Unit Definition and 1000 Threads

[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...

I know the units of measurement for this are: MPa m^0.5 However a question I am working on has it as MPa m^-0.5 What is the difference and does it affect the way I calculate the answer? Would appreciate your insight. Thanks Pete

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...

It's been a little bit since I have studied multi-particle quantum mechanics and I am a little rusty on the notation. Let's say I have a wave function, that consists of the tensor product of two spaces, one for each particle moving, ##|\psi_1,\psi_2>##. Each of these particles is moving in a...

Homework Statement How am I supposed to know my unit conversions? like for example 1 pound is equal to 453.592 grams I don't know how people do it, it's like they have it all memorized in their head I can't think of a way for me to be able to memorize any of it or know it am I supposed to do...

Hello, I am attempting to calculate unit normal and tangent vectors for a scalar field I have, Φ(x,y). For my unit normal, I simply used: \hat{n}=\frac{\nabla \phi}{|\nabla \phi|} However, I'm struggling with using this approach to calculate the unit tangent. I need to express it in terms of the...

Homework Statement Is intensity related to this question? The answer is B. Homework Equations I^2 ∝ A^2 I=P/A, where I is intensity, P is power, and A is area The Attempt at a Solution I tried using I=P/A, and after substituting, I get, A^2=E/S, which gives E=A^2 S And then, the new wave...

Homework Statement Calculate the approximate number of board feet (one board foot is defined as a volume of ##1 in \times 1 ft \times1 ft## of lumber that would be available in a log that has a diameter of ##34 cm## and a length of ##3 m##. Assume the log is a right cylinder and that the saw...

Dear Friends, The stress-wave propagation speed is calculated using : sqrt (elastic modulus/density) The unit of elastic modulus is GPa, and that of density is gram/cm^dim Can anyone please tell me how I can convert the resulting value to m/s (meter/second)? Regards

I'm a mechanical engineering student 1st yr . I need suggestions regarding books for basic mechanical engineering and engineering mechanics . A book with basics n proper language.

Homework Statement Coaxial cable has double layered dielectric. a=2mm, b=4mm, c=8mm, εr1=3, εr2=4.5, Uab=1000V 1. Calculate capacitance per unit length of a cable. 2. Calculate inner and outer charge densities of a cable. 2. Homework Equations Gauss law C'=Q'/U σ = nD σp = nP 3. The Attempt...

Homework Statement Two cylindrical conductors, of distance between them d and radius a (a<<d), have dielectric layer of relative permitivitty εr and thickness a. Calculate capacitance per unit length of this system. Homework Equations Capacitance per unit length, C'=Q'/U Gauss law, cylindrical...

I'm reading a paper on a simulation of graphene and carbon nanotube growth on SiC, in the paper they give a few computational details about the structural optimization of the SiC model using a conjugate gradient method and they state the maximal force component as 1x10^{-4}Ha/a_o What is this...

Homework Statement From Kleppner and Kolenkow Chapter 1 (Just checking to see if I'm right) Given vector A=<3, 4, -4> a) Find a unit vector B that lies in the x-y plane and is perpendicular to A. b) Find a unit vector C that is perpendicular to both A and B. c)Show that A is perpendicular to...

Dear PF Forum, I have a problem concerning the unit of acceleration. All this time in Relativity, we have been talking about c. Either as a distance unit (light travel for 1 second) or as speed. Sometimes we describe it as 300,000. Sometimes as 300,000,000 or 186,000. The time unit is always...

I get the dynamics of what the question is asking. What I don't get is how to know what pi/8 is. What I've been doing this entire time is plugging it into the calculator as a fraction, and getting the decimal value of it and comparing it to other values I know. I know that pi radians = 180...

if acceleration is defined as rate of change in velocity, then how do you find out the unit of rate of change of acceleration?

Hi, I am a bit confused about the units of MI...I read that MI of rectangle is b*d^3/12,so unit is mm^4..Also i read in wiki that unit of MI is kg.mm^2... Both are correct,but why this difference is?

Hi all, In quantum mechanics, we consider the squared modulo of a wave function has meaning of probability, so does it mean a wave packet should be unitless? I am reading some materials online about the Gaussian wave packet...

Sorry if this was addressed in another thread, but I couldn't find a discussion of it in a preliminary search. If it is discussed elsewhere, I'll appreciate being directed to it. Okay, well here's my question. If I take the divergence of the unit radial vector field, I get the result: \vec...

Hi ALL i need to unit Conversion : from: 28.8 Volts/(Meter/Second) to (....) Volts/(Inch/Second) from: 28.8 Volts/(Meter/Second) to (....) milliVolts/(milliMeter/Second) Thanks

What's j2 in this problem? 1. Homework Statement Homework Equations The Attempt at a Solution a. What's j2 in this problem? b. How did we use the fact that we have a unit impulse? c. What are our first thoughts and strategies when seeing the problem ? What is our strategy? It looks...

