I define ##\theta## to be the angle a rope makes relative to z and ##\phi## is the angle relative to x. The branch is in the xz plane. From conservation of energy I got
$$ \frac{r_A^2}{2} \left[\left(\frac{\partial\theta_A}{\partial t}\right)^2 + \left(\frac{\partial\phi_A}{\partial...
AB is the seat. AC and BD are the ropes. CD is the branch. I assume the system remains under tension. The initial kick could be positioning the swing away from the minimum energy position then releasing. Mass is centered on the swing seat with some non zero moment of inertia.
A swing is suspended from a non-horizontal tree branch. Points C and D are fixed in space. All 4 line segments in the diagram have constant distance. After some initial "kick" imparts energy to the system the only force acting externally on the system is gravity.
Is it possible to predict the...
It seems to me slope is computed as a ratio. I don't see how this explicitly requires zero. In modern calculus the rise and run both approach zero but zero itself is a no go for the denominator at least. I don't see why we can't keep the numerator and denominator largish but increasingly more...
What good is the additive identity in symbolic math? Is it actually necessary? Why cant our number system be based on multiplication rather than addition and use 1 as the identity to which transformations are made to get other numbers? I think I read somewhere that that would work under group...
Why do we have the number zero? What makes it important? Can we create math like system that don't use zero but are nonetheless useful. What limits or biases does having or not having zero create when we do science?
I have been looking at my old calculus textbook because to my dismay I seem to have forgotten most of the calculus I learned. I am given 3 cases of ##(f+g)(x) ##.
Case 1 both f and g are even:
I know ##f(x) = f(-x) ## and ##g(x)=g(-x) ## for the domain of the function. I can reason by...
universe is "fine tuned" for life
http://web.mit.edu/rog/www/papers/fine_tuning.pdf
There is some evidence that the universe is "fine tuned" for life. If the fundamental constants of the universe were a little bit different then we couldn't exist. Roger White considers this evidence of a...
If I know the percentage by weight of elements in a formula I can calculate the relative ratios of atoms in the formula no problem.
What I can't figure out is how to turn that ratio into an empirical formula.
To put it mathematically how do I turn a decimal number into a an approximate...
1. Homework Statement [/b]
Consider a double-paned window consisting of two panes of glass, each with a thickness of 0.500 cm and an area of separated by a layer of air with a thickness of 1.75 cm. The temperature on one side of the window is 0.00 °C; the temperature on the other side is 20.0...
Is that how the question is exactly worded? I think this is one those questions that tries to get you to discover something by thinking about it but from the way its worded I'm just not sure.
Is it possible to use a linear accelerator to fire a magnetic fluid.
I have this idea for a science fiction story that uses a coil gun and liquid oxygen for rocket propulsion.
Is this feasible?
As always thank you for your input.
This is not a homework problem. It is personal project of mine. Pleases help
Say you have a space craft that for some advanced propulsion technology is able to accelerate at 1 gee or more indefinitely. This allows the crew walk around as in a gravity and, I think, permit slower than travel...
If you look at a chart of redshift vs distance of observed galaxies you might notice something odd. If inflation is left over momentum from the big bang then the graph would appear linear or even curve up. What actually is happening is that graph seems to flatten as you view galaxies further...
This is a tough question to answer but I keep thinking about it. Let me get back to you in about a month or so when we will be studying magnetic flux in my class.
It has to do with something called divergence. The idea is that if we make more field lines pass through the body of the saucer...
Light has mass because it has energy. E = mc^2. Light has no rest mass.
As you accelerate an object it gains mass as you approach the speed of light. If you could reach the speed of light the object's mass becomes infinite (one good reason why thats impossible). If you could accelerate an...
The two are synonyms, however momentum also means a quantitative value which is the objects mass times its velocity.
p = mv
Inertia is more qualitative, though it is sometimes just equated with mass.
after rereading your question I realize that you seem to be asking for a horizontal menu. Most people use list for menus these days. Div isn't the best tag for defining layouts. I'm not sure who you mean by everyone. Tables are still an acceptable way to layout your page. I use div to...