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. G

    Normal and centrifugal force for arbitrary curves

    Hi, i have a curve g:[0,t]->IR² with g(t)=(x(t),y(t)) in a homogenous gravitational field and i want to look at a ball rolling down this curve. therefore i want to derive some equations in order to calculate the normal force and the centripetal force at each point of this curve in order to see...
  2. M

    Jordan Normal Form: Find Basis B in $\mathbb{Z}_{5}^{3}$

    Hi Homework Statement Let f:\:\mathbb{Z}_{5}^{3}\rightarrow \mathbb{Z}_{5}^{3} be a linear operator and let [f]_{e_{3}}^{e_{3}}=A=\begin{pmatrix}3 & 1 & 4\\ 3 & 0 & 2\\ 4 & 4 & 3 \end{pmatrix} over \mathbb{Z}_{5}. Find a basis B of \mathbb{Z}_{5}^{3} such that...
  3. A

    Proving that a subgroup is normal.

    Homework Statement How can we prove that a subgroup H of Gl_2(Z_3) is normal? These are the elements of H: \begin{pmatrix}1&1\\1&2 \end{pmatrix} \begin{pmatrix}1&2\\2&2 \end{pmatrix} \begin{pmatrix}2&1\\1&1 \end{pmatrix} \begin{pmatrix}2&2\\2&1 \end{pmatrix}...
  4. Petrus

    MHB Find Equation of Normal Line to y=x^2-5x+4 Parallel to x-3y=5

    Hello, i know how to calculate normal line on point but i don't know how to do this problem. "find an equation of the normal line o the parabola y=x^2-5x+4 tha is parallel to the line x-3y=5."
  5. S

    Why are there two different equations for normal force on an angle?

    Homework Statement I feel like I am being told that there two different kinds of normal force. 1st. In grade 11 we were always told that normal force on an angle equals m*g*cosθ, where Fn equals the y-component, and θ is the angle between Fn and mg. 2nd. Now in university we are told...
  6. G

    How do I find the normal force?

    Homework Statement Let's say I'm holding a crate up against the ceiling with a force of 'P', and the crate is stationary. What is the normal force? Homework Equations Newton's 1st law: ƩF=0 The Attempt at a Solution I have three forces acting on the crate - The normal force...
  7. nomadreid

    Checking if the residues are normal ad nauseum?

    If I am checking whether my data fits a curve C1, I have to check to see whether the residues R1n are normally distributed, which is checking R1n against a normal curve C2, giving me residues R2m; which must be normally distributed, that is, must be checked against a normal curve C3, giving me...
  8. nomadreid

    Chi-squared dist. converges to normal as df goes to infinity, but

    chi-squared dist. converges to normal as df goes to infinity, but... This is surely going to sound naive, but at least this will make it easy to answer. For a chi-squared distribution, if k = the degrees of freedom, then [a] k = μ = (1/2) σ2 [b] as k goes to infinity, the distribution...
  9. L

    Calculate Heat of Vaporization and normal boing point (in degree C).?

    Using line equation y = -4058.7x + 16.10 with the experiment pressure measured in kPa instead of atm. I already solved for heat of vaporization thus: (-4058.7K)(-8.314 J/mol \astK)=heat of vaporization = 33444 J/mol = 33.44 kJ/mol. Also, the vapor pressure for normal boiling point...
  10. J

    Normal Order of A + B Homework

    Homework Statement Hi, guys, I just wondering what's the normal order of A +B Homework Equations if N[A+B]=N[A]+N[B] then I have N[aa^{\dagger}]=N[1-a^{\dagger}a]=1-a^{\dagger}a however we know that N[aa^{\dagger}]=-a^{\dagger}a] what's wrong? The Attempt at a Solution...
  11. N

    Conformal Mapping and flow normal to ellipse

    Hi, Given that the flow normal to a thin disk or radius r is given by \phi = -\frac{2rU}{\pi}\sqrt{1-\frac{x^2+y^2}{r^2}} where U is the speed of the flow normal to the disk, find the flow normal to an ellipse of major axis a and minor axis b. I can only find the answer in the...
  12. N

    Find the Magnitude of the Normal Force on the Slider and v'

