Applying math to real world problems

[uperkurk]

Equations are all well and good when you have things like "Let x = something" "Let b = the spin" "Let y = the weight" ect...

But if you wanted to really do your own experiement at home. I have a penny on my desk, I'm sure you have all done it before but if I hold it on it's edge and then spin it, I want to measure with precision the rate at which the angle of the penny changes.

I also want to measure the rate at which the spin slows down per second. How would someone, without any kind of computer or anything prove anything like this?

The point I'm getting at is Newton used calculus to show the orbits of planets... no technology existed then that could possibly help him.

 

[WannabeNewton]

Do you mean theoretically? If so then (to some extent) this is a common mechanics textbook problem (IIRC, Kleppner works it out in the text itself and Morin has a problem on it). It is called Euler's disk and has been studied quite a bit actually.

 

[tahayassen]

Do you mean theoretically? If so then (to some extent) this is a common mechanics textbook problem (IIRC, Kleppner works it out in the text itself and Morin has a problem on it). It is called Euler's disk and has been studied quite a bit actually.

Really? How accurate would you be without a calculator? I'm curious too. Math is easy without a calculator. Physics? Not a chance.

 

[WannabeNewton]

Really? How accurate would you be without a calculator? I'm curious too. Math is easy without a calculator. Physics? Not a chance.

You'll have to forgive me but I'm not understanding the question - I'm not seeing why we need a calculator.

 

[Adyssa]

I got through pretty much all of my university maths courses without a calculator. The only times I found the need for one was computing with numerical methods and the occasional trig function. Most everything was pen and paper. Until you input your actual measurements, the numbers don't really matter, and when you have those, it's a simple exercise to sub them in and calculate.

 

[OmCheeto]

Equations are all well and good when you have things like "Let x = something" "Let b = the spin" "Let y = the weight" ect...

But if you wanted to really do your own experiement at home. I have a penny on my desk, I'm sure you have all done it before but if I hold it on it's edge and then spin it, I want to measure with precision the rate at which the angle of the penny changes.

I also want to measure the rate at which the spin slows down per second. How would someone, without any kind of computer or anything prove anything like this?

The point I'm getting at is Newton used calculus to show the orbits of planets... no technology existed then that could possibly help him.

That's weird. I calculated the orbital period of two pennies when I was about 12. I don't think calculators were common back in 1971. How on Earth did I do that?

I should re-post my paper in the physics section and get some feedback.

Though I do recall that when I was about 14, I converted a 4 function calculator into a stopwatch. I wish I knew half as much now as when I was young.

---------------------------------
I once told someone that I was the ultimate nerd whilst growing up. They questioned my assertion. I should go find that guy. Like many a senile person, my childhood is slowly coming back to me...

 

[zoobyshoe]

But if you wanted to really do your own experiement at home. I have a penny on my desk, I'm sure you have all done it before but if I hold it on it's edge and then spin it, I want to measure with precision the rate at which the angle of the penny changes.

I also want to measure the rate at which the spin slows down per second. How would someone, without any kind of computer or anything prove anything like this?

http://89.28.209.150/go/print/Apparatus_56.html;jsessionid=a9a2P9GyK2ig

People figure out extremely clever ways to measure things with low tech devices aided by some math.

 

[uperkurk]

So show me how you would go about working this out... for those of you that can be bothered you actually have to get a real penny, spin it, write down your calculations ect. Sure you can use a calculator if you really wanted to.

But I'm interested to see calculations for your actual spinning penny.

 

[ImaLooser]

Really? How accurate would you be without a calculator? I'm curious too. Math is easy without a calculator. Physics? Not a chance.

Isaac Newton seemed to do OK without one.

 

[uperkurk]

Isaac Newton seemed to do OK without one.

This is what I mean though... how is it possible to INVENT equations that can predict the orbit of planets?! It just seems impossible without actually being able to take a tape measure to it...

 

[Astronuc]

This is what I mean though... how is it possible to INVENT equations that can predict the orbit of planets?! It just seems impossible without actually being able to take a tape measure to it...

Knowledge of geometry and mechanics, and use of observational astronomy. One only needs to be able to determine time, distance, speed/velocity, acceleration, mass. Equations are then written to describe the mechanics, and then compared to experimental (observational) measurements.

