm's explanation though, the circumference of the small circle only makes contact three times on the circumference of the big circle, which is why anyone would give an answer of three.

                            Regards Nick.

                            #566327
                            david bennett 8
                            Participant
                              @davidbennett8
                              Posted by Martin Connelly on 09/10/2021 20:36:37:

                              Its like asking how many times does the earth revolve on its axis in a year if viewed from outside the solar system. The answer is 366 because on earth one rotation around the sun looks like no rotation as it would look if tidally locked, we only see 365 days. This is also why the sidereal day is slightly less than 24 hours.

                              Martin C

                              I have never seen that explanation before. Interesting.

                              Dave8

                              #566341
                              Alan Charleston
                              Participant
                                @alancharleston78882

                                I don't think the video is correct. If you look at Macolms drawing, there are only 3 points on the large circle where the A on the small circle touches which means it revolves 3 times around the large circle, not 4 times.

                                I tested it using back gears from my lathe which ensures there is no slippage between the circumferences. I took 2 40 tooth gears, marked the teeth where they meshed and rotated one gear around the other until the marks lined up again. It took one revolution, not two as suggested in the video. I then took a 28 tooth and a 56 tooth gear and rotated the 28 tooth gear around the 56 tooth gear. It took 2 revolutions for the small gear to return to its original position, not the 3 suggested in the video.

                                Regards,

                                Alan C.

                                #566349
                                Nicholas Farr
                                Participant
                                  @nicholasfarr14254

                                  Hi Alan, if you look at Macolm's explanation again, you'll see that each position that the small circle is in, the letters A, B, C and D are all in the same position, thus for every quarter of roll around the big circle, the same distance has occurred to the circumference to the small circle, which is 3 / 4 of it, but the small circle has rotated once and this happens four times. As I've pointed out, the full circumference of the same circle only makes contact three times. Each of the letters on the small circle will line up with the same letters on the big circle, so when the two A's on the first quarter line up, the small circle has rotated more than once, so you get four times 3 / 4 plus four times 1 / 4.

                                  Regards Nick.

                                  Edited By Nicholas Farr on 11/10/2021 07:44:47

                                  #566353
                                  Alan Charleston
                                  Participant
                                    @alancharleston78882

                                    Hi Nick,

                                    Try looking at it in reverse. If the small gear turns 4 times when it travels around the large gear, then it should also turn 4 times if the large gear is turned once. That wouldn't happen as the small gear would turn once each time an A came past – i.e. 3 times.

                                    Regards,

                                    Alan C.

                                    #566362
                                    Nicholas Farr
                                    Participant
                                      @nicholasfarr14254

                                      Hi Alan, yes the ratio is three to one, but in the question, the big circle is stationary and the small circle Rolls around the big circle, hence four revolutions of the small circle and if the small circle was stationary, it would take four quarters of the big circle to revolve around the small circle once.

                                      Regards Nick.

                                      Edited By Nicholas Farr on 11/10/2021 09:11:53

                                      #566370
                                      Nicholas Farr
                                      Participant
                                        @nicholasfarr14254

                                        Hi Alan, a couple of photos and Macolm's sketch with a 60T and 20T back gear (3 to 1 ratio) first photo shows start position and second photo shows first quarter on 60T gear, which shows the first rotation of the 20T gear, note that the small hole in the 20T gear in both photos is at the bottom, which will always be in position of A on the small circle.

                                        circles 1.jpg

                                        circles 2.jpg

                                        Regards Nick.

                                        #566375
                                        Tony Pratt 1
                                        Participant
                                          @tonypratt1

                                          Damm I didn't want to get involved in this, obvious answer is 3 but I now have to go and prove it to myself.crying

                                          Tony

                                          #566377
                                          Tony Pratt 1
                                          Participant
                                            @tonypratt1

                                            Yes it's 3, I can sleep easy tonight.

                                            Tony

                                            #566386
                                            duncan webster 1
                                            Participant
                                              @duncanwebster1

                                              Sorry to disturb your sleep but it's 4, Chris LH explained it

                                              #566396
                                              Nicholas Farr
                                              Participant
                                                @nicholasfarr14254

                                                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

                                                #566403
                                                Nicholas Farr
                                                Participant
                                                  @nicholasfarr14254
                                                  Posted by Nicholas Farr on 11/10/2021 11:30:51:

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

                                                   

                                                  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

                                                  #566411
                                                  not done it yet
                                                  Participant
                                                    @notdoneityet

                                                    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

                                                    #566416
                                                    Tony Pratt 1
                                                    Participant
                                                      @tonypratt1

                                                      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 4surpriseThis 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

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