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. M

    I Normal order and overlap of states

    I have trouble understanding the solution to a homework problem. Consider the interaction Lagragian ##\mathcal{L}_{\rm int} = -iqA_\mu \bar{\psi}\gamma^\mu \psi##, i.e. photon-electron/positron interaction. We want to focus on the Compton scattering $$e^-(\vec p_1, \alpha) + \gamma(\vec p_2...
  2. C

    MHB Modifying Normal Subgroups of a Group: Q&A

    Dear Every one, I have a question about when is to a good idea to mod out a normal subgroup of group. Any examples would help me out. Thanks Cbarker1
  3. VapeL

    Equation of motion and normal modes of a coupled oscillator

    This is a question from an exercise I don't have the answers to. I have been trying to figure this out for a long time and don't know what to do after writing mx''¨(t)=−kx(t)+mg I figure that the frequency ω=√(k/m) since the mg term is constant and the kx term is the only term that changes. I...
  4. theudster

    Effects of hypersonic speed on the behaviour of normal shocks

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  5. D

    Normal incidence of a plane polarized wave through multiple mediums

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  6. A

    Calculating the normal force with Newton's Laws

    Block A is accelerating at a= 49.6/0.5 m/s (99.2m/s) Block B force is F= 3kg * 99.2 = 297.6N but I'm not sure where to go from here?
  7. C

    I How can phonons "travel" if they are excitations of normal modes?

    My understanding is that you can describe the complicated motion of atoms in a crystal as a sum of standing waves (normal modes). A phonon is an excitation of a normal mode in the sense that it increases the vibration amplitude of that normal mode and the energy of that mode by a quantized...
  8. t2r

    Conservation of Energy: Why are Normal Forces Zero?

    Hello everyone, someone could explain me please, why the work of the normals forces are 0 ? He used with conservation energy equations. How should I refer to the displacement point ? Thx everyone !
  9. H

    What's the normal low-load working temperature for an SMPS transformer?

    Hi! I have question about high frequency transformers inside switch mode power supplies (SMPS). Is it normal for them to become hot under no load or low load? For example if power supply is rated for 144A at 13.8V and I only pull from it 2A at 9.6V, it normal that transformer becomes about 50C...
  10. R

    Show N is a normal subgroup and G/N has finite element

    Clearly e ∈ N. If a, b ∈ N, say ##a^k = b^l = e##, for some k,l ∈ N, then ##(ab)^{kl} = (a^k )^l (b^l )^k = e^l e^k = e##; thus, ab ∈ N. Also, ##|a|=|a^{−1}|##, so ##a^{−1}## ∈ N. Thus, N is a subgroup. As G is abelian, it is normal. Take any c ∈ G. If, for some n ∈ N, we have ##(cN)^n = eN##...
  11. P

    Two pendula connected by a spring - normal modes

    I found the equations of motion as ##m\frac{\mathrm{d}^2x_1 }{\mathrm{d} t^2} = -\frac{mg}{l}x_1 + k(x_2-x_1)## and ##m\frac{\mathrm{d}^2x_2 }{\mathrm{d} t^2} = -\frac{mg}{l}x_2 + k(x_1-x_2)## I think the k matrix might be ##\begin{bmatrix} mg/l + k & -k \\ -k & mg/l + k \end{bmatrix}##...
  12. R

    Can the Normal Force Produce a Torque on an Object on an Incline?

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  13. J

    MHB Weak Convergence to Normal Distribution

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  14. ContagiousKnowledge

    Normal modes of a rectangular elastic membrane

    Let's try inputting a solution of the following form into the two-dimensional wave equation: $$ \psi(x, y, t) = X(x)Y(y)T(t) $$ Solving using the method of separation of variables yields $$ \frac {v^2} {X(x)} \frac {\partial^2 X(x)} {\partial x^2} + \frac {v^2} {Y(y)} \frac {\partial^2 Y(y)}...
  15. jackattack825

    Normal force between stacked boxes

    Σ F= -F(gravity from earth) + F(normal from earth) -F(normal from top box) +F(normal from bottom box) = (2+5) * 2.5 The forces from gravity and it's normal force cancel out, leaving us with the normal forces from the boxes. F(net of normal from boxes) = (2+5) * 2.5 = 17.5N
  16. V

    Calculating the normal force due to moment load on a thrust bearing

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  17. Biochemgirl2002

    Calculating general normal random probability

    a) P(X<18) = (18-20)/sqrt25 =-2/5 =-0.4 then you use the standard normal table and find that; P(X<18)=0.3446 b) P(X>27) = (27-20)/5 = 7/5 = 1.4 P(Z>1.4) =P(Z<-1.4) =0.0808 C) =(13<X<23) =13-20/5 , 23-20/5 =-7/5 , 3/5 =-1.4 , 0.6 P(Z<0.6)-P(Z<-1.4) =0.7257-0.0808 =0.6449
  18. A

    MHB Finding a value from normal density funciton -- help me

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  19. Physics4Eva

    B Is Normal Force a Contact Force Despite Atomic Repulsion?

