Unit Definition and 1000 Threads

Homework Statement Let ##z_1,z_2,z_3## be three complex numbers that lie on the unit circle in the complex plane, and ##z_1+z_2+z_3=0##. Show that the numbers are located at the vertices of an equilateral triangle. Homework EquationsThe Attempt at a Solution As far as I understand, I need to...

Homework Statement I can't figure out why the unit of Reluctance is At/Wb and not (At/Wb)m2 This is what I have from my textbook, with the red oval area being the part that I'm totally confused about Homework EquationsThe Attempt at a Solution So the m/m cancels out to 1 making it...

With Watts Bar Unit 2 expected to begin operating this month, will it have any significant effect on the industry? It's somewhat a milestone.

To make it useful for any angles. I need a good explanation for this.

Hi everybody! I'm currently learning special relativity, and I'm going through the chapter of tangent, normal and binormal vectors. In my teacher's script, the definition of the normal vector eN says: \vec{e_N} = \frac{d}{ds} \vec{e_T} \cdot \frac{1}{\mid \frac{d}{ds} \cdot \vec{e_T} \mid} =...

Let the surface $S \subset \mathbb{R}^3$ be the graph of the function $f: \mathbb{R}^2 \to \mathbb{R}$, $f(x,y)= \sqrt{x^2+y^2+1}$. Let $U$ be the finite region of $S$ below the plane $z = 2$ and let $D$ be the finite region of the plane $z = 2$ for which $x^2 + y^2 \le 3$. Let $n_U (x, y, z)$...

For example, when you have a function that describes the amount of water (liters) in a cup relative to time (the amount fluctuates for whatever reason). If you wanted to find the average amount of water in the cup in the interval [a,b], you would take the integral of the function in that...

From the de Broglie wave formula we know, Rhamda=h/p [SIZE=16px]In actual examples of course the answer would be 'something [meters]' I am having hardtime to understand how unit of h/mv [J*s]/[kg]*[m/s] turn into wavelength unit [m] I studied the Mass-Energy relation part earlier, But still...

I got one correct for my code...what i am missing...any tips or guide? Write a unit test for addInventory(). Call redSweater.addInventory() with parameter sweaterShipment. Print the shown error if the subsequent quantity is incorrect. Sample output for failed unit test given initial quantity is...

Dear PF Forum, I'm trying to make sense about Hawking radiation in Black Hole. And that leads me into entropy. I read this equation in https://en.wikipedia.org/wiki/Entropy What does that mean? S is the change of Entropy What does Qrev mean there? Is it in Calorie? then Joule? T, I think is in...

Homework Statement The 500-mg balance wheel of a certain clock is made up of a thin metal ring of radius 16 mm connected by spokes of negligible mass to a fine suspension fiber as in(Figure 1) . The back-and-forth twisting of the fiber causes the wheel to move in simple harmonic motion with...

1) My teacher said that to analyze the properties of entire crystalline solid, we just need to analyze the properties of a unit cell, which is the smallest repeating unit of a crystalline solid. 2) But crystalline solids are known to be anisotropic, i.e. they have different properties in...

Hey, I'm currently working a problem that looks like this: There's more to this problem, but I'm sure I can solve the rest of it, there are just things I'm uncertain about. Actually, it's only one thing I'm uncertain about. I'm looking through my notes, and when converting the voltage...

In my lectures and notes my professor keeps writing out density as lbs/ft3 and unit weight as lbs/ft3. For a material such as concrete it could have a density of 167 lbs/ft3 but a unit weight of 103 lbs/ft3. I am confused as to how these two values are different even though they have the exact...

Homework Statement is the equation in the 3rd photo wrong ? since there are 2 exits , why shouldn't the eqaution become (P1 / y) + z + (8.33^2) / (2x9.81) = 0 + z +[ 2 (12^2) / (2x9.81) ] ? Homework EquationsThe Attempt at a Solution

What's the unit used to measure α ? if α=(Kd/C)0.5 where Kd is the dissociation constant and C is the total concentration of electrolyte .

I'm doing some numerics on a system, where the relevant length scale is nanometers and energy scale is electronvolts. But are these two scales not affected by the choice of each other? I'm kind of confused. What should I choose as units for a system like mine.

When creating a right triangle in a unit circle how do you know where to place the leg from the terminal side? My textbook and Khan academy don't really explain this and it's just sort of assumed that I'd know. For example, If theta is equal to 135 degrees, where does the leg to complete the...

