Johnny5

If the space was created in the bigbang then why can we consider that point as the 0,0,0 cordinate for the universe ?

There's no way of telling where that point is.

How about look towards polaris?

Yes no?

A car engine produces a maximum power of 95 kw at 6000rpm how can i calculate the torque at the maximum power?

Power has units of joules per second, which is energy per unit time.

Here is the definition of torque:

Torque = T = r X F

If we disregard the direction of the torque, we can focus on it's magnitude which is given by:

|T| = |r||F| sin(r,F)

Torque has units of energy. If you differentiate both sides with respect to time, each side will have units of power.

d|T|/dt = d/dt (|r||F| sin(r,F))

So, here is what happens in a car engine...

Gasoline is ignited, actually a mixture of gasoline vapor and air, regulated by the carburator, inside a chamber, by a spark which comes from the spark plug. So there is a tiny explosion which pushes the piston in a valve down, and then there is a firing sequence, if you have a four valve, there are four spark plugs.

So the plugs fire in an order, i think its 1324.

But regardless, as the pistons go up and down, the camshaft is turned.

A DOHC is the easist engine to learn first. Dual overhead cam.

So energy in the gas, is converted into rotational energy.

There are places on the web where you could investigate how a real DOHC engine works, they will have diagrams and you can see what I'm talking about.

But the principle is very basic, the explosions are used to make the wheel axis spin.

Camshaft animation

So the goal is to take the given information, and calculate torque.

You are told that the maximum power delivered is 95,000 watts. One watt is a joule per second.

Now, in that torque formula, you see the symbol r, you have to know what that is. I've always called it the "moment arm." I'm sure there are other terms for it. If you take a class, either in Statics or Dynamics, you will come across that formula.

here is one way to think about the torque formula:

You are walking towards a door, which is ajar. You want to enter the room beyond, so you have to push the door open. The door hinges are to your left, and the doorknob to your right, and the door opens inwards, that is you have to push. So where is the intelligent place to apply force?

You can either use trial and error, or you can use the torque formula and deduce the answer.

Here is the correct answer, regardless of your method of learning it:

Do not push near the hinges, push as far away from them as you can. You want to maximize the moment arm R, so that you can apply the least force possible, to produce a given torque.

Now, the hinges are located along the axis of rotation of the door.

A typical door has a width of about 4 feet, so we will call that the maximum radius, at which you can apply the external force F.

Now, when you push, you can either push perpendicular to the two dimensional plane which the door is in, or you can push at some other angle.

So what would be the best choice for the direction of your applied force?

Again, either you can use trial and error, or you can use the torque formula.

Now, the letter r, and the letter F, as well as torque T, that you see in the torque formula are actually vectors, and which i will now boldface, so...

t = r X F

I just switched to the Greek letter tau, instead of T, because it is common practice to use that symbol to denote torque.

Now, here is the definition of moment arm r, in the formula above, in the context of the door problem...

The vector r, has its tail located along the axis of rotation, its head is located at the exact place of contact, at which the force is applied, and r vector is perpendicular to the axis of rotation (which we know is located where the door hinges are). (From experience, you should already realize that if you push the edge of the door towards the axis of rotation, the door will not rotate at all, no matter how hard you push)

So let me take the time to explain the cross product briefly.

The cross product of two vectors, is another vector, which is perpendicular to the other two. And the direction is given by the right hand rule.

I should be able to find a place on the web with an illustration.

Here is a brief article on "right-hand rule" at Wolfram, I strongly urge that you read it, and then come back. As far as I know, the direction is by convention. Hence this is something you must memorize.

Now, I will use the diagram at Wolfram, to talk about the cross product of r with F.

As you can see in the diagram, the vector u X v is perpendicular to both u, as well as v. Let that axis be the axis of rotation, and let U be the moment arm vector, so that v is the applied force vector.

Thus, the direction of the torque points along the axis of rotation.

