Circumference question (warning maths content)

[Not-All-Here]

Right then, I seem to have forgotten how to do maths. So I decided to see if PH could help.

Here goes.

You have two circles, one with a radius of 200mm and one with a radius of 165mm

You draw a line at 0 degrees and a line at 40 degrees on both circles.

you then draw a line between both of these points on both circles (i believe this is called a chord).

What is the size difference in percent of the two chords?

Thanks

Thom

[Not-All-Here]

Or does anyone know of a site i can bash all the relevent info into and then i can do it myself

Thanks

Thom

[Oldandslow]

Not entirely clear from your description but I'll have a go. In my head it looks like you have an identical pair of circle drawing except one is larger than the other by a factor of 200/165 therefore all line segments on the circle with r=200 are 200/165 times longer than those on the one where r=165 (ie 121%). Or conversely the second ones are 82.5% of the first.

[Graham E]

Not-All-Here said:

Right then, I seem to have forgotten how to do maths. So I decided to see if PH could help.

Here goes.

You have two circles, one with a radius of 200mm and one with a radius of 165mm

You draw a line at 0 degrees and a line at 40 degrees on both circles.

you then draw a line between both of these points on both circles (i believe this is called a chord).

What is the size difference in percent of the two chords?

Thanks

Thom

Both form triangles with 2 sides = radius (200mm or 165mm) Therfore, since you;re scaling one to fit the other, the 3 sides will scale in proportion.
165/200*100 = 82.5%

OR, i'm wrong, GCSE maths was significantly more than a decade ago =)

[john_p]

A straight line between the two points, or a line following the circle?

[Graham E]

Oldandslow said:

Not entirely clear from your description but I'll have a go. In my head it looks like you have an identical pair of circle drawing except one is larger than the other by a factor of 200/165 therefore all line segments on the circle with r=200 are 200/165 times longer than those on the one where r=165 (ie 121%). Or conversely the second ones are 82.5% of the first.

To paraphrase Captain Jack, we have an accord =)

sorry

[Oldandslow]

Doesn't matter it's a scaling problem, no need to find actual lengths. (I think)

[Not-All-Here]

I just found a VERY simple way of wokring it out.

Draw a line and mark 165mm and 200mm, then from the same point draw another line at a different angle, mark off same points, draw a line between corresponding points, meassure and work out the difference.

well done those who got 21% you are correct.

Sorry, its late and my brain didnt work.

[Dyl]

I thought I was the only one bored enough to answer

Smaller chord is 82.5% of the larger (112.867mm & 136.808mm respectively)

Alternatively, the larger chord are 21.2% greater than the small chord.

Dylan

ETA Graham E answered it very simply!

Edited by Dyl on Tuesday 12th May 01:31

[Not-All-Here]

Dyl said:

I thought I was the only one bored enough to answer :hehe;

Smaller chord is 82.5% of the larger (112.867mm & 136.808mm respectively)

Alternatively, the larger chord are 21.2% greater than the small chord.

Dylan

Ooook thats confusing.

So is the distance 21% shorter or 17.5% shorter??

Now im really confused!!!!

[Dyl]

Not-All-Here said:

Dyl said:

I thought I was the only one bored enough to answer :hehe;

Smaller chord is 82.5% of the larger (112.867mm & 136.808mm respectively)

Alternatively, the larger chord are 21.2% greater than the small chord.

Dylan

Ooook thats confusing.

So is the distance 21% shorter or 17.5% shorter??

Now im really confused!!!!

It's late so doesn't make much sense.

The distance of the small chord relative to the large chord is 17.5% smaller...I think

ETA Even that makes little sense!

Edited by Dyl on Tuesday 12th May 01:36

[Not-All-Here]

right, so in practicle aplication if you had a lever 165mm long and you made it 200mm ling it would become 21% less efficient, but if you had a 200mm lever to start and made it 165mm it would then become 17.5% more efficient??