    Homework Statement A 2.4-lb slider is propelled upward at A along the fixed curved bar which lies in a vertical plane. If the slider is observed to have a speed of 11.3 ft/sec as it passes position B, determine (a) the magnitude N of the force exerted by the fixed rod on the slider and (b) the...
  13. N

    Finding the Force P from Normal Stress

    Homework Statement In the steel structure shown, a 6‐mm‐diameter pin is used at C and 10‐mm‐diameter pins are used at B and D. The ultimate shearing stress is 150 MPa at all connections, and the ultimate normal stress is 400 MPa in link BD. Knowing that a factor of safety of 3.0 is desired...
  14. O

    Prove that the extension is Normal

    Prove that the field Q(√2,√3,u) where u^2=(9-5√3)(2√2) is normal over Q. I'm supposed to show that this field is the splitting field of some polynomial over Q. u is clearly algebraic over Q. Do i just take the higher powers of u and try to find the minimal polynomial over Q or is there a...
  15. C

    FBDs for Box and Magnet Lifting by a Rope Attached to Ceiling

    Homework Statement A box is lifted by a magnet suspended from the ceiling by a rope attached to the magnet as illustrated in Fig 3.65. Draw free body diagram for the box and for the magnet so the picture is basically there is a ceiling , and the rope hanging from the ceiling to the...
  16. A

    Dynamics - Normal and Tangential Motion

    Homework Statement The tires on a car are capable of exerting a maximum frictional force of 1753 lb. If the car is traveling at 75 ft.s and the curvature of the road is ρ=560 ft, what is the maximum acceleration that the car can have without sliding? Homework Equations ƩFn = man The...
  17. J

    Normal Distribution of Means

    Homework Statement A biologist interested in the mass of Chickadees (Poecile atricapillus) in North Glenmore Park collects the 3 samples shown below: Sample 1: 9 individuals with a mean mass of 13.23 grams Sample 2: 16 individuals with a mean mass of 9.64 grams Sample 3: 13 individuals...
  18. C

    Rotational Equilibrium and Normal Forces

    Hi, The question I have is not for a numerical answer but for clarification. Some of the questions involving torque/rotational equilibrium describe a person standing on a plank. I know that the gravitational force of the person on the plank needs to be considered for translational and...
  19. N

    Each Car has Speed Corresponding to Max Normal Acceleration. Find Time Elasped

    Homework Statement The two cars A and B enter an unbanked and level turn. They cross line C-C simultaneously, and each car has the speed corresponding to a maximum normal acceleration of 0.94g in the turn. Determine the elapsed time for each car between its two crossings of line C-C. What is...
  20. U

    Proof on why del is normal to surface?

    Homework Statement Simple proof on why ∇∅ is normal to surface of ∅(x,y,z) = constant Homework Equations The Attempt at a Solution
  21. Ascendant78

    Courses Is this normal for Chem I and Chem II courses?

    I just finished Chemistry I last semester and am taking Chemistry II this semester. These are the "101" type prerequisite Chemistry courses required for the AA. Although I earned a 98 in Chem I (with a class average of 75), I still feel like I didn't learn much. To sum it up, here are the...
  22. A

    Normal and Tangential Acceleration

    Homework Statement A motorcyclist travels around a curved path that has a radius of 450 ft. While traveling around the curved path, the motorcyclist increases speed by 1.10\frac{ft}{s}. Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 7.00...
  23. K

    Is it normal to be so discouraged by abstract algebra?

    I'm currently in my first abstract algebra course, focused on sets, groups, arithmetic modulo, rings, fields etc. I've never taken an abstract course before. I've taken: Pre-calc Calc 1-2 Linear Algebra Advanced Applied Linear Algebra so the concept of abstraction is very new to me; I...
  24. F

    How to Calculate Normal Force on an Inclined Surface with Tension Force?