Now, here is the formula for the magnitude of torque again:

| t | = |r||F| sin(r,F)

sin(r,F) stands for the sine of the angle between r, and F.

if the angle between r,F is zero, then the torque would be zero, because sin(0)=0. Thus, there would be no "turning force" the door would not spin, and this corresponds to pushing the edge of the door directly towards the axis of spin. So clearly the door won't spin, if the angle between the moment arm r, and the applied force F is zero.

Now, sine takes on its maximum value when the angle is 90 degrees.

Thus, torque is maximized precisely when the angle between r and F is 90 degrees. In fact, sin(90)=1.

So now back to the car engine problem.

The force is being applied to a steel axis, namely the wheel axis.

Let me try to find the radius of an actual wheel axis, in a car assembly.

These places are, if you will, non-technical - they are not necessarily reflective of what happens in mathematics. Mathworld is from wolfram who are more applied than pure, wikipedia is written by the general public, presumably hyperphysics is written by physicists.

Speaking of hyperphysics, do you know who runs that site? It is seriously well organized.

I mean if i only read their whole site, I would learn a few things.

Do you know anything about who designed it?

 

Wow' date=' did you not understand my post. Shall we try another one?

 

Paraphrasing Johnny: does sqrt(2) lead to a contradiction?

 

It is just a meaningless statement vague and open ended - objects do no lead to contradictions; propositions may do so. In this case "the square root of two is rational" would led to a contradiction. You can't get a contradiction if there is notthing to reason from.[/quote']

 

hmmm just hmmm Really i wanted a smiley face with one eyebrow raised, but we don't have that so i chose the dude with the dark glasses.

What I mean is that one stays right here' date=' while the other one goes off in a spaceship. At some time when the two are together (for example, let's say the first goes around once), they synchronize their watches. The one in the spaceship zooms off into the distance, and eventually comes right back around. Therefore, there will have been no acceleration, and the standard objection cannot be used. As the spaceship twin's time is slower (to me), his time should read less when he comes back around. However, it would appear the same way to him, and therefore it would seem to him as if mine should read less. As no acceleration occurred between the synchronization and the re-reading, each view seems to be correct. How is this possible?

-Uncool-[/quote']

 

Let me really focus here.

 

Ok I followed. You are going to do an analysis, over a period in which their is no linear acceleration. But, if the guy goes around in a circle, was their not change in direction? Which implies acceleration? Yes or no?

 

 

In other words, if there is no acceleration, there is no change in the velocity vector, in which case the universe isn't hyperspherical. On the other hand, if the universe is hyperspherical, then there had to be change in direction, in which case there was acceleration.

 

Or what?

 

You tell me.

Rate and phase are not the same thing. "Reading less" does not mean the same as "ticking slower

Would you please elaborate, because under certain conditions, they (reading less, ticking slower) would correspond, under others they would not.

Regards

PS: Perhaps this should be moved to another thread, since the original poster wanted to talk about hypersphere. You know, sometimes it is difficult to stay precisely on topic.

No' date=' that's not true. In the standard twin paradox setup, the acceleration is not part of the initial problem.

[/quote']

 

Well it must enter somewhere, in order to be realistic.

 

Actually, my analysis of SR, and I mean my personal one, is extrodinarily complex. Far more than anything I've shown here.

 

And in the analysis, i have to define the "rest rate" of the clocks. Though I've never heard anyone discuss rest rate of clocks, at least not in those words. I hear talk of proper time, but such talk is not more clear than what is done in my analysis.

 

And to finally make the point, in that analysis when two clocks with the same rest rate, are initially in sync, and one of them is accelerated, the formulas of SR lead to a clear contradiction.

 

I can elaborate, but it gets highly mathematical, and I would prefer to do it in latex. But I have learned that once I get that mathematical, I lose everyone.

 

So...

 

so...

 

so there you go.