Thanks

Thom

[Graham E]

Not-All-Here said:

Dyl said:

I thought I was the only one bored enough to answer :hehe;

Smaller chord is 82.5% of the larger (112.867mm & 136.808mm respectively)

Alternatively, the larger chord are 21.2% greater than the small chord.

Dylan

Ooook thats confusing.

So is the distance 21% shorter or 17.5% shorter??

Now im really confused!!!!

Percentages have to be relative:

10 % of 100 is 10. 100 less 10% is 90.

10% of 90 is 9. 90+ 10% is 99.

See?

Therefore, the small circle is 17.5% smaller than the big circle (or "is only 82.5% as big as the large circle)
The large circle is 21% bigger than the small circle.

Etc.

[Dyl]

Not-All-Here said:

right, so in practicle aplication if you had a lever 165mm long and you made it 200mm ling it would become 21% less efficient, but if you had a 200mm lever to start and made it 165mm it would then become 17.5% more efficient??

Thanks

Thom

The opoosite is it not? Longer levers require less effort for the same effect

[Graham E]

Not-All-Here said:

right, so in practicle aplication if you had a lever 165mm long and you made it 200mm ling it would become 21% less efficient, but if you had a 200mm lever to start and made it 165mm it would then become 17.5% more efficient??

Thanks

Thom

Not exactly. If you made something 200mm Ling, it would try to sell you a teeny, tiny car on credit using only pidgeon english.

[Not-All-Here]

Dyl said:

Not-All-Here said:

right, so in practicle aplication if you had a lever 165mm long and you made it 200mm ling it would become 21% less efficient, but if you had a 200mm lever to start and made it 165mm it would then become 17.5% more efficient??

Thanks

Thom

The opoosite is it not? Longer levers require less effort for the same effect

Sorry i mean quicker, not efficient.

as in if you had a lever 200mm long made it 35mm shorter (165mm) and pushed it at a set pace it would move from point a to point b 17.5% faster (as in take less time). But if you had a 165mm lever and made it 200mm, when pushed at the same pace it would move from point a to point b 21% slower.

God its late.. why did i ask this!

Edited by Not-All-Here on Tuesday 12th May 01:46

[Dyl]

Not-All-Here said:

Sorry i mean quicker, not efficient.

as in if you had a lever 200mm long made it 35mm shorter (165mm) and pushed it at a set pace it would move from point a to point b 17.5% faster. But if you had a 165mm lever and made it 200mm, when pushed at the same pace it would move from point a to point b 21% slower.

God its late.. why did i ask this!

Take the 2nd example, you are taking the 165mm up to 200mm. Push the 165mm at a certain velocity, the 200mm end will move a larger displacement in the same time relative to the 165mm point. So larger displacement = larger velocity. Meaning the 200mm end will be rotating faster than the 165mm point. (I hope this is making sense or I'll look like a tit )

I think thats what explains larger wheels on a car offsetting the speedometer...

[Not-All-Here]

Dyl said:

Not-All-Here said:

Sorry i mean quicker, not efficient.

as in if you had a lever 200mm long made it 35mm shorter (165mm) and pushed it at a set pace it would move from point a to point b 17.5% faster. But if you had a 165mm lever and made it 200mm, when pushed at the same pace it would move from point a to point b 21% slower.

God its late.. why did i ask this!

Take the 2nd example, you are taking the 165mm up to 200mm. Push the 165mm at a certain velocity, the 200mm end will move a larger displacement in the same time relative to the 165mm point. So larger displacement = larger velocity. Meaning the 200mm end will be rotating faster than the 165mm point. (I hope this is making sense or I'll look like a tit )

I think thats what explains larger wheels on a car offsetting the speedometer...

Ok lets try again.

You have a LOOOOONG lever. and a ram that pushes at 10m/s

you set the ram to push the lever 10cm up, you then set it to push the lever 20cm up and so one.

At each point up the lever it will take longer to move the lever through its full travel as the distance the ram has to push is bigger.

Does that make sense now?

or am i really really getting confused!