It was also possible to measure the speed of light using geometry (surveying with reliable/accurate instruments to determine distance) and a reliable chronometer. Over time, improved methods have been developed.

 

[tahayassen]

@upperkurk: You don't really need a calculator to invent equations. All you need is calculus and the ability to substitute equations to derive the kinematics equations (so inventing equations is pretty much the same as math).

In high school, physics teachers were plugging numbers into equations that physics seemed impossible without a calculator. If I were to do a simple kinematics problem in the real world, could I get an accurate value without a calculator?

 

[Curious3141]

Isaac Newton seemed to do OK without one.

We shouldn't also lose sight of the fact that Newton was one of the greatest geniuses to ever have lived. Despite the lack of tools that we take for granted, he came up with earth-shattering discoveries.

What is the work of genius today is the work of tinsmiths tomorrow.

 

[tahayassen]

If I have seen further it is by standing on the shoulders of giants.

That was in his letter to Robert Hooke in February 1676. By giants, he is referring to Galileo and Kepler.

 

[WannabeNewton]

uperkurk I'm not sure how rigorous a calculation you want but here is a fairly in depth version (it is higher level than what you would see in Kleppner or Morin): http://math.arizona.edu/~dcomeau/research/Termpresentation.pdf

 

[uperkurk]

@OmCheeto, you say you calculated stuff like this when you were 12? Using the equation and notation I just saw in that PDF file? That stuff looks crazy difficult...

@WannabeNewton, so if I could actually understand these equations I could grab a penny from my draw, spin it and accurately work out the angle at which the penny changes over time? Then if you were to spin it the exact same speed and have a computer measure it, I would get the same result?

 

[WannabeNewton]

@WannabeNewton, so if I could actually understand these equations I could grab a penny from my draw, spin it and accurately work out the angle at which the penny changes over time? Then if you were to spin it the exact same speed and have a computer measure it, I would get the same result?

As with any experiment you will have a margin of error but other than that you should be able to predict it up to a very reasonable approximation.

 

[OmCheeto]

@OmCheeto, you say you calculated stuff like this when you were 12? Using the equation and notation I just saw in that PDF file? That stuff looks crazy difficult...

Going over my notes, it appears that I am incorrect. It appears that I placed the pennies a certain distance apart and calculated the time it would take gravity to bring them together in how long a time. The notes are not very good. I didn't include the original separation distance, nor the mass of the pennies.

8,650,000,000,000,000,000 years
acceleration = 5.16e-38 cm/sec²
speed upon collision = ~1.41e-11 cm/sec

Gads I was a nerd.

But I used to be able to do those calculations in my head, hence never wrote down the intermediate steps, and therefore have no clue now as how I calculated these numbers.

I have only the equations. And given that I was using a manual typewriter probably built in the 40's, I used all manner of substitutions for the greek symbols. I substituted a lower case "w" for omega, "@" for angular acceleration, etc, etc.

I do not recall ever taking a physics course in grades 1 through 12, so I assume I retrieved all the equations from our encyclopedia.

Here's a clue that perhaps I had intended to solve the orbital problem:

(please don't take note from the following. It appears I was putting together the jigsaw puzzle of physics, and made a few errors.)

orbit velocity = the square foot^* of gravitational acceleration at the distance of r * the distance from the Earth's center.
angular velocity = w(omega)
v=rw
w=radians per unit of time
1 radian = 57.3^o
impulse <> momentum
momentum is a vector
momentum is conversational(sic) (I think I meant conservational. Although perhaps not, as I probably didn't understand the concept at the time, and decided that they had made a typographical error. )
things do not really fall.
the Earth and the thing attract each other and meet at a point of zero.
v=2*pi*r*w
v=r*w
v=r*w/57.3
t=f*r

(then there were the numbers I mentioned earlier)
8,650,000,000,000,000,000 years
acceleration = 5.16e-38 cm/sec²
speed upon collision = ~1.41e-11 cm/sec

(then I continued)

angular acceleration @
angular velocity w
torque t
linear acceleration a
a = r@
f=mr@
t=(mr@)(r)=mr²@
I=mr₂² = moment of inertia
angular momentum = Iw
w=fd
w=mv²/2
work=mass*acc*dist

And that was it.

