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matheson: Post your entire calculation process. Not just the answer. Post why you think something is a certain way, ie: why did you think T^2 is proportional to R^3? ... who cares if you are wrong, that is fine. I definitely don't know what I'm doing half the time, and I'm sure a good portion of the people on this forum are the same way. Part of learning is making mistakes. But making the same mistake over and over again is not helpful to yourself. A big part of physics (from the little I know, and have had) is having a good approach to fixing your mistakes.

So, here's an example of a possible though process to an equation. (Please bear with me here, this might be a little tedious and not needed, but it will be easy to understand and therefore the "heart" of this example will not be lost in interpretation.

ok... so we have:

T^2 = R^3

hmmm... time^2.

Well time is something that occurs, at a steady pace (not getting into reference frames, near speed of light calculations, yadda yadda)... and it squared means that the quantity of itself is growing very fast. Like if we assume that T is measured in seconds, and we plug in 5 seconds into T^2 we have 25 seconds. If we plug 10 seconds into T^2 we have 100 seconds... cool... ok that's what T^2 does... it grows fast.

Now R^3... the radius to the power of 3. So we plug in a small radius and boom, a huge radius is returned... ok... so that's what R^3 does... it grows even faster then time.

ok so now if we just analyze time, then we have (i.e. getting rid of any mathematical operator on our variable that we are interpretting.)

T=sqrt(R^3)... so lets say we plug in a radius of 5... well we know that R^3 grows really fast... and of course we can compute it as 125 that's simple. The thing is though. Yes in this case it is quite simple to compute 5 to the power of 3, but a lot of times we will not have numbers... We will just have to understand what the variable means. Most times it is best anyhow, not to use "numbers" until the end, so that means you HAVE to understand each expression, so when you do the robotic chore of plugging in numbers, you understand WHY you are plugging those numbers in.

so anyhow...

Now we just have the sqrt() to deal with. So the sqrt is asking for a number multiplied by a number equals the square rooted number (in this case 125), so hmm I don't have a calculator... but its around 11.2.... so yeah... we plug in a radius of 5 and out comes roughly 11.2.

yes, ok... so plugging in numbers yielded.

11.2 seconds (or whatever time unit) = 5 meters (or whatever radius)

???

now that doesn't make any sense.. you can't say red = blue.

ok so yeah, I killed a really simple eqauation with a lot of detail, but my point is this... when you begin to think about what everything is doing to one another, you can start to narrow down your "problem" into something formidable. So give that a shot for your expressions and see what you are coming up with. Like, many times you mentioned the 1/r^2 "law" well what does that mean? ... what does that mean when you are comparing it to objects that uphold to this same "law"....

so anyways... write down your expressions, and answers for everything.. understand each expression, and narrow down your problem...yadda yadda

So, here's an example of a possible though process to an equation. (Please bear with me here, this might be a little tedious and not needed, but it will be easy to understand and therefore the "heart" of this example will not be lost in interpretation.

ok... so we have:

T^2 = R^3

hmmm... time^2.

Well time is something that occurs, at a steady pace (not getting into reference frames, near speed of light calculations, yadda yadda)... and it squared means that the quantity of itself is growing very fast. Like if we assume that T is measured in seconds, and we plug in 5 seconds into T^2 we have 25 seconds. If we plug 10 seconds into T^2 we have 100 seconds... cool... ok that's what T^2 does... it grows fast.

Now R^3... the radius to the power of 3. So we plug in a small radius and boom, a huge radius is returned... ok... so that's what R^3 does... it grows even faster then time.

ok so now if we just analyze time, then we have (i.e. getting rid of any mathematical operator on our variable that we are interpretting.)

T=sqrt(R^3)... so lets say we plug in a radius of 5... well we know that R^3 grows really fast... and of course we can compute it as 125 that's simple. The thing is though. Yes in this case it is quite simple to compute 5 to the power of 3, but a lot of times we will not have numbers... We will just have to understand what the variable means. Most times it is best anyhow, not to use "numbers" until the end, so that means you HAVE to understand each expression, so when you do the robotic chore of plugging in numbers, you understand WHY you are plugging those numbers in.

so anyhow...

Now we just have the sqrt() to deal with. So the sqrt is asking for a number multiplied by a number equals the square rooted number (in this case 125), so hmm I don't have a calculator... but its around 11.2.... so yeah... we plug in a radius of 5 and out comes roughly 11.2.

yes, ok... so plugging in numbers yielded.

11.2 seconds (or whatever time unit) = 5 meters (or whatever radius)

???

now that doesn't make any sense.. you can't say red = blue.

ok so yeah, I killed a really simple eqauation with a lot of detail, but my point is this... when you begin to think about what everything is doing to one another, you can start to narrow down your "problem" into something formidable. So give that a shot for your expressions and see what you are coming up with. Like, many times you mentioned the 1/r^2 "law" well what does that mean? ... what does that mean when you are comparing it to objects that uphold to this same "law"....

so anyways... write down your expressions, and answers for everything.. understand each expression, and narrow down your problem...yadda yadda

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