physics

[Dagman]

I enjoyed the timetravel question. Here's a couple of old ones;

Imagine a disc turning like an LP on a record deck. at a constant rate 33rpm. The outside of the disc is turning quickly, but the further towards the centre you go the slower that part of the disc turns, so if you keep gradually going to the centre where it is slower and slower what happens when you hit the dead centre,is it so slow it's undetectable? (by the way it's a full disc with no hole in the middle like an LP!) 

You are walking 1 mile from A to B at 1 mph. in 1/2 hr you're half way in another 15 mins you're 3/4 there in 71/2 mins you're 7/8 there and so on and so on. each part halved in distance and time as you go which surely means it could go on forever!!!??? so you never reach point B.

Both pointless ones but good for a pub argument! Enjoy thinking about them.

[IndieSinger]

I remember watching a much-repeated Open University episode on infinity where they used a similar analogy. Some bloke somewhere once "proved" (hmm...) that movement is impossible.

He used the idea of a bow firing an arrow towards a target. Say the distance between the arrow and the target is twelve foot (go on, say it). That means it has to go through six foot to get there. Which means it must travel through three foot to get there. And so on and so forth... so because the number of stages the arrow must pass through is infinite, then it can never reach its target and therefore (ha!) movement is impossible.

 

Crazy man.

[matchtrick]

Your second question goes all the way back to Plato and involves all sorts of imaginary arrows and turtles and rabbits, so I won't try to second guess two millennia of virtually unremitting philosphy.

However, there's a very simple answer to the first question: when you get to the centre of the disc, you stop moving around the turntable, but you keep moving.

In short, you rotate.

[Dagman]

Perhaps there's something in "impossible movement" but due to constant speed it is overcome, who knows? it's a deep one this!

If you're rotating on the turntable yourself then you become like the disc with the outside of your body rotating quicker than the inside. This would go down to molecular movement which in turn down to atoms etc etc, where does it end? or does the last smallest physical item, whatever it is, have a hole in the middle to allow such movement? another deep one!  

[bernardo]

In the second bit, you are erroneously thinking that the sum of an infinite series is always infinite.

[bobbyx]

The Disc question:

I'm no scientific genius, but here's my take

If I placed a pencil on the disc (stretching from the outside edge to the centre) It would appear to move at a constant speed. The disc isn't moving faster on the inside at all, it is a constant - If it was, then the pencil would break or fly off the turntable.

[OBonio]

Bernardo is right.  If the infinite steps converge towards zero (ie, the arrow hitting the target) then it will, of course get to 0.

[phl666]

The disk question. The inside and outside move at the same speed. The outside moves further though

[IndieSinger]

But it won't ever reach 0, will it? You can keep dividing into halves infinitely, surely? Even though you will soon get to numbers that we have yet think up a name for... if you half a number forever, you will never ever reach 0.

[Dagman]

phl666, the disc moves at the same rate ie 33 revs per min but not the same speed. Half way into the disc is still 33rpm but at this point the disc speed is halved. Its like being on a carousel, the outside horses move fast but the inside ones move slower because they're closer to the middle. The rate is the same for people outside and inside, the whole carousel rotates together at the same rate but the riders experience different speeds.  

[Tweed]

The disc's angular speed is constant, but the linear speed varies depending on the distance fromthe centre. If you're in the centre, you'll just be rotating at the same angular speed, though the linear speed will be zero.

[Uriah Heep]

Nothing deep about this, time to cut the bull.  An arrow fired at a target will get there as Harold once found out.  Not to mention Will Tells apple.....

[bernardo]

IndieSinger - you are getting confused between

• the time it takes to add up an infinite number of things

and

• the total you reach when you have done so.

 

The distance travelled is a finite amount, and the thing which is travelling does not have to stop at each bit to add it on.

[Dagman]

Yes I know it gets there, it's only a fun question! just to provoke thinking about distance can always be halved at every point in the journey but it comes to an end by hitting something, but on paper halving the distance goes on forever!

[Gef]

It's all answered by quantum mechanics.

[IndieSinger]

His post must have been banned, Gef.