I was going through this link -...

http://tutorial.math.lamar.edu/Classes/CalcIII/CurlDivergence.aspx In the above link, in the 2nd to last blue box on the page (where it tells how to solve a line integral with respect to a vector field using the curl), it says that the line integral of vector field F with respect to r (with an...

Homework Statement Consider the following hypothetical question: (5 lbs•m^2) =a (5 rad/s^2) =b If (a) and (b) are each multiplied by 2 what do the units become? Similarly if (a) and (b) are squared what do the units become ?

Hi guys, My first time here. Looks like a nice forum with friendly members. I have a question. I'm kinda confused by this (and I know it's a shame since I'm on my third year University, almost making my degree). What I remember from my kinematics/dynamics classes this (or similar) equation...

Homework Statement I am having difficulty understanding the very first step of the following solved problem (I understand the rest of the solution). How did they obtain the expressions for ##\hat{n}## (the direction of polarization), and ##\hat{k}## (the unit vector pointing in the direction...

Hello every one i have question what is the unit vector of time component like c^2 t^2 -x^2-y^2-z^2 = 0 OR if we need to calculate the d'alembert cross some 4 vector have 3 space component x y z and unit vector i j k and ct component what is the unit vector in Ct direction ?

Hi I'm converting some numbers to atomic units, and it's important that I get it right. Would be happy if someone could reassure me. I want to convert the units of an electric field measured in kV/cm to atomic units. Here is what I got: \frac{kV}{cm}=\frac{10^3}{10^{-2}}\frac{J}{C\cdot...

The Ford Model T, affectionately known as the Tin Lizzie, is thought to have been the first widely affordable/accessible automobile. Production of the Model T started in 1908. I'm looking for a cosmo-friendly time unit that is short enough to be real and familiar to all of us, but at least an...

1- Let the linear operator on R^2 have the following matrix:A = 1 0 -1 3 What is the area of the figure that results from applying this transformation to the unit square? 2- I am abit confused here, I thought that the matrix for the unit square would be, 0 0 1 0 0 1 1 1... But...

Hello everyone I have a question regarding radians and the unit of rotational energy (which has been probably asked several times elsewhere but is still confusing for me :-) ). As I understand radian (rad) is a UNIT that is dimensionless (thus cannot be omitted), correct ? Now if I want to...

Homework Statement Find a unit normal to the plane containing a and b. a=(3;-1; 2) and b=(1; 3;-2) Homework Equations \frac{V}{|V|} where V = a+b The Attempt at a Solution (3;-1; 2) +1; 3;-2)=(4,2,0)=V |V| = \sqrt{4^2+2^} = 2\sqrt{5} there fore the unit vector is (\frac{2}{\sqrt{5}}...

Is there an error, perhaps typographical, in the famous 1939 Oppenheimer-Snyder paper "On Continued Gravitational Contraction" (Phys Rev v56 Sept 1, 1956 pp 455-459)? Do the units balance in equation 37? The last term inside the last parantheses ##\frac{3r_0^{1/2} \tau}{2R_b^2}## where...

Homework Statement For f(x,y)=x^2-xy+y^2 and the vector u=i+j. ii)Find two unit vectors such D_vf=0 Homework Equations N/A. The Attempt at a Solution Not sure if relevant but the previous questions were asking for the unit vector u - which I got \hat{u}=\frac{1}{\sqrt{2}}(i+j) for the maximum...

Hi, I was wondering if anyone could help with a vector question that I have. If I have a unit vector defined in cartesian co-ordinates as p= (0,1,0) how would I go about converting this vector to a cylindrical geometry. I understand that I will probably need to use p_r=sqrt(px^2+py^2) and...

Homework Statement An Indy 500 race car's velocity increases from 4m/s to 36m/s over a 4 second time interval. What is its acceleration? 4m/s is the initial velocity, 36 m/s is the final velocity, and time is 4 seconds. Homework Equations final velocity = initial velocity + (acceleration x...

Flux is the no. Of electric field lines per unit area..how can it have a unit

Just simple questions and I need clarifications why is that your answer please. 1,602 ×10^−19 C write to SI Unit Prefixes

Homework Statement A rectangular loop of wire is placed next to a straight wire, as shown above. There is a current I in both the straight wire and the loop. The dimensions shown in the figure are a, b = 2.2a, and c = 8a. What is the magnitude of the force on the loop? Express your answer in...

What is the unit value of coulomb constant(k)? I just want to know the CGS unit value of k. In my book it is said the CGS unit value of k is 1. By i don't know how it come.?

Homework Statement Homework Equations Laplace Trasformations The Attempt at a Solution a. done b. f(t)= t -3*t*u(t-1) + 4*u(t-1) -3*u(t-2) -2*t*(t-2) c. 1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s d. 1/(s-1) * (1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s) These are the...

Hi Assume an x-coordinate from the unit circle is picked from a uniform distribution. This is the outcome of the random variable X with probability density function Xden(x) = 0.5 (-1 < x < 1). The random variable Y is related to the random variable X by Y = f(X) = √(1-X2) and X = g(Y) =...