What is Normal: Definition and 1000 Discussions

In geometry, a normal is an object such as a line, ray, or vector that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the (infinite) line perpendicular to the tangent line to the curve at the point.
A normal vector may have length one (a unit vector) or its length may represent the curvature of the object (a curvature vector); its algebraic sign may indicate sides (interior or exterior).
In three dimensions, a surface normal, or simply normal, to a surface at point P is a vector perpendicular to the tangent plane of the surface at P. The word "normal" is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality (right angles).
The concept has been generalized to differentiable manifolds of arbitrary dimension embedded in a Euclidean space. The normal vector space or normal space of a manifold at point P is the set of vectors which are orthogonal to the tangent space at P.
Normal vectors are of special interest in the case of smooth curves and smooth surfaces.
The normal is often used in 3D computer graphics (notice the singular, as only one normal will be defined) to determine a surface's orientation toward a light source for flat shading, or the orientation of each of the surface's corners (vertices) to mimic a curved surface with Phong shading.

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  1. PsychonautQQ

    Is this field extension normal?

    Homework Statement Consider the field extension Q(c):Q, where c is a primitive nth root of unity. Is this extension normal? Homework EquationsThe Attempt at a Solution I believe this polynomial splits in x^n - 1,where it's n roots are exactly the powers of c. Thus this extension is normal...
  2. M

    MHB The extension is Galois iff H_i is a normal subgroup of H_{i-1}

    Hey! :o Let $E/F$ be a finite Galois extension and let the chain of extensions $F = K_0 \leq K_1 \leq \dots \leq K_n = E$. Let $G = Gal(E/F)$ and, for $i = 0, 1, \dots , n$, let $H_i$ be the subgroup of $G$, that corresponds to $K_i$ through the Galois mapping. I want to show that, for any...
  3. L

    I feel like I am very stupid and different from normal people

    Often when I ask questions in class, people laugh at them, so I stopped asking. What can I do? Am I more brain damanged than I think? I don't think university or any place is the place for me. I never see others or met others who talk or think like me, it makes me very angry and sad. Yesterday...
  4. PsychonautQQ

    Prove an extension is not normal

    Homework Statement let b be a square root of 1+i, show that Q(b):Q is not a normal extension. Also, what is the Galois group of the extension? Homework EquationsThe Attempt at a Solution so b = +/- (1+i)^(1/2), and it's minimal polynomial is x^4+4 which has roots -(2)^1/2 and 2^(1/2) that are...
  5. M

    MHB Extension of degree 2 is normal

    Hey! :o I want to show that each extension of degree $2$ is normal. I have done the following: Let $K/F$ the field extension with $[F:K]=2$. Let $a\in K\setminus F$. Then we have that $F\leq F(a)\leq K$. We have that $[K:F]=2\Rightarrow [K:F(a)][F(a):F]=2$. There are the following...
  6. A

    Help understanding answers: kinetic friction

    https://scontent-dft4-1.xx.fbcdn.net/v/t35.0-12/14796269_10210868496286479_1115393743_o.jpg?oh=0ccd692c60a1d0bab84d5fbaf7e6197b&oe=580A1894 In the figure, a 6-kg box is sliding up an incline that makes an angle of theta=30 degree (with respect to the horizontal). As it slides up the incline, a...
  7. MaxKang

    Difference between normal viscous stress and pressure

    Hello, I came to know that a normal component of the viscous stress can exist at a solid surface for unsteady, compressible flows(though even in that case, the normal component of the viscous stress is typically much smaller than the tangential component). I tried googling it myself but could...
  8. A

    Centripetal Force, Friction, Loop de Loop, and Normal Forces

    Two questions I had: 1. How is the force of friction of the tires pointed inwards to cause centripetal acceleration? If the tire is rotated when trying to turn, the car is still traveling with a velocity perpendicular to the circle and force of friction would still be counteracting the...
  9. S

    The normal reaction between blocks A and B is?