    Homework Statement I've been having a little bit of trouble answering this question: "An 8.0 kg wooden sled is pulled over the snow by means of a rope that makes an angle of 40° with the horizontal. If the rope has a tension of 70.0 N, what is the normal force acting on the sled?"...
  25. U

    Normal Modes - 2 springs question

    Homework Statement Homework Equations The Attempt at a Solution When i do the matrix multiplication of the 2x2 and 2x1 matrix, I get 2 conflicting solutions that don't match at all! So which one do i take to find ratio of X and Y?
  26. K

    Find period of astronaut when Normal force of ship = normal force on earth

    Homework Statement If the gravitational acceleration at Earth's surface is given by: g = GMe/Re^2, show that the period of rotation of a spaceship needed to make an astronaut feel the same normal force on the ship that they would feel on Earth, when it is given by T = √[(4pi^2)(Rs)(Re^2)/GMe]...
  27. brainpushups

    Normal Modes; Rod suspended from strings

    Homework Statement A thin uniform rod of length 2b is suspended by two vertical light strings, both of fixed length l, fasted to the ceiling. Assuming only small displacements from equilibrium, find the Lagrangian of the system and the normal frequencies. Find and describe the normal...
  28. S

    Probability related to Normal Distribution

    Homework Statement Variable A has mean 55 and variance 9, variable B has mean 65 and variance 25. If A and B are normally distributed, find P (B > A) Homework Equations z = (x - μ) / σ The Attempt at a Solution Can this be solved? What is the meaning of P (B > A)? The probability...
  29. P

    Calculate the mean for a normal distribution

    Homework Statement Given: Standard Deviation = 500 Homework Equations How I calculate the μ (mean) using standard deviation for a norma distribution. Thanks. The Attempt at a Solution
  30. dexterdev

    Transmit With 5W FM Transmitter & Dipole Antenna: Range & Radiation Pattern

    With a 5W FM transmitter and a normal dipole antenna , to what range can I transmit. To be more specific, what will be the radiation pattern like (Can I get signal uniformly as in a circle where the center is antenna). Using which antenna, can I achieve maximum range omnidirectionally...
  31. O

    MHB Ideals and Varieties, Rational Normal Cone

    I have the ideal I = <f1, f2, f3>, where f1 = x0x2-x12, f2 = x0x3 - x2x1, f3 = x1x3 - x22. I also have the parametrization of some surface given by \phi: \mathbb{C}^2 \rightarrow \mathbb{C}^4 defined by \phi(s, t) = (s^3, s^2t, st^2, t^3) = (x_0, x_1, x_2, x_3) . I want to show that V(I) =...
  32. nomadreid

    P(x=mean) of normal PDF with low sigma - not allowed?

    P(x=mean) of normal PDF with low sigma -- not allowed? About the normal probability distribution: with formula P(X=x) = (1/(σ*sqrt(2π))*exp(-(x-μ)2/2σ2), what happens when you look at P(X=μ) if σ<(1/sqrt(2π))? You get P(X=μ)>1, an absurdity. What is going on? Second question is one about...
  33. B

    Small oscillations: How to find normal modes?

    Hi, I'm studying Small Oscillations and I'm having a problem with normal modes. In some texts, there is written that normal modes are the eigenvectors of the matrix $V- \omega^2 V$ where V is the matrix of potential energy and T is the matrix of kinetic energy. Some of them normalize the...
  34. PhanthomJay

    Space between objects when Normal force equals 0

    Ok, so 2 objects in contact with one another exert a normal force pair between the 2, but it is my understanding that they never 'touch' each other, rather, it is the repulsion of the outer electrons that create the electromagnetic 'normal' force. QUESTION 1: Is there physical space betwen the...
  35. B

    When does the normal force act on something?

    A bit confused about the operation of normal forces. When does a normal force act due to some surface on an object? When the object touches the surface or when the object actually applies a force on the surface? The reason I ask this is because I am confused about normal forces...
  36. F

    Normal force max min constraints on a roller coaster

    Homework Statement passengers cannot have a normal force equal to 0 or greater than 4 times their weight. What are the heights H1 and H2. Coaster starts at H1 and and ends at H2. H1>H2 and there is a low point between the two hills defined as zero height. The radius of the curve at the...
  37. C

    Normal strain of cable through arc

    Homework Statement See attachment Homework Equations eAB=(Lf-Lo)/(Lo) The Attempt at a Solution Ok, this is not for HW. I am preparing for a mechanics of materials class next semester. I don't understand when CB goes through the 0.3 degree arc, they say the height is still 300mm. Shouldn't...
  38. A

