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A few random ideas

(1) Last night I watched <MOVIE>Carry on Dick</MOVIE>. There was a word that got me curious as to its origin - diggler. I searched a few slang books I got, but couldn't find a mention of the negolism. Anyone know its origin? I am not asking the meaning, it was clear watching the movie ;-)

(2) Acceleration due to gravity is given as the rate of change in velocity. The concept still doesn't sink in. What does it mean to say distance/(time^2)?

Sathyaish Chakravarthy
Sunday, May 09, 2004

"Acceleration due to gravity is given as the rate of change in velocity"

You need to take an intorductory course in calculus.

Velocity is the change in position per unit of time (feet per second).

Acceleration is the change in velocity per unit of time (feet per second) per second

If the rate at which you are accelerating is changing, you have ((feet per second) per second) per second

And so on, ad infinitum

Tom H
Sunday, May 09, 2004

Speed and accereleration won't really make full proper sense until you do some calculus.

For now though, try not to be mislead or confused by the /units/ of the quantity, m/s^2, when thinking about /how it's calculated/, finding the rate of change of speed (strictly speaking to find this you need to take limits in an approximation, although drawing a tangent to a graph is a good way of visualising it).

You don't (typically) calculate acceleration by dividing a length in meters by the square of a time in seconds. What you'd do would be something like:

(speed(now) - speed(a second ago)) / 1 second

as a first approximation, then

(speed(now) - speed(a millisecond ago)) / 1 millisecond

then

(speed(now) - speed(a microsecond ago)) / 1 microsecond

and take the limit as the time period gets closer and closer to zero. Calculus gives you easy ways of doing this (differentiating) if you have a formula for the speed, say.

Matt
Sunday, May 09, 2004

>Acceleration is the change in velocity per unit of time (feet per second) per second

I know that, and that was what I said - rate of change in velocity (implied per unit of time, or in terms of differential calculus, the change in velocity due to a very small change in time that tends to zero.)

>If the rate at which you are accelerating is changing...

But I couldn't think of it as something I could understand. I still don't understand it. Although this statement of yours makes it pretty much easy to understand, I am still thinking what it means to measure speed every second. Meaning what is the meaning of measuring the change in speed per unit of time.

Sathyaish Chakravarthy
Sunday, May 09, 2004

>(speed(now) - speed(a microsecond ago)) / 1 microsecond

Thanks, Matt. I got that. But I still dont seem to understand how to think of it out of mathematics. Speed is already a function of time, given a distance. Then what good is it measuring, "how much change in speed in this time?"

Sathyaish Chakravarthy
Sunday, May 09, 2004

"Meaning what is the meaning of measuring the change in speed per unit of time"

The concept of "rate of change" is the same no matter what it is that's changing. If you are gaining weight, the rate of change is how much gain per day (or whatever time increment). If the velocity is changing (getting faster or slower), the rate at which it's getting faster or slower is called acceleration. I think you're trying to find something complicated where it isn't complicated at all.

Tom H
Sunday, May 09, 2004

As a complete aside, I was once working on some magnetic field data provided by the British Geological Survey. This data is collected every 5 - 10 years and used to estimate the angle between true and magnetic north (i.e. the magnetic field vector at some position and the earth's spin vector) for surveying and navigation. To estimate this into the future you need to know not only the rate of change of the angle with time (velocity, if you like), but the rate at which that rate changes (c.f. acceralation).

Every now and then there would be an unexpected change in the 'acceleration', which they called ....

A jerk

David Roper
Sunday, May 09, 2004

Think of it in terms of driving your car.  At rest you are going 0 meters per second.  You hit the gas and 10 seconds later you are going 25 meters per second.  If you were undergoing constant acceleration, then you were accelerating at a rate of 2.5 meters per second per second, which is to say that every second you were accelerating your speed increased by 2.5 meters per second.

I find that concrete examples in terms that we can relate to in everday life sometimes help explain what are otherwise difficult and abstract concepts.  (I used units of meters and seconds because that's what most physics students are taught, and the speeds given are pretty realistic for cars.)

Aaron F Stanton
Sunday, May 09, 2004

By the way, David Roper is right - change in acceleration is indeed called jerk.  It's typically felt in everyday life in the moment you hit the gas - you're sitting in the car, minding your own business, when suddenly - wham! - an invisible hand slams you back into your seat.  You have abruptly increased the acceleration of your vehicle.

Aaron F Stanton
Sunday, May 09, 2004

> Then what good is it measuring, "how much change in speed in this time?"

Because you want to know the answer to "How rapidly is my speed changing?"

For example, you jump off a tall building: half a second later, your speed is only 5 metres per second. If you ignored acceleration, you might think "so far, so good" ...

It's easier to think of acceleration as "(metres per second) per second" than to think of it as "metres per (second squared)".

Christopher Wells
Sunday, May 09, 2004

That makes perfect sense in terms of coding and flow.  When someone interupts me with inanities and my acceleration changes.  They are invariably referred to as 'Jerk!"

_
Sunday, May 09, 2004

Talk to me about this <MOVIE> tag you were using - are there some sites that will insert links to movie databases automatically? And likewise <BOOK> for an amazon link by title? That would be cool.