    Homework Statement 2. The attempt at a solution Let rightward acceleration of the block (A+B) be $$a$$. Let downward acceleration of block (A) be $$a'$$ down. For block A: $$mg-T=ma'$$ $$N+ma=0$$ For block B: $$T+N=Ma$$ On solving $$N=-\dfrac{m^2g}{M+2m}$$ by taking $$a=a'$$.But...
  10. nysnacc

    Tangential and Normal of a rotating mass

    Homework Statement Homework Equations at = Rα an = V2/ R = Rω2 Vt Rω Vn =0 The Attempt at a Solution I found at=0 an=5.66 m/s vt=3.364 vn=0 So v = vt = 3.364 m/s[/B] Correct?
  11. C

    Calculating Area of Normal Stress: Solving for σBC in a Thin Rectangular Rod

    Homework Statement For σBC end , i don't understand how the author get (20mm)(40mm-25mm) = 300x10^-6 (m^2) ... Homework EquationsThe Attempt at a Solution IMO, , the area should be the circled part (thin rectangular part of the rod) , but i only know one dimension only , which is 40mm , i don't...
  12. S

    Find the center of the circle of curvature

    Homework Statement For the curve with equation y={ x }^{ 2 } at the point (1, 1) find the curvature, the radius of curvature, the equation of the normal line, the center of the circle of curvature, and the circle of curvature. Homework EquationsThe Attempt at a Solution \kappa \left( 1 \right)...
  13. Crush1986

    Testing Mastering Normal Modes: Tips for Solving Physics GRE Questions Quickly

    I'm just looking for any tips one might have for finding normal modes quickly? The GRE always seems to have a question or two on them and I have no idea how they expect someone to do a problem like that in the time given. I know that there is normally, in the problems given, a symmetric and an...
  14. E

    Other Can a normal IQ person study Physics?

    I love physics and maths,I am17,from Malaysia...My questions:Should I have a high IQ to study physics in university?Is it useful in the future?Are there many girls like to study physics?Or I am a weirdo? Haha, just kidding.I need answers and thank you!I hope Albert Einstein always...
  15. J

    MHB Statistics Normal Distribution

    Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 547 and standard deviation 85. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 21.3 and...
  16. K

    MHB Normal Extensions and Normal Subgroups

    I have answered Q1-Q3. I am unsure of my answer for Q4 and am stuck on Q5. Notation: \(I^*=Gal(K:I)\). That is the subgroup of G=Gal(K:F) that fixes I. Q4. I2 is conjugate to I1. iff \(\exists i \in G:I_2=i(I_1)\) iff \( I^*_2=[i(I_1)]^*=iI_1^*i^{-1}\) by Q3. iff \( I^*_2=iI_1^*i^{-1}\) iff...
  17. OrlandoLewis

    Why Is the Normal Force the Same on Both Blocks in a Frictional System?

    Homework Statement The two blocks (m=16kg and M=88kg) are not attached to each other. The coefficient of static friction between the blocks is us=0.38, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force F required to keep the smaller...
  18. R

    MHB A question about 'properties of multivariate normal distributions'.

    hello guys, i have a question and looking for an answer quickly... question; prove that, Z is a vector.thank you.
  19. S

    Tangent line and normal on a parabola

    Homework Statement If the normal at P(ap^2 ,2ap) to the parabola y^2 = 4ax meets the curve again at Q(aq^2, 2aq), show that p^2 +pq+2=0 Homework Equations Point-slope form The Attempt at a Solution I tried putting y=2aq and x=aq^2 but I can seem to simplify the whole thing other than...
  20. Mr-R

    A Canonical quantisation of the EM field

    I have just gone through chapter 14 on the QFT for the gifted amateur by Lancaster and Blundell. Quantising the electromagnetic field results in the Hamiltonian: $$\hat{H}=\int d^3p \sum^{2}_{\lambda=1} E_p \hat{a}^\dagger_{p\lambda} \hat{a}_{p\lambda}$$ with ##E_p=|p|##. In this post ##p##...
  21. M

    B Understanding the Horizontal Component of Normal Force in Banked Curves

    Why during a banked curve is the horizontal component of the normal force considered as the net force and the centripetal force? The horizontal component of Normal force, N·sinθ, is not even ponting towards the centre of the curvature.
  22. perplexabot

    A Derivative of log of normal distribution

    Hey all, I've had this point of confusion for a bit and I have thought that with time I may be able to clear it out myself. Nope, hasn't happened. I think I need help. Let us say we have the following \phi_{k+1}=\phi_{k}+v_k where, v_k\overset{iid}{\sim}\mathcal{N}(0,\sigma^2) and...
  23. Saracen Rue

