If I have a point r=4, phi=pi/8 and z=z; in cylindrical coordinates.
sqrt( (r*cos(phi) )2 + (r*sin(phi) )2 ) = 4
So taking r*cos(phi) as the x component and r*sin(phi) as the y component seems to be enough to get the same point represented in both coordinate systems? What am I missing?
Homework Statement
It's just an example in the textbook. A vector in cylindrical coordinates.
A=arAr+aΦAΦ+azAz
to be expressed in cartesian coordinates.
Start with the Ax component:
Ax=A⋅ax=Arar⋅ax+AΦaΦ⋅ax
ar⋅ax=cosΦ
aΦ⋅ax=-sinΦ
Ax=ArcosΦ - AΦsinΦ
Looking at a figure of the unit vectors I...
A group 2 metal always forms 2+ ions, since the second electron is harder to remove how come you don't find 1+ ions of these in ionic compound formations, How does it always manage to lose both outer electrons?
So it takes a certain amount of energy to break a bond, how does water molecules...
Yea I'm sorry I should be consistent with notation. I'm only talking about the fluctuating part. So second moment is really just measure of deviation from the mean and third moment is measure of skewness?
Thank you for your reply. I understand the standard deviation, meaning the root of the second moment. But in the models the second moment is used directly.
For example the v3 is skewness and v4 is something else. Now I don't understand how v3 is skewness but I kind of understand what it is. I...
Yes, thank you.
Funny you should respond today. I was thinking about this again today and I reason as such that momentum is m*v and the rate at which momentum is traveling is (m*v)*v which is kinetic energy. I like the way you put it very much too.
I'm studying CFD and I'm on turbulence. It states that the fluctuating part of velocity squared and time averaged is the variance but variance in statistical terms is the deviation from the mean squared and averaged. So what is variance in turbulent fluctuating velocity?
This variance is also...
KE is proportional to v^2. In a gravitational field KE=1/2 m*v^2.
It's easy to find mathematically Work=Fd=mad=m(v/t)(v*t)=m*v^2.
But how to visualize it or get an intuitively "feel" for this v^2 relationship?
Homework Statement
Two equal isolated metallic bodies A & B start with no charge and zero potential. A is given a charge giving B the potential U. B is then Grounded giving A the potential U.
What potential did A have before B was grounded?
Hint: Use symmetry and use potential coefficients...
Decide the linear interpolant
f(-pi)=4 f(-pi/2)=5/4 f(0)=1 f(pi/2)=-3/4 f(pi)=0
the function is (1/pi2 ) (x-pi)2 - cos2 (x-pi/2)
Don't know how to do this. I tried lagrange basis functions f(x0)(x1-x)/(x1-x0)+f(x1)(x-x0)/(x1-x0)
But it doesn't turn out right.
The answer for the first...