These notes were transcribed in the summer of 1977, along with 11 more pages of things I thought were important. I was about to enter the Navy, and was afraid my mother would throw everything out.

The problem of the orbit of the pennies did not re-enter my mind until yesterday. Thank you.

*I would not discover white-out until years later.

 

[uperkurk]

Going over my notes, it appears that I am incorrect. It appears that I placed the pennies a certain distance apart and calculated the time it would take gravity to bring them together in how long a time. The notes are not very good. I didn't include the original separation distance, nor the mass of the pennies.



Gads I was a nerd.

But I used to be able to do those calculations in my head, hence never wrote down the intermediate steps, and therefore have no clue now as how I calculated these numbers.

I have only the equations. And given that I was using a manual typewriter probably built in the 40's, I used all manner of substitutions for the greek symbols. I substituted a lower case "w" for omega, "@" for angular acceleration, etc, etc.

I do not recall ever taking a physics course in grades 1 through 12, so I assume I retrieved all the equations from our encyclopedia.

Here's a clue that perhaps I had intended to solve the orbital problem:

(please don't take note from the following. It appears I was putting together the jigsaw puzzle of physics, and made a few errors.)


And that was it.

These notes were transcribed in the summer of 1977, along with 11 more pages of things I thought were important. I was about to enter the Navy, and was afraid my mother would throw everything out.

The problem of the orbit of the pennies did not re-enter my mind until yesterday. Thank you.

*I would not discover white-out until years later.

You must literally be a genius... At 12 years old I was playing video games and failing my times tables lol...

 

[OmCheeto]

You must literally be a genius... At 12 years old I was playing video games and failing my times tables lol...

The only purchasable video game available when I was growing up was called "Pong".

Or more specifically Odyssey, by Magnavox.

My oldest brother bought one. Mastered it in 12 seconds.

Boop! ... Boop! ... Boop!

And as for times tables, did you not see my comment on how I was an uber-nerd?

I sat down, during the summer, after I was told that there was more than one number base, and wrote out the multiplication tables, for all bases between 2 and 16.

This was long before computers were available, and a bit of a while before I would realize that knowing binary and recognizing hexadecimal would become important tools in dealing with these demon machines, with which I. hmmm... Computers are awesome.

When I got my last job, I discovered that the oldsters were using computers as if they were typewriters with TV screens. ie., They had not a clue of the inherent power of microprocessors and well written software.

I went on to write several pieces of software for that job. I'm pretty sure it eliminated at least 3 positions over the years.

As I've said before; "I somehow feel responsible for a bit of the unemployment problem."

Or something like that.


-------------------------------
ps. I was a genius. Mostly due to long hours of mind pleasing mental massage. It was the only thing to do as a child during our long cold rainy PNW months. Now I just sit and surf in a Lay-Z-Boy recliner, and burp once in awhile. So no, I am not a patent clerk.

 

[tahayassen]

uperkurk: you're being trolled so hard :P Notice the best humor 2012 PF award.

 

[OmCheeto]

uperkurk: you're being trolled so hard :P Notice the best humor 2012 PF award.

and the confusion sets in...

"trolled so hard"? google google google

Strawman!

 

[tahayassen]

and the confusion sets in...

"trolled so hard"? google google google

Strawman!

Opps. Made an oopsie. I thought you were joking when you wrote "Though I do recall that when I was about 14, I converted a 4 function calculator into a stopwatch. I wish I knew half as much now as when I was young." Trolling is the art of deceiving someone.

 

[Drakkith]

Trolling is the art of deceiving someone.

Deception is the art of deceiving someone! Trolling is something else entirely!
From wiki:

In Internet slang, a troll (pron.: /ˈtroʊl/, /ˈtrɒl/) is someone who posts inflammatory,[1] extraneous, or off-topic messages in an online community, such as a forum, chat room, or blog, with the primary intent of provoking readers into an emotional response[2] or of otherwise disrupting normal on-topic discussion

Trolls can use deception however. It is one of several tools.

