If I may introduce another point, I would be careful even when studying for a degree in something you're passionate about not to let yourself get 'burned out'. My wife has her degree in computer animation, but the process (which included the way the school tried to push her and her peers toward...
I have not done this kind of thing before, so this is all new to me.
Can you explain some of the steps in the routine method you mentioned so that I can look them up? Someone I know had suggested going through a rather drawn-out process of plotting--inaccurate--points using the shadow of the...
But in order to obtain the equation for a non-uniform rod's linear density, do I not have to take the piecewise function modeling its cross-section, write the equation in unit step notation, take the Laplace transform, and so on?
How would one go about finding the center of mass of a non-uniform rod when its cross-section has been modeling using a piecewise-defined function?
For a specific case let's use a drumstick, noting its volume as a sum of half of a sphere (the 'butt' end), a cylinder (the 'shaft'), the majority...
I have tried showing your posts to my Pre-Calculus professor as a 'last ditch' effort (explaining the forum rules beforehand), and after mulling it over even they don't know how to solve for ##r_i##. They did make the concession, though, that its method could be rooted in physics. Way back when...
What I think I'm trying to find I believe has to do with the 'center of percussion', but it's almost like it's other way around...
It's not the point where a force doesn't result in a rotation, but more like a point where a torque doesn't result in a translation (which I'm guessing is the...
The more I work on this the more I wonder if you had accidentally defined ##r_i## twice, as both a radial location and as a radius of its own, because I'm getting frustrated with the problem, and feel as though I can't do anything.
I tried solving for the logarithm and ##r_i## separately, but I still don't feel as if I've gotten any warmer,
because by substituting those expressions in it seems I wind up losing ##δ## ...
Regarding your expression ##\frac{ln(ξ)}{ξ}## , I know it is equal to ##\frac{ξ'}{ξ}## , but it's...
I'm hoping to derive a formula which provides the distance from the stick's center of gravity to the pivot point along its length that displays a balance between minimizing the torque needed to achieve a particular angular momentum when traveling through an angle of π/2, and yet also minimizes...
When playing a percussion instrument with drumsticks there are two main gripping types: "Matched" (where the grip of one hand is the mirror image of the other), and "Traditional" (where the grip, and consequently the motion, of one hand, usually the 'weaker' hand, is transformed from...
In order to calculate the center of mass of this non-uniform cylinder it becomes necessary to find its volume, followed by its mass (assuming it's isotropic)
I honestly had never heard of that term until now, but after reading the cursory explanation on Wikipedia that may be at least close...
I understand. I could write a piecewise-defined 2-D equation r(x) describing the changing radius from 0 to L, take the indefinite integral, then multiply it by 2π.
Vstick = 2π * [integral;0,L] r(x) dx
However, I already have this information, and the integral would just result in the exact...
I really don't have much experience with calculus ( :sarcasm: Hooray! ), but earlier I was reading an introductory article explaining the usefulness of the Lagrange multiplier in dimensional optimization,
http://www.slimy.com/~steuard/teaching/tutorials/Lagrange.html
and it reminded me that...
Whenever I try to solve for ##r_i## I keep getting stuck with it either 1) both inside and outside a logarithm, as when I started, or 2) when solved for ##r_0##, it is both a coefficient and an exponent of an exponential function.