 

Regards

 

PS: the analysis i am speaking of, was for submission to the AJOP, but I'm not gonna bother. In that analysis, I do discuss clock readings. And I pay very careful attention to frame transformations.

Still waitin' for you to derive this.

I am trying to stay on topic, so it will have to be in another thread. It's not hard at all.

Kind regards Dr Mattson ?

I know the original poster wanted to know about motion on a hypersphere, but you flubbed that up, so I thought you might benefit from looking at a more simplified model.

Well unless i introduce coordinate systems, it's hard to know exactly what I did. Then after having done that, we can get very mathematical. I felt the more relaxed Gonzo Bonzo error was sufficient to elucidate the point, rather than introducing coordinate transformations from one frame to the other.

Is that what you want to see?

Rather than complicate matters with circular travel' date=' you can work it out with one straight line path outwards and another inwards.

[/quote']

 

What do you mean one straight line path outwards and another inwards?

 

I thought the person wanted Bonzo to travel in some great big giant circle, even though really he is moving in a straight line.

 

That is almost what I had been thinking.

However' date=' I want to do away with the acceleration, just leave the velocity. For example: he accelerates from earth, goes around once, and then once he sees the earth again, he synchronizes the watches. He then passes the earth, and goes in another orbit.[/quote']

 

Ok so regardless of how this happened, at the moment he passes his brother, he is not accelerating, the relative speed is v.

 

Then, he travels in a huge circle spanning the whole universe, at a constant relative speed v.

 

When he passes by his brother for the second time, and compares his watch to his brother's, will they still be synchronous.

 

That is your question.

 

According to SR theory, the laws of physics are the same in all inertial frames.

 

Each brother is in an inertial reference frame, at the moment the second orbit begins, and throughout the second orbit, each is still in an inertial frame.

 

According to SR, each brothers clock will read less than the other's.

 

The only flaw that I can see in that conclusion, is that since the orbit is curved, they really aren't in an inertial frame, since an object must move in a straight line at a constant speed in an inertial frame.

 

The logical conclusion is this.

 

The universe is not hyperspherical.

Quaternions

Not only this, but Hamilton had in a sense invented the cross and dot products of vector algebra. Hamilton also described a quaternion as an ordered quadruple (4-tuple) of real numbers, and described the first coordinate as the 'scalar' part, and the remaining three as the 'vector' part. If two quaternions with zero scalar parts are multiplied, the scalar part of the product is the negative of the dot product of the vector parts, while the vector part of the product is the cross product. But the significance of these was still to be discovered. Hamilton proceeded to popularize quaternions with several books, the last of which, Elements of Quaternions, had 800 pages and was published shortly after his death.

Is this correct? Did William Rowan Hamilton invent the vector cross product, by inventing quaternions?

I am going to start myself off, generate my own knowledge as it were.

Here is a definition for "moment of inertia"

Definition: moment of inertia

Moment of inertia quantifies the resistance of a physical object to angular acceleration. Moment of inertia is to rotational motion as mass is to linear motion.

So at least that is a start, if anyone here objects to this definition, please tell me why. PS, completely disregard the theory of relativity. I would like a total non relativistic treatment of the subject.

The reason being, is that my toy top is not spinning at the speed of light.

Now, here is something they say at the site, which I now have permanently memorized:

the greater the concentration of material away from the object's centroid, the larger the moment of inertia.

The above is quite understandable. Every object has its own unique center of mass, which can be described in its own rest frame. This was explained in the mechanics book i was talking about, but the author did a poor job explaining it.

To paraphrase... the greater the concentration of material away from the objects center of mass, the larger is its resistance to being made to spin faster. (resistance to angular acceleration)

Right now I am fixated on a bicycle wheel for some reason.

This site also mentions the parallel axis theorem which i dont know. I vaguely remember it, but I surely did not memorize it.

As I recall, once I accept the universality of conservation of angular momentum, the rest follows.

Perhaps someone will take that route.