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  20. Zouatine

    The normal and shear stresses

    Hi! i have this exercise and solution : Exercise: steel plate given in figure (a) is joined by an inclined butt weld ,the plate is subjected to tensile stresses in both x and y directions, σ(x)=54 N/mm^2 and σ(y)=38 N/mm^2 , 1) Determine the normal and shear stresses of the butt weld...
  21. Like Tony Stark

    Is the Normal Force on m2 Affected by Vertical Acceleration in Different Cases?

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  22. K

    What is the normal force in A and B?

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  23. Q

    A Do the time and normal ordering operators commute?

    Does the time ordering operator ##\mathcal{T}## commute with the normal ordering operator ##\hat{N}##? i.e. is $$[ \mathcal{T},\hat{N}] =0$$ correct?
  24. MPavsic

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  25. E

    I Pressure vs Normal Stress: Exploring Bird Transport Phenomena

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  26. Shashwat02

    B Normal force of a body over a circular bridge

    I am not able to understand why normal force on top in a vertical circular motion the least. Also please help me with normal force of a body over convex and concave bridges. Why do we get these equations: N=mg-mv2/r (convex bridge) N=mg+mv2/r (concave bridge)
  27. PainterGuy

    B Questions about a normal distribution (discrete to continuous)

    Hi, I was watching this Youtube video (please remove the parentheses) : https://youtu.(be/mtH1fmUVkfE?t=215) While watching it, a question came to my mind. In the picture, you can easily calculate the total number of customers. It's 1000. For my question, I'm going to use the same picture...
  28. brotherbobby

    Normal reactions at the bases of two light supports

    For equilibrium, using ##\Sigma \vec F = 0##, we get ##n_1 + n_2 = 300\; \text{N}##. Taking the system as a whole and applying ##\Sigma \vec \tau = 0## about the hinge (pin) at the top from where the load is hung, we get ##n_1 \times (0.8) \times 4 = n_2 \times (0.6) \times 3##, by taking...
  29. Benjamin_harsh

    What does "an axis normal to the plane containing the structure" look like?

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  30. PainterGuy

    B Normal form of the conic section equation

    Hi, The following is called normal form of the conic section equation: x²+y²+2ax+2by+c=0 A circle is one of the conic sections when considered as a special of ellipse. I'm confused as to why the the given equation is called "normal form of the conic section equation" when, in my opinion, the...
  31. Amitayas Banerjee

    What is the angle between the velocity of and the normal to the racket?

    My approach: Let us take two orthogonal axes: x, parallel to the racket's plane and y, perpendicular to it. For the ball to not spin, the components of initial velocities of the racket and the ball along x-axis must be same. Also, as the line of collision is along the normal to the racket's...
  32. T

    A Forgetting Non-GR Physics: How Specialists Can Stay Sharp

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  33. A

    Normal Velocity Gradient Across a Surface: Proving a Result

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  34. N

    I Variable transformation for a multivariate normal distribution

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  35. Svelte1

    Understanding Hinge Reactions: Debunking Common Misconceptions

    https://postimg.cc/JtP2h113 I think I may have forgotten some more basic elements of tension and normal reactions. I do not understand why the vertical component of the normal reaction =Tsin60-15g Because Tsin60-15g is negative when resolving upwards, i would have thought this meant that the...
  36. Miles123K

    Normal mode of an infinite spring pendulum system

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  37. M

    Thickness of normal and tempered glass for aquarium

    Summary: Calculations of glass thickness for aquarium 140cm (length), 55cm (width) and 80cm (height). Scenarios for normal glass and tempered glass. Hi everyone ! I want to ask you for help to calculate how thick (minimum version and save version) should be a glass for aquarium with sizes...
  38. Caio Graco

    Is the Normal Force in an Elevator Conservative?

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  39. C

    MHB Can You Prove These Properties of Normal Subgroups in Group Theory?

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  40. karush

    MHB 25.3 Find the Jordan Normal Form of A

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  41. karush

    MHB 25.1 find all possible Jordan Normal Forms of A

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  42. D

    I Vacuum projection operator and normal ordering

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  43. R

    Finding Average Normal Stress in Rod

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  44. WMDhamnekar

    MHB Force normal and force along the incline

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  45. Eclair_de_XII

    Is it normal for professors to allow cheat-sheets in tests?

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  46. hagopbul

    Using a normal processors for HPC

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  47. R

    Find normal force, shear force, bending moment

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  48. T

    Normal Stress Balance at a Fluid-fluid Interface

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  49. WMDhamnekar

    MHB Two normal independent random variables

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  50. A

    Normal incidence of light on a denser medium

    When light, traveling through a rarer medium, gets reflected off at an interface with a medium of higher refractive index, it suffers a phase shift of half-wavelength. Now if it was normal incidence, the phase-shifted light would retrace its path. Does that mean the wave would cancel out?
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