If the unit of gravitational force is the Newton (where the value will be positive) would the unit for a hypothetical anti- gravitational force be a negative Newton?

Homework Statement A block of wood measuring 5 cm x 3 cm x 10 cm has a mass of 90 grams. What is the density of the wood in kg/m^3? Homework Equations D=m/V The Attempt at a Solution I know this seems trivial but I need to get the math down to a T. I know that it s 06.g/cm^3 but how is this...

Work unit is said to be Joule and Energy unit is also Joule. Work formulas in F x S ( Force x Displacement) . We know 1 J = 1 F x `1 s Now Energy is also measured in Joule(J) So can we state : E = 1 F x 1 s as 1 J = 1 F x 1 s that is E = W Then why work and energy are different by definition...

Homework Statement Say I have a vector F something like F = c1(t) x^ + c2(t) y^ were c1 and c2 are some scalar functions of time were you plug in time to into the equation and are given some magnitude. My question seems to be can we define unit vectors/basis vector as a function of time as...

Homework Statement why the author said the equation 3-4 as energy per unit weight ? as gamma = rho g , gamma has the unit of kg(m^-3)(ms^-2) = kg(m^-2)(s^-2) , gamma is clearly not weight ... Homework EquationsThe Attempt at a Solution

Homework Statement g(t) = (t+1)us(t) - (t-1)us(t-1) - 2us(t-1) - (t - 2)us(t-2) + (t-3)us)(t - 3) + us(t-3) Homework Equations unit step function us(t-3) is same as u3 (t) Shift in time: L[f(t - T)us(t-T)] = e-TsF(s) us(t) ↔ 1/s t ⇔ 1/s2 The Attempt at a Solution 1/s2 + 1/s - e-s/s2 + e-s/s -...

Quick question (a little rusty on this): Why don't unit vectors in Cartesian Coordinates not change with time? For example, suppose \mathbf{r} (t) = x(t) \mathbf{x} + y(t) \mathbf{y} + z(t) \mathbf{z} How exactly do we know that the unit vectors don't change with time? Or in other words...

Homework Statement Find two unit vectors in 2-space that make an angle of 45(deg) with 7i + 6j. Homework Equations Unit Vector = u = (1/||v||)*v Dot Product = u . v = ||u|| ||v|| cos(theta) The Attempt at a Solution I've been thinking about a way to do this. I originally thought that...

I want to do a little inquiry involving water, and I need to know what the 'cooling down speed' of water is (how much heat a certain volume or surface of water emits per second). Can anyone tell me if there is a unit and/or formula for this?

Please can you help me with this question. A surface h in the three dimensions is given by the equation z=g(x,y) Find the unit normal at any point h in two separate ways: a)By identifying h with an equipotential for some scalar field φ to be determined and computing ∇φ. b)By expressing the...

Hi all, I was wandering on the web to collect some solid and justifiable reasons to answer a question "Why we always choose a unit circle."? I saw several websites and meanwhile I saw this post https://www.physicsforums.com/threads/trig-unit-circle-why.475575/. I saved it. But overall, I...

In the same sense that Newtons (N) are the unit for measuring gravitational force, is there a unit for measuring electromagnetic force and if so what is it and what symbol denotes it? Thank you for your help and time!

I am confused about the concept of a mole. Avogadro's # says that 1 mole has 6.023*10^23 particles. Does it make sense to talk about moles in a non-integer sense? For example, can you say that 1/2 mole has 1/2*(6.023*10^23) particles?

Hi Folks, I got stuck towards the end where it ask to derive the unit normal (eqn 3.2.29 I don't know how they arrived at n_x. I have looked at trig identities...and I have assumed the following n_x=\frac{N_x}{|N_x|} I don't see the (r+p) term anywhere in neither the top nor bottom. PS: I...

Hi Folks, I got stuck towards the end where it ask to derive the unit normal. I don't know how they arrived at n_x. I have looked at trig identities... n_x=\frac{N_x}{|N_x|}= 1) I don't see the (r+p) term anywhere in neither the top nor bottom. 2) Is the bottom just based on simple trig...

Homework Statement I am supposed to find the tangent and normal unit vector to r(t)=<2sint,5t,cost>.Homework Equations . The Attempt at a Solution r1(t)=<2cost,5,-sint> which is a tangent vector to the curve, and then to make it a unit vector I would multiply by 1/(sqrt(4cos^2t+25+sin^2t)...