Once latex is working again, I am going to go heavy on the mathematical treatement of this.

Definition: L = r X P

r is the moment arm, F the applied force. All three are vectors.

Ok here is a question, who came up with this formula, it is like so totally non-intuitive...

I = moment of inertia = S m_i (r_i)²

People just don't know things like this by magic.

Here is the thing which I apparently keep missing:

However, in the general case of an object being rotated about an arbitrary axis, the moment of inertia becomes a tensor, such that the angular momentum need not be parallel to the angular velocity. The definition of the moment of inertia tensor is very similiar to that above, except that it is now expressed as a matrix:

This site is good.

Ok they kind of start off with this:

Angular momentum in classical mechanics

The traditional mathematical definition of the angular momentum of a particle about some origin is:

 

L=R X P

 

 

 

where

 

L is the angular momentum of the particle,

 

r is the position of the particle expressed as a displacement vector from the origin

 

p is the linear momentum of the particle.

 

If a system consists of several particles, the total angular momentum about an origin can be obtained by adding (or integrating) all the angular momenta of the constituent particles. Angular momentum can also be calculated by multiplying the square of the distance to the point of rotation, the mass of the particle and the angular velocity.

That's a place to start.

Now, they aren't clear where this origin is to be located though.

As I've noted several times before' date=' this is the sort of thing that someone else has undoubtedly done, and is available somewhere in a book and/or on the internet.

 

Thinsg like this are not something I feel compelled to spend the time to work out or track down, and transcribe for you. If I had a link handy, I'd post it. In the absence of that, you are capable of Googling for information yourself.[/quote']

 

Fair enough.

 

I already know the answer, I wanted to see if you did too.

 

It's ok.

 

Regards

I want to understand the following formula:

t=I a

Where t denotes torque, a denotes angular acceleration, and I denotes the moment of inertia tensor.

I've been doing a great deal of reading, looking for someone who understands it more clearly than any other, and I've had no luck.

I really really want to understand "moment of inertia tensor"

Is there anyone who has a deep understanding of it, who can shed some light.

Even historical information is welcome. Like who developed the formula, when why how.

I have those kinds of questions.

Also, I think this thread might ultimately be quite valuable to others, who don't understand that formula either.

I would like the thread to be moderated, remain on topic, and be professional.

I would like it to proceed from the simple to the complex.

I will not ask dumb questions, and am prepared to do some independent study. I currently have gathered several books which discuss it to varying degrees, but again... I haven't read a single person's coverage of the matter, to the point where I can say, wow that guy's good.

There are some brilliant people that frequent this site, and I know this.

I want to understand precession especially.

The boomerang question also got me back to this question.

I've never understood the moment of inertia tensor, so I can rectify that now.

Umm... lets see... there was something else I wanted to say...

Oh yeah...

Yesterday, I was thinking about how I would proceed to teach the topic, if i already understood it, and I came up with this...

I would buy a tiny toy spinning top.

Then, to my pretend student, I could repeatedly perform a simple experiment.

Set the top spinning on the floor, and have them watch the precession of the axis of rotation.

Then, slowly I would develop a mathematical model of the toy.

I could mark places on the top, where imaginary axes go.

I could say, there is a frame, attached to the top, whose axes spin with it.

The axes of this spinning frame pass through the points I've made on this toy top, and one of the axes of this three dimensional coordinate system is permanently the axis of rotation.

So we need to come up with formulas which predict the precession of this top, which motion we can see by repeatedly performing the experiment.

I might then talk about density, mass per unit volume of the top, then again perhaps not.

I might touch on the integral calculus, and how it is used to "discuss" the location of the center of mass of the top.

But what I really have no idea about, is how to get to "moment of inertia tensor" from just watching the thing spin.

So that's what I really want to do.

Thank you

PS: Now here is wolfram on moment of inertia

Here is a site that is beyond understandable: Rotation of rigid bodies

Now in something I was recently reading, it was Euler who extended Newton's laws to rotational motion. I don't know how true that is.