    Finding μ and σ from a normal cumulative distribution function

    Homework Statement The relationship between the expected value and the variance for a particular normal CDF is known to follow the rule ##E(X)=arcsin(ln(Var(X)))##. Given that ##Pr(0.32<Z<2.32)=Pr(12.9<X<74.275)##, determine the possible values of the mean and the standard deviation correct to...
  24. C

    Finding shear and normal stress after rotation

    Homework Statement http://ocw.nthu.edu.tw/ocw/upload/8/256/Chapter_7-98.pdf refer to page 3 in the 2nd, 3rd pictures, i have problem of finding σx'Homework EquationsThe Attempt at a Solution why can't use the formula to find σs ? it's given that σx' = ( σx+ σy)(0.5) + (0.5)( σx- σy)cos2θ +...
  25. C

    Unit tangent vector vs principal normal vector

    Homework Statement http://mathwiki.ucdavis.edu/Core/Calculus/Vector_Calculus/Vector-Valued_Functions_and_Motion_in_Space/The_Unit_Tangent_and_the_Unit_Normal_Vectors In the link, I can't understand that why the Principal Unit Normal Vector is defined by N(t) = T'(t) / | T'(t) | ,can someone...
  26. F

    Normal vector in surface integral of vector field

    Homework Statement when the normal vector n is oriented upward , why the dz/dx and dz/dy is negative ? shouldn't the k = positive , while the dz/dx and dz/dy is also positive? Homework EquationsThe Attempt at a Solution is the author wrong ? [/B]
  27. Eclair_de_XII

    What's a fast way to find the normal and binormal vectors?

    Homework Statement ##r(t)=(t^2)i+(1+\frac{1}{3}t^3)j+(t-\frac{1}{3}t^3)k## Find the tangential, normal, and binormal vectors for this TNB frame. Homework Equations ##T(t)=\frac{v(t)}{|v(t)|}## ##N(t)=\frac{T`(t)}{|T`(t)|}## ##B(t)=T(t)×N(t)## The Attempt at a Solution The problem isn't that I...
  28. Conductivity

    Is it normal to keep forgetting?

    Hello PF members, I just wanted to initiate a discussion about this topic. It always has bugged me and I don't ever like something like this to happen to me. So the whole point is that I (Personally) keep forgetting what I studied in math for the past year. It is not because I didn't...
  29. I

    Normal approximation to Poisson random variable

    Homework Statement Suppose that the number of asbestos particles in a sam- ple of 1 squared centimeter of dust is a Poisson random variable with a mean of 1000. What is the probability that 10 squared cen- timeters of dust contains more than 10,000 particles? Homework Equations E(aX+b) =...
  30. A

    Physics Is it normal to lose motivation/concentration after 2 years?

    Hello, My title is a little too long. I have graduated two years ago in applied physics at a master level and did nothing since then. I am isolated and I feel a lack of motivation to apply for PhD offers (and never had any motivation to apply for any other kind of job offers) and I lack...
  31. C

    Angle of shear stress vs normal stress

    Homework Statement why the angle of shear stress ( θs) is given by θp - 45 ?? Homework EquationsThe Attempt at a Solution the difference in angle of shear stress and normal stress is90 degree , am i right? why it's negative 45 degree? is it wrong?
  32. A

    Static friction vs. Normal force on an incline

    I have two surfaces that have a coifficent of friction of .6. Disregarding mass (if possible) at what angle would the force of static friction and the normal force be equal
  33. F

    Shear stress and normal stress

    Homework Statement why the shear stress is maximum at the center ? while the normal stress is maximum at the boundary ? Homework EquationsThe Attempt at a Solution why shouldn't the shear stresss maximum at the boundary ? this is because shear stress is to pull the 2 surface apart [/B]
  34. D

    Calculating Normal Forces on a Wooden Stick Supported by Two Chairs

    Homework Statement An ##D## meter long wooden stick with a mass of ##M## is placed on two chairs of neglegible lenght. The left is ##L## meters from the left end and the right is ##X## meters from the right end. Find the expression for the both Normal forces that act from the chairs. Homework...
  35. D

    Normal Acceleration of a Thrown Ball: What Is It?