 

[tahayassen]

Deception is the art of deceiving someone! Trolling is something else entirely!
From wiki:

In Internet slang, a troll (pron.: /ˈtroʊl/, /ˈtrɒl/) is someone who posts inflammatory,[1] extraneous, or off-topic messages in an online community, such as a forum, chat room, or blog, with the primary intent of provoking readers into an emotional response[2] or of otherwise disrupting normal on-topic discussion

Trolls can use deception however. It is one of several tools.

It seems you know quite a bit about trolling. Perhaps too much...'

Not drawing any conclusions or anything...

^{you undercover troll!}​

 

[Drakkith]

It seems you know quite a bit about trolling. Perhaps too much...'

Not drawing any conclusions or anything...

^{you undercover troll!}​

 

[uperkurk]

:( the worst thing about talking to people about a topic you have no clue about is you have no idea when you're being trolled :(

 

[BobG]

This is what I mean though... how is it possible to INVENT equations that can predict the orbit of planets?! It just seems impossible without actually being able to take a tape measure to it...

1) The equations were to describe motion in general.

2) If the laws of motion were true, they should apply to celestial objects, as well as everyday objects.

2) Using observations already made by astronomers, Newton could see if his equations matched real observations. In other words, by plugging observation #1 into his equations, did the results of his equation match observation #2.

In other words, he predicted nothing (at least originally).

3) And, actually, a tape measure would have come in handy. While Newton (and Keppler) could tell you Jupiter has to be x times further from the Sun than the Earth, he had no way of telling you what either of distances (Earth's or Jupiter's) were in kilometers. (This is why "astronomical unit" is historically such a popular unit of measure.)

And perhaps a great deal of his success was as much a result of DesCartes as Galileo and Keppler. It's no coincidence that two separate men 'invented' calculus within 10 years of each other shortly after DesCarte's Cartesian coordinates, etc, created the need to calculate the 'slope' of a curved graph.

 

[Integral]

That was in his letter to Robert Hooke in February 1676. By giants, he is referring to Galileo and Kepler.

As a side note, Hooke was a very short man. This comment is also a direct put down of Hooke, who was no giant.

This according to John Gribbin.

On Topic.
It is easy to observe changes in motion. That is why Newton developed Differential calculus, to analyze the changes in motion of the planets. To create a mathematical model you start by expressing the problem in terms of differentials, once you have a differential equation for your system you can then solve it to arrive at simple time dependent equations of motion.

 

[Rob D]

And he did it at 26, just because of boredom during sequestration from the plague rampant in the cities. And to piss off Leibniz.

I find myself doing most calculus in physics on my graph lined notebook. Only use the computer to do tough graphs and watch Lenny do incredible physics whilst munching chocolate chip cookies. My hero.

 

[OmCheeto]

:( the worst thing about talking to people about a topic you have no clue about is you have no idea when you're being trolled :(

We will let you know when we start trolling you.

As to your spinning penny, I have no interest in solving the problem, as I see little "real world" use of the answer. (How long will it take a 300 kg generator to spin down with a coefficient of friction x, radius y, length z, once motive power is removed with no load? My answer: Who cares)

You might go to the physics or homework section and request guidance on how to solve the problem. Off the top of my head, you will need to know the following:

Mass of the penny
Initial angular velocity
(Some basic knowledge of Rotational Dynamics: Halliday & Resnick, 2nd Edition, Revised Printing, 1986, page 198)

From here you would measure the amount of time it takes for the penny to stop spinning.
This would yield, mathematically, a deceleration rate.
From that, I believe you could determine the coefficient of kinetic friction between the penny and your surface.

Then, with some mathematical knowledge of physics, you could extrapolate an equation which relates time, angular velocity, mass, etc.

Actually, I wouldn't solve the problem for you even if I found it to be a useful bit of knowledge. It's not allowed here.

 

[BobG]

As to your spinning penny, I have no interest in solving the problem, as I see little "real world" use of the answer.

Obviously, you should have picked a more interesting problem, such as:

If you spin a class ring, why does it almost always to seem wind up spinning with the jewel part on top?

(And there is an obvious answer why the jewel part has to wind up either directly on top or directly on the bottom, but only a slightly satisfying answer why it has to wind up on top.)