There are "rotational analog" formulas, to Newton's linear ones.

I know the formulas, here is a link:

Rotational Dynamics

At the site above, they say "fixed axis" I'm not sure what that means.

Here is a site that looks good: Rotational Dynamics

And here is exactly what I was looking for, a side by side comparison of the formulas:

Hyperphysics on Moment Of Inertia

I think the first question to answer, is why doesn't the spinning top fall to the ground, it stays up in a manner of speaking. If you nudge it, it pushes back, to remain spinning.

And also, there is the ice skater.

She pulls her arms in, and spins faster.

I know many of you know how to handle this topic.

I am hoping for a clear presentation, something i cannot seem to find in my books.

I recently went back to a classical mechanics book, written by umm

I can't remember his name, but it doesn't matter.

He glossed over things. his treatement of the subject was ultimately incoherent. I could tell he understood it on some level, yet well here I am asking for someone who knows how to teach to try to explain.

I really think the presentation needs to be based upon some real experiment with a spinning top, and not be overly mathematical. however, you have to go from a spinning top, to tensors, so eventually things get abstract. I'm ok with that.

but if someone were to come to me right now, and ask me why doesn't a spinning top fall to the ground, I would be unable to impress them with my answer.

That's going to change.

No' date=' you won't, since you are going against the notation used by a not unreasonable number of mathematicians - every one educated at Cambridge, not to mention every analyst I've ever met and so on. The only time logs are ever taken in *maths* (ie not physics or engineering) where base e is not the chosen base is log base 2 for use in coding theory. Of course that is guaranteed to have rebuttals, but I carefully qualify this as any reasonable mature treatment of analysis.

 

I must confess I have exactly one analysis textbook to hand, Goursat's classic text, and it uses log to mean base e, as would almost any other proper analysis book I@d be prepared to wager, and I've never seen ln used in complex analysis proper, writing as someone who's taken (several) graduate courses in (complex) analysis.

 

log is just the usual standard, johnny in *pure mathematics*, it is the only one that makes sense, just as radians are the only unit of angle that make sense really.

 

 

ln just signifies another dmbing down *sigh*, what next? Calling it the Argand plane?[/quote']

 

Matt, it's not that important.

 

Here is Wolfram's discourse on natural log

 

They used ln there.

 

Here is wikipedia's article on natural logarithm

 

They mention both usages, but seem to favor ln.

 

Here is hyperphysics on natural logarithm.

 

They also used ln.

 

Here is Planet math on natural logarithm.

 

They used ln there.

 

Perhaps you went to Cambridge, I do not know. But I will say this... if going there helps you to know your stuff, then good.

 

Use either or... you will end up being followed.

 

Regards

You can measure the acceleration of an object using SR, because you can look at things from an inertial reference frame. But an observer in the accelerating frame, who attempts to apply SR, is going to get wrong answers from measurements.

Dr Swanson, can you explain why. You are right, under the assumption that the SRT time dilation formula is true, you are right. The frames are not identical.

But how would you explain why mathematically?

Your discussion would involve derivatives with respect to time of SRT formulas yes?

That is what I'm interested in seeing. How you perform the derivatives. which frame do you differentiate time in.

Regards

A small question I thought of recently:

If the universe is the surface of a hypersphere' date=' then what happens if an item goes 'around' the hypersphere and meets back up with the earth? Who will have aged more and why? (Assuming constant velocity and all that) Both will think that the other was moving and therefore slowed down, and each one would be equally correct.

-Uncool-[/quote']

 

I think this is something i thought of long ago, but maybe not, because I'm not sure what you mean.

 

You make reference to "aging more"

 

Right?

 

So the argument operates under the assumption that SRT time dilation is a real phenomenon right?

 

And then you add to that argument the concept of a "hypersphere."