    Homework Statement a ball is thrown from some height horizontally with some velocity. After 1 second what is its normal acceleration? Ignore air friction Homework EquationsThe Attempt at a Solution I was absolutely certain that it is 10m/s2 couse that doesn't change and it has no acceleration...
  36. H

    I Normal contact force for a sliding slope

    For the following question, how do we know that the acceleration of ##M## is constant over time? And is the normal contact force between the two masses smaller as compared to that where ##M## is fixed? The acceleration depends on the net force on ##M##, which depends on the normal contact...
  37. AntonPannekoek

    I What is “normal” about normal frequencies and normal modes?

    So, my question is what does the "normal" part mean when one talks about normal frequencies and normal modes in coupled oscillations. Does it have to do with the normal coordinates that one uses when solving some problems, or with normal in the sense of orthogonal. Thanks for your help.
  38. StarWarsNerd

    Generalizing collision normal between two arbitrary shapes

    I am working on a physics engine, and I have a question about the collision normal. There are a lot of different ways people say to calculate this, perpendicular to the collision angle, perpendicular to the edge of body 'B', etc. I was wondering if it would be okay to assume the collision...
  39. Surya97

    Four things -- Normal force, friction, Pressure, breakage

    I understand that every force has an equal and opposite reaction, and the reason things can move is because the forces acts on different things. Also, F=MA is why the heavier object is accelerated less. The equal and opposite reaction to gravity pulling down towards the Earth's core on a book...
  40. D

    A Normal applied by a disk on a rod

    Hi all. I'm trying to figure out how is the normal (direction) applied by two disks on a rod which connects the two disks, in order to build the second law of dynamics. See figure. Hope you could help Thanks
  41. C

    Mechanical energy in an harmonic wave and in normal modes

    I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still...
  42. W

    A Normal velocity to the surface in Spherical Coordinate System

    Let's say we have r=R( theta, phi, t) on the surface of the particle and need to find the normal vector in Spherical Coordinate system. We know that, the unit vector =grad(r-R( theta, phi, t)) / |grad((r-R( theta, phi, t))| where grad is Spherical gradient operator in term of e_r, e_\theta...
  43. L

    A Image force in normal metal electrode tunneling

    Hi there, I have a question that I think has an answer but I cannot find it in the literature in any convincing way: I am using two models, WKB based and TMM based to calculate the transmission probability of electrons through a (initially rectangular) thin potential of the order of 1-2nm...
  44. H

    Normal Distribution Question. Need help

    [MENTOR note] Post moved from General Math forum hence no template. Assume that a random variable follows a normal distribution with a mean of 80 and a standard deviation of 24. What percentage of this distribution is not between 32 and 116? My approach is to calculate the Probability for (mean...
  45. chwala

    Problem on normal distribution

    Homework Statement The time Rafa spends on his homework each day is normally distributed with mean 1.9hrs and standard deviation σ. On 80% of these days he spends more than 1.35 hours on his homework. i. find the value of σ ii. find the probability that Rafa spends less than 2 hours on his...
  46. physea

    Normal reaction in banked road circular motion

    Homework Statement Homework Equations ΣF=0 The Attempt at a Solution Basically I don't agree with this solution, I think it is R1 + R2 - mgcos5 + mv^2sin5/r = 0. Can you help me please? thanks!
  47. physea

    Normal reaction in banked road circular motion problem

    What is the equation of forces please for the axis parallel to the banked road? Is it R1+R2-mgcosθ=mV^2/r or R1+R2-mgcosθ=-mV^2/r? Can you advise me please?
  48. B

    MHB Normal vector of a sphere

    I am given the sphere V= x^2 + y^2 + z^2 =< 1 I have converted it to spherical coordinates: x = rsin(t)cos(f) y = rsin(t)cos(f) z = rcos(t) where t ranges from 0 to pi, and f ranges from 0 to 2pi. I am unsure how to go about this problem from here. Any guidance would be really appreciated :)
  49. Erland

    I Why is so much well described by the normal distribution?

    Why are so many phenomena well described by the normal distribution? For example: the height of 18 year old males in Sweden, the weight of apples on a particular tree, the volume of coke cans (supposed to be 33 cl), etc. etc. are all well described by the normal distribution. How come? A...
  50. Biker

    B Normal Force: Questioning the Physics Behind It

    In the past I used to understand it in some kind of way. But it doesn't make a lot of sense sometimes. In high school, we usually take examples where the object is placed in an incline and the Normal force is equal to mg cos theta where theta is the angle of the incline. It should equal to that...
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