Normal Definition and 1000 Threads

Homework Statement Let ##\{N_i ~|~ i \in I\}## be family of normal subgroups of G such that (i) ##G = \left\langle \bigcup_{i \in I} N_i \right\rangle## (ii) for each ##k \in I##, ##N_k \cap \left\langle \bigcup_{i \neq k} N_i \right\rangle = \{e\}## Then ##G \simeq \prod_{i \in I}^w...

Homework Statement The system shown is initially at rest when the bent bar starts to rotate about the vertical axis AB with constant angular acceleration a 0 = 3 rad/ s2 . The coefficient of static friction between the collar of mass m = 2 kg and the bent bar is f.Ls = 0.35, and the collar is...

Homework Statement A 74.0 kg person is standing inside an elevator. The elevator is moving from the 3rd floor to the 21st floor. As the elevator passes the 4th floor it is moving at 2.30 m/s and is increasing speed at a rate of 1.43 m/s2 . At this moment, what is the normal force that acts on...

Hello! I am not really sure I understand the idea of tensors and the difference between them and normal matrices, for example (for rank 2 tensors). Can someone explain this to me, or give me a good resource for this? I don't want a complete introduction to GR math, I just want to understand the...

I am a fresh graduate on my way to get a permanent placement as a Design Engineer. I've been interning and working temporally before but this "real" job offer invites all sorts of ideas about settling down. I just can't see myself going there every day sitting by the pc just to wake up and...

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1263 chips and a standard deviation of 117chips. ​(a) Determine the 26th percentile for the number of chocolate chips in a bag. ​(b) Determine the number of chocolate chips in...

Hello. This did not come from a topology book, but we were asked to prove Urysohn's Lemma. We are familiar with standard proofs for this, which are all likely simpler to exhibit than our attempt here, but we were just curious about where our method here went wrong. At a glance, the lemma...

(I am not very sure if this is a high-school level question or a undergraduate level question. Sorry.) Does our normal differentiation rules, like the product rule and quotient rule apply to vectors? Say for example, differentiate ##r \times \dot r## ##r## is radius vector, ##\dot r## is the...

Homework Statement A hemispherical bowl of mass m and radius R is placed on a rough horizontal surface. Initially the centre C of the bowl is vertically above the point of contact with the ground(see figure). Now the bowl is released from rest. Find the normal force acting on the hemisphere...

In my experiments, on a flat plane, when I incrementally increase the normal force acting on a rubber block, I am measuring a decrease in the static coefficient of friction. I am also measuring the friction force, which increases as normal force increases BUT this is not a proportional increase...

So ##\vec Y##~MVN(X##\vec\beta##, ##\sigma^2##I) and ##\hat {\vec Y}##~MVN(X##\vec\beta##, ##\sigma^2##H) and I want to show ##\hat{\vec e}##~MVN(##\vec 0##, ##\sigma^2##(I-H)) Where ##\hat{\vec e}## is the vector of observed residuals( ##\vec e=\vec Y- \hat{\vec Y}=(I-H) \vec Y ##). And...

I just found that applying an axial load of magnitude σ on both sides of a ductile rod will produce a max in plane shear stress of magnitude σ/2. Why is this? How can there be shear stress if only a normal force is applied?

I am a high school student in Hong Kong studying Physics. I am having some problems about atmospheric pressure. Imagine there is a cube block with volume 1 m3 and top surface area 1 m2 . The cube block is being placed on the floor and it has mass of 1 kg. What is the normal reaction force F...

Homework Statement Hi guys I am a bit stuck on how I am suppose to show, that thse funcitons are normal to level surface. I am I suppose to do a derivation of some sort, alls my notes say in a tiny box, that grad f is always in the direction to the normal of the surface. Do I have to calculate...

The tangent and the normal to the conic \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 at a point (a\cos\left({\theta}\right), b\sin\left({\theta}\right)) meet the major axis in the points P and P', where PP'=a Show that e^2cos^2\theta + cos\theta -1 = 0, where e is the eccentricity of the conic

Homework Statement Let's say that I have a potential ##U(x) = \beta (x^2-\alpha ^2)^2## with minima at ##x=\pm \alpha##. I need to find the normal modes and vibrational frequencies. How do I do this? Homework Equations ##U(x) = \beta (x^2-\alpha ^2)^2## ##F=-kx=-m\omega ^2 x## ##\omega =...