 

You mix the two together, to see if the ideas are consistent with one another. Either they are logically compatible, or not.

 

So, please correct me if I am wrong, but you mean something like this:

 

Suppose the time dilation formula is a true statement in frame S.

 

Let Gonzo and Bonzo, identical twins, be currently at rest in inertial reference frame S.

 

Gonzo and Bonzo both own a 24th century digital Timex, which can measure time to one part in ten to the fiftieth.

 

For all practical intent and purpose, their watches, given to them by their father as a birthday present, are identical.

 

Currently, their watches are synchronous.

 

If you put the two watches next to each other, you see the same number on the display. That is the meaning of synchronicity.

 

Ok so Bonzo gets in a spaceship in reference frame S, which accelerates off to the right with magnitude A.

 

Rather than ever decelerating, Bonzo travels all the way around a Hypersphere, until he passes Gonzo.

 

On the flyby, which took time t in Bonzo's spaceship frame, Bonzo sticks his arm out the spaceship window and Gonzo takes a polaroid of his brother's wrist as Bonzo passes by.

 

Gonzo then compares his wrist watch's reading with the snapshot, and notes what?????

 

Or as a variation, to illucidate the problem,

 

Suppose that both Gonzo and Bonzo get in identical spaceships, and accelerate identically, perfect symmetrical accelerations, and they both travel until they meet each other again.

 

Relativity implies that each brothers watch must be less than the other's.

 

Yet they are in a common reality.

 

Therefore, SRT and the universe being a hypersphere are not compatible ideas.

 

Is that what you were thinking, something along these lines or no?

What kind of texts Johnny? Speaking as a professional mathematician who's worked in both the US and the UK I'd say that log is the one I'd expect to read in any paper or decent book. Of course if you're basing this on reading some engineering text...

Well i have hundreds of books, graduate level mostly.

In the overwhelming majority, ln is used exclusively for natural log.

And in complex variables, Ln (x) is used.

I'd prefer to see people use ln for natural log, Log for log base 10, and log for arbitrary logarithms.

But of course i wont get what i want.

I have just completed some serious thinking on the matter and I believe I have arrived at a solution that is neither ' date=' SRT , nor Sagnac.

I will be posting shortiy. [/indent']

Special relativity can handle accelerating reference frames[/url']. In special relativity velocities are relative but acceleration is treated as absolute. In general relativity all motion is relative.

I love that site... Wolfram.

Regards

kiesel is tranlated literally as "pebbles". Now everybody knows!.

 

Hint I simply broke the motion into convenient segments. The first ct the distance the photon move initially. . vt the distance the frame moves in time t. How far away from the right clock is the right photon after moving ct *the same distance the left photon just moved? Look at the left photon : if d is the distance of midpoint to clock then the left photon has reached vt short of the clock' date=''s initial position., so then put the right photon also vt short of the right clock, plus the vt the frame has moved when the photons moved a distance ct.[/indent']

Note' date=' it is common practice to use log for natural log, rather than ln.

[/quote']

 

 

Actually, in the states at least, it is common practice to write ln (x), and that is an L not an i.

 

Certainly this has been my experience regarding various texts.

 

Log is used for base ten, and log_a (x) for arbitrary bases.

 

When the latex is working again, I will try and answer this. I have a treatise on the integral calculus on this exact question, and as I recall, the answer was exceedingly clear, and I've never read a better discussion on the natural log before, or since. I'll find it and post the answer here, using latex, if they ever get it working again that is.

 

Regards

I'm no expert but i think relativity applies only to inertial reference frames. In the case of an accelerating reference frame, special relativity does not apply.

SR has formulas in v.

Differentiate them to give you formulas in a.

Then investigate the meaning of the symbolic statements, and decide whether or not the meaning is inconsistent with something you already know. This is a rather complex task by the way.

Regards

(Johnny5)... anybody ever tell you .... well... your wordy little bugger

Not exactly in quite those words no.