Homework Statement Show that δ(x-x') = d/dx Θ(x-x') Homework Equations ∫ f(x') δ(x-x') dx' = f(x) Θ(x-x') vanishes if x-x' is negative and 1 if x-x' is positive The Attempt at a Solution I saw a relation of the δ function but I don't know why is it like that. Integral of δ(x-x') from -∞ to x...

I'm confused about what situations you should use unit vectors in... and it seems that when I approach the same problem using unit vectors vs. without unit vectors, I get different answers. Why? To illustrate my confusion, here's an example that I tried solving using unit vectors, and without...

If you took: VBase / ZBase does that give you IActual or IBase or what? Because it seemed to give me IActual. Cheers

I wanted to study electrical behavior of thin films. Can anybody suggest me suitable source measure unit please? (also of low budget) Power supply: Voltage (few volts) measurement: current (micro- milliamps)

Homework Statement A ski gondola is connected to the top of a hill by a steel cable of length L and radius R . As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took T seconds for the pulse to return. What is...

I am having the hardest time calculating q, the load per unit length. This question is in relation to my previous question I posted here. I have a cylinder laying horizontally that is fixed on its ends. The cylinder is filled with water. To calculate the deflection I am simplifying the problem...

Please take a look below example (the attached image below). How do I know that the angle ##\sin (\frac{7π}{4})## is corresponds to the coordinates ##(\frac{\sqrt {2}}{2}, -\frac{\sqrt{2}}{2})##? I know that ##\frac{7π}{4}## is 315°.

[Moderator note: Post moved from New Member Introductions forum, so no template] I am having trouble understanding how to multiply unit vectors. I know that: (please excuse the notation) i^×j^ = k^ j^×k^ = i^ k^×i^ = j^ The question I am stuck on is: What is (i^×j^)×k^? So far I have (i^×j^)...

Homework Statement Hi! I have the 3x3 matrix for L below, which I calculated. But now I need to figure out how the equation below actually means! Is it just the inverse of L (L^-1)? I cannot proceed if I don't know this step. Homework Equations See image The Attempt at a Solution I put in...

1. The problem statement, all variables and given/known dat A car travels 20 mi at 60 degrees north of west, then 35 mi at 45 degrees north of east. Express each displacement vector in unit vector notation. Take the +x-axis due east and the +y-axis due north. Use the component method to obtain...

Homework Statement Consider a unit sphere centered at the origin. In terms of the Cartesian unit vectors i, j and k, find the unit normal vector on the surface Homework Equations A dot B = AB cos(theta) A cross B = AB (normal vector) sin(theta) Unit sphere radius = 1 The Attempt at a...

Homework Statement The air near a water heater in the basement of an old home is measured for carbon monoxide (CO) and found to contain 0.1% by volume CO at 22*C and 1 atm. Express the CO concentration in the basement in micro-gram/m^3 . Homework Equations PV=nRT P = absolute pressure (atm); V...

Homework Statement if a =3i-4j find a unit vector perpendicular a Homework Equations Vector The Attempt at a Solution <a> = <3 , -4> <n> = <x, y> : x² + y² = 1 <a>•<n> = 3x-4y = 0 y = (3/4)x x² + (9/16)x² = 1 25x² = 16 x = -4/5, 4/5 y = -3/5, 3/5 There are two unit vectors normal...

Homework Statement Convert 1 ##Gev## to Kelvin, and convert ##GeV^{-1}## to meters, seconds, and convert ##GeV^4## to density ##(kg/ m^3).## Homework Equations natural units ##c=h=k_B=1## The Attempt at a Solution I know to convert energy to meters, I can use ##\lambda =hc/E##, I get the...

Homework Statement Does the line through the points (−1, −1, −2) and (1, 2, 1) intersect the unit sphere? If so, find the point(s) of intersection. Homework EquationsThe Attempt at a Solution do i also use r = r0 + vt but instead , use equation of sphere this time? so it would be: v=<2,3,3>...

Homework Statement Evaluate the integral. \int_{-\infty}^\infty f(2 -t) \delta(3 -t) \, dt Homework Equations The Unit Impulse function is defined \hspace{18mm} \delta(0) = 0 \hspace{10mm} t \neq 0 \hspace{-15mm} \int_{-\infty}^\infty \delta(t) \, dt = 1 The Attempt at a Solution Using...