Working through Schutz "First course in general relativity" + Carroll, Hartle and Collier, with some help from Wikipedia and older posts on this forum. I am confused about the gradient one-form and whether or not it is normal to a surface. In the words of Wikipedia (gradient): If f is...

The Central Limit Theorem specifically calls out a sample mean to be following normal distribution (for n>=30 ), But I am referring to certain text, and it is calculating z values for sample skewness and sample kurtosis assuming that these follow Normal distribution. Is it correct? In short...

Can someone explain to me why normal Zeeman effect splits spectral line into three components and not into 4, 5 or any other number?

Homework Statement A small car with mass .800 kg travels at a constant speed of 12m/s on the inside of a track that is a vertical circle with radius 5.0m. If the normal force exerted by the track on the car when it is at the top of the track is 6.00N, what is the normal force at the bottom of...

Hi all, This is a followup to a question from a couple of months ago regarding vacuum energy and cutoffs, basically to clarify some ideas. Given the usual picture of the vacuum as containing quantized harmonic oscillators at every point, it is not possible to apply a 'fixed' energy cutoff (at...

Homework Statement 2. Homework Equations [/B] Consider a particle that is described by $$x(t)=(2.0-0.1t) \cos(0.5t)$$ and $$y(t)=(2.0-0.1t) \sin(0.5t)$$ t in seconds and x,y in meters. In previous subquestions we were asked to determine an expression for the module of the velocity vector and...

I am unable to find a paper on this only the abstract, but it seems to be saying that there is no Dark Matter? The tightness of this relation is difficult to understand in terms of dark matter as it's currently understood, the researchers said. It also challenges the current understanding of...

Homework Statement The texts are taken from http://ingforum.haninge.kth.se/armin/fluid/exer/deriv_navier_stokes.pdf and https://simple.wikipedia.org/wiki/Stress_(mechanics)Homework EquationsThe Attempt at a Solution The formula for stress is ##\sigma=\frac{F}{A}## (I). From the document...

Hi all, I have problem to solve this question: Wb=150N Wa=50N T=150N alph =? µ =? - There is friction between A and B only(Between A and the ramp there isn't). - A and B not moving(first Newton's law). 3. I tried to solve as: But the answer is wrong, can anyone help me please, and...

For a particle undergoing a constant velocity circular motion. I thought friction always acted in the direction of motion which would be in the tangential direction.

Homework Statement A car starts at rest at point A, with a tangential component of acceleration a_t = 0.6m/s^2. Students approximate the acceleration of the car to be 0.6 m/s^2. What are the normal and tangential components of it's speed and acceleration at point B? NOTE : the ends are...

Maybe "dunce" is the wrong word, but I'm pretty weak on stat mech/thermo. I've had a few courses in them but not to the point where I can understand anything but the most rudimentary basics (each time I took a course in them I happened to have been distracted with other things). I'm a thirdish...

Homework Statement The problem asks for the tangential and normal acceleration of the acceleration. We were given that: $$a_x=c*cos[d*t]$$ and $$a_y=c*sin[d*t]$$ where c and d are constants. Homework Equations The book gives us $$a_t=(r\ddot{\theta}+2\dot{r}\dot{\theta})$$, (1)...

Homework Statement a cylinder sits inside of another fixed cylinder without friction and an internal force acts on the cylinder as shown in the diagram. Draw the normal force vector and write down the force and moment equations. I drew in my normal vector to counteract the A force vector and...

Hi All, This question is about vector calculus, gradient, directional derivative and normal line. If the gradient is the direction of the steepest ascent: >> gradient(x, y) = [ derivative_f_x(x, y), derivative_f_y(x, y) ] Then it really confuse me as when calculating the normal line...

So let's say I do some measurements and obtain a set of measured values. The measurement is characterized by random errors so by making enough measurements, they approach a normal distribution. In other words, my set of measured values can be approximated by a normal distribution characterized...

So, the Wiki page on the Poynting vector has this image: I remember hearing/reading somewhere that the energy transmission in a circuit like this is actually not traveling through the wire, but that it actually happens through the electromagnetic field, I.e. essentially the Poynting vectors...