Dennis Atkins
Sunday, May 09, 2004

Based on the title of the movie and they way you implied it's connotation, is it possible it is in reference to Dirk Diggler, the porn star who's life was chronicled in Boogie Nights?

JWA
Sunday, May 09, 2004

i would love to see cary on my dick, but that's another movie

and another post that will be deleted soon when Joel reads is


Sunday, May 09, 2004

The other way to think of acceleration is as a consequence to a force. Using Newtons Second law, force = mass x acceleration. Also, trying not to confuse you even more, acceleration is change in velocity, which is the vector of speed, meaning its speed in a given direction. Therefore if you change direction you are accelerating - which is why you feel a force when going round a corner in a car. First thing you learn in mechanics at A-Level, before calclus in relation to mechanics

Chris Crawshaw
Sunday, May 09, 2004

OK, sorry i thought you were puzzled about the actual maths.

In terms of visualising it/seeing what it's good for... look up/think about newton's laws of motion.

As a random example... think about travelling up and down in a lift for example. If the lift is going at constant speed (zero acceleration) it feels to someone inside like it's doing nothing at all. But when it's actually accerlerating, you feel the force acting on you, one way or the other. If it's in free fall then it's like you're weightless inside the lift...

Think about things floating about in space. Something in space could carry on moving at a constant speed forever, without any work being done. But to make it actually /accelerate/, you need to apply a force to it and do actual work. Eg squirt fuel out the back of a rocket or something. When things accelerate they are gaining kinetic energy

Dunno what to say really, perhaps an introductory mechanics textbook would help connect the maths to real world problems and show you what it's good for.

Matt
Sunday, May 09, 2004

Is not accleration gravity? And gravity the force of attraction between two masses? So metres/second ^ 2 should be the units for the force of attraction between 2 masses and metres/second, units for the result of the force.

Car at rest. Pedal pushed. Car moves. Velocity increases. Rate of increase in velocity is acceleration. More pushing, more accleration. Car reaches the chequred flag. Champagne sprayed and drunk. Half naked cute chicks hug and kiss you. Lucky !@#$$!

Car at rest. Pedal pushed. Car moves. Velocity increases. Rate of increase in velocity is the rate of increase the attraction between the car and that hot babe with chequred  flag around her waist, and nothing else. More acceleration means increased attraction. Car reaches the chequred flag. Champagne sprayed and drunk. Half naked cute chicks hug and kiss you. Lucky !@#$$!

KayJay
Monday, May 10, 2004

==> what is the meaning of measuring the change in speed per unit of time.

Umm ...

Acceleration!

That, to me, is the textbook definition of "acceleration". The change in speed per unit of time.

Was there a real question here?

Sgt. Sausage
Monday, May 10, 2004

>Was there a real question here?

If you were me, you'd know how itching the mental blockages are that I have.

Sathyaish Chakravarthy
Monday, May 10, 2004

> So metres/second ^ 2 should be the units for the force of attraction

Not exactly: force isn't the same as acceleration. Force is the thing required to accelerate an object *of a given mass*: the larger the mass, the larger the force required to accelerate it. Force is like "weight" and is measured in "newtons"; its dimension is "metres * kilograms / (seconds squared)".

When I was in Singapore, I saw notices (e.g. in the hotel, and in the computer room, etc.) stating the strength of the floors ... with the signs saying something like "10 KN / square metre" ... because this information is needed by fire-fighters.

Christopher Wells
Monday, May 10, 2004

One small explanation may be in place: m/s^2 is just a funky way of writing 'meters per second per second'.

Jonas B.
Monday, May 10, 2004

Sathyaish Chakravarthy wrote:
"what is the meaning of measuring the change in speed per unit of time?"

Maybe some specific examples are called for:

***** Example 1 ******
When I drop an object, its downward acceleration is approximately 32.2 feet/second/second.

After one second, its downward speed is 32.2 feet/second.
After two seconds, its 32.2 + 32.2 = 64.4 feet/second
After 3 seconds, its 32.2 + 64.4 = 96.6 feet/second
After 4 seconds, its 32.2 + 96.6 = 128.8 feet/second.

In short, the object increases its speed by "32.2 feet/second" every second.

***** Example 2 *****
Many car advertisements say something like "Car goes from 0 to 60 mph in 10 seconds."  The average acceleration is 60/10 = 6mph/second

i.e., the car increases its speed by 6mph every second.

Note:  mph = miles per hour

ArnoldW
Tuesday, May 11, 2004

Thank you guys, many many times. I enjoyed reading every bit of it. You're all the most delightful company one can have. I love the nerd kingdom.

Thanks, David, for such an interesting account. Thank you Tom and Matt, for being so patient with me. Aaron, you make a wonderful teacher. Thank you so much.

Thank you Christopher. Nice joke, <one blank space/>.

<NO DENNIS/>

>Based on the title of the movie and they way you implied it's connotation, is it possible it is in reference to Dirk Diggler, the porn star who's life was chronicled in Boogie Nights?

I am sorry, I wouldn't know, JWA.

Thanks, Chris, thank, KayJay and thanks, Arnold.

Thanks, mom. Thanks, dad! I couldn't have done this without you. Thank you to the people of...ahem...<SANITY_CHECK/>

Sathyaish Chakravarthy
Tuesday, May 11, 2004

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