    Normal Force While Going Up Stairs

    In my high school physics class, we are doing an experiment where we go up a flight of steps, record the time it takes, and calculate the work done in the vertical direction. I understand everything (I am a pretty bright student) except one part that I simply cannot wrap my head around. To...
  39. E

    Gas Dynamics (Compressible Flow) Normal Shock Wave

    Homework Statement Suppose that a blast wave, which might have been initiated by an atomic bomb explosion, is traveling through air at standard atmospheric conditions with a speed of 60,000 m/s find change in ( pressure , temperature , stagnation pressure , velocity ) produced by the wave...
  40. U

    Normal to a fixed concentric ellipse

    Homework Statement PM and PN are perpendiculars upon the axes from any point 'P' on the ellipse. Prove that MN is always normal to a fixed concentric ellipse Homework Equations The Attempt at a Solution I assume point P to be (acosθ, bsinθ) The eqn of line MN is then given by...
  41. A

    Bivariate Normal Distribution with Covariance Matrix and Linear Transformation

    Homework Statement Z is a 2x1 multivariate gaussian random vector, where Z = (X Y)^t , X,Y are real numbers, with mean zero and covariance matrix \Gamma which is a 2x2 matrix whose entries are \Gamma_{1,1} = 1 \Gamma_{1,2} = \alpha \Gamma_{2,1} = \alpha \Gamma_{2,2} = 1...
  42. B

    How to go from limit of vector norm to 'normal' limit

    This is not really a homework question, but I've come across this while preparing for a test Homework Statement Let f:U \subseteq R^n -> R^m be a function which is differentiable at a \in U, and u \in R^n It is then stated that it is clear that: lim_{t \to 0}...
  43. T

    Max value of the average normal stress in the links.

    Homework Statement Here is the problem along with the solution: I am confused about part (a). Why is it that the area used is 2*0.008*(0.036-0.016). If you draw a cross section at just one of the holes, wouldn't that give you the max average stress? So the area used should instead be...
  44. C

    Normal force in rotational motion

    Hi there, I've got a conceptual question about the normal force as applied to rotational motion. Suppose you have an object like a uniform disk. If the disk were set up so that its axis of rotation were about its centre of mass, it would just sit there and the normal force would be equal to...
  45. A

    Solve Bivariate Normal: X,Y,G,F Homework

    Homework Statement 1. Show that X is independent of Y- \alpha X where |\alpha| < 1 2. Find the joint distribution of F = X and G = X + Y X,Y,G,F are random variables Homework Equations The vector W = (X, Y)^{t} is a 2x1 multivariate Gaussian random vector with zero mean...
  46. V

    How fast can you 'switch' between superconducting and normal modes?

    The title, basically. If we're at a temperature below the critical temperature (let's just say for a Type 1 superconductor) and an applied magnetic field less than the critical magnetic field, it will be in the superconducting state. But if we increase the field beyond the critical point, it...
  47. A

    Normal force in circular motion

    Hi, Suppose we have a fellow on a ferris wheel. Would the normal force be greater on the top or at the bottom of the ferris wheel? I'm thinking that it would be greater at the top, or am I wrong? Thanks,
  48. L

    What affects tangential acceleration and normal or c?

    I was wondering if acceleration (a) is the speed in which speed changes how come it can b higher than 0 and still v=0? like when there is a force pulling from the other side, the body won't move but since there is force there is acceleration. So which is which? Does the tangential...
  49. T

    How can I construct 2 x 2 normal matrices A and B such that A + B is not normal?

    Normal Matrices Examples (URGENT) I need to produce 2 x 2 normal matrices A and B such that A + B is not normal. I have proven that AB is normal if AB = BA using the Householder matrix form. But I can't find a form for A + B failing to be normal. A matrix A with entries a, b, c, d is going...
  50. A

    Exploring the Normal & Anormal Zeeman Effects

    There are two types of zeeman effect, one normal and the other one anormal, but why are they called so? I mean what is so normal about the normal zeeman effect and what is so anormal about the anormal zeeman effect??
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