Hey! :o I am looking at the following: The average tallest men live in Netherlands and Montenegro mit $1.83$m=$183$cm. The average shortest men live in Indonesia mit $1.58$m=$158$cm. The standard deviation of the height in Netherlands/Montenegro is $9.7$cm and in Indonesia it is $7.8$cm...

Homework Statement Homework Equations Equation of Equilibrium (Horizontal and Vertical Forces, Moments) Normal Stress = F/A The Attempt at a Solution I have already solved the solution for this problem. For part (a), I simply found the force in the link, and used the cross area where the...

If 3 blocks have some mass(a,b,c) are kept on one another (Vertically i mean)...Why block a doesn't experience the normal force exerted by the ground on block c? won't that force get transferred through b to a?

If the normalized probability density of the normal distribution is ## p(x) = \frac {1}{\sqrt{2\pi}\sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} ##, then if ##\sigma = 0.0001## and in the special case ## x = \mu##, wouldn't the probability density at this point, ##p(\mu)##, exceed 1 since it is equal...

I have calculated characteristic function of normal distribution f_{X}(k)=e^{(ika-\frac{\sigma ^{2}k^{2}}{2})} and now I would like to find the moments, so I know that you could expand characteristic function by Taylor series f_{X}(k)=exp(1+\frac{1}{1!}(ika -...

1. Homework Statement This isn't really a problem but an example in an online lecture. I'm trying to understand everything for when I get to harder questions but am having trouble understanding the "d/b" part of the equation. Homework Equations How does dividing d by b help solve for the...

In a digital communication channel, assume that the number of bits received in error can be modeled by a binomial random variable, and assumed that a bit is received in error is 1×〖10〗^(−5) . if 16 million bits are transmitted, What is the probability that more than 150 errors occur? Find the...

Assuming that the number of marks scored by a candidate is normally distributed, find the mean and the standard deviation, if the number of first class students(60% or more marks) is 25, the number of failed students(less than 30%marks) is 90 and the total number of candidates appearing for the...

Hey! :o We have that $E=\mathbb{Q}(a)$, where $a\in \mathbb{C}$ is a root of the irreducible polynomial $x^3-3x-1\in \mathbb{Q}[x]$. I want to show that $E/\mathbb{Q}$ is normal. I have done the following: Let $b\in E$. A basis of the extension is $1, a, a^2$. So, $b$ can be written as...

Can somebody pls explain this to me?

I'm confused; forgive me if this dumb. I'm trying to reason what "force" is, on a molecular level. I'm only concerned about normal forces here (pushes and pulls), not field forces. Forces in Newtons are vector quantities and only represent relationships between two things right? It isn't...

This is kind of a silly question. I always get "regular" spaces and "normal" spaces confused in topology. This will be a problem if I am asked on a qualifier to prove something about one of these spaces. Is there any linguistic or historical justification to why a regular space deals with a...

Homework Statement I know that on a horizontal surface. if the net force is 0 in the y direction the weight of object=the normal force, but wouldn't the normal force always equal the magnitude of gravity on an object, just in opposite directions? Because if the weight is stronger than the...

so a pilot is spining in a circle at a constant speed, the g forces he will feel will be the same than normal acceleration dependant on wr but now you put him inside a tube where he can move along varying the radius of the circle now the normal acceleration will be zero because he is in the...

Homework Statement In the book "Quantum Optics" written by Scully and Zubairy, there is an equation (1.1.5). The equation is presented directly and not explained how to be deduced. The content is as follows. Homework Equations The Attempt at a Solution I know the solution should have the form...

Homework Statement I'm following the solutions to a homework tutorial and I'm having trouble understanding why what they're saying is true. Question: Let f be a polynomial in K[x] and let S be the splitting field of f over K. decide whether the extension S:K is galois and describe the...

If ##M^{2} \subset \mathbb{R}^{3}## is a surface with given normal field, we define the Gauss (normal) map $$n:M^{2} \rightarrow \text{unit sphere}\ S^{2}$$ by $$n(p) = \textbf{N}(p), \qquad \text{the unit normal to $M$ at $p$}.$$...