What is Angle: Definition and 1000 Discussions

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves define also an angle, which is the angle of the tangents at the intersection point. For example, the spherical angle formed by two great circles on a sphere equals the dihedral angle between the planes containing the great circles.
Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.

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  1. B

    B How to draw a plane intersecting a cylinder at a "compound angle"

    Hello. For a project I am working on I need to draw a template of a "curve of intersection" of a plane (B) intersecting a cylinder at a "compound angle".. I do not know the correct terminology so I added a sketch of what I wish to achieve. If it is not understandable please say so and I will...
  2. G

    I Realistic steering wheel angle when car follows points along a path

    Good morning , I managed to simplify the physics of my car with only the centrifugal and traction forces. If I'm in control of it, the realism is acceptable for a city builder. On the other hand, I encounter a problem when the car follows an array of points. The path of the car on my graph...
  3. G

    I Angle of Sun by date and zip code?

    I don't know the correct works search to find this info online. I have been doing word searches since about Dec 15, 2022 but not finding what I want.??????? Some where there much be a chart by date and zip code for sun angle. I built a sun dial in the yard to learn the angle of the sun on...
  4. Asem

    Find Initial Velocity of a projectile given flight time and angle

    Vix=Vcosθ Vix=0.76604*V Xf=Vixt Xf=0.77604V*2 V=Xf/1.55208
  5. L

    Rearrange formula and work out phase angle

    so far i think Ip = 10 f = 1000hz struggling with the phase angle
  6. C

    Proof of angle in path difference formula for two slits

    For this I am trying to prove that angle theta between PQ and QO is equal to theta highlighted so that I know I can use theta is the path difference formula. I assume that the rays ##r_1## and ##r_2## are parallel since ##L >> d## My proof gives that the two thetas are equal, however I am...
  7. C

    Graphing Power vs Polarizer Angle using Intensity

    The data collected from the experiment is, The first column is the polarizer angle measured in degrees. The second column is recorded intensity measured in lux. The third column is the transmitted intensity measured in lux. This is equal to the recorded lux - ambient lux The fourth column is...
  8. paulimerci

    At what angle must the boat travel so that it moves in a straight line

    I'm assuming the boat is traveling north at an 8 m/s and the river is flowing east at a 2 m/s. For the boat to move in a straight line, it has to aim at an upstream angle given by #theta#. Using SOH CAH TOA, ##v_r = 2m/s##, ##v_b = 8m/s## $$\theta =\sin^{-1} \frac{v_r}{v_b}$$ $$\theta = 14...
  9. E

    B Basic Angle Explanation for Statics

    My textbook introduces this angle concept really early on and I still don't understand it. It just shows that a normal to a line and some other random angle shown is the same. I don't see any transversal angles or anything. Where did they get the secondary line to form theta for the normal line?
  10. C

    Angle of acceleration in non-uniform circular motion

    For (c), Solution is Can someone please explain how they calculated that angle? I thought they would do ##arc\tan (\frac {32}{3.35})## Many thanks!
  11. C

    Finding the launch angle for a projectile if the range is 3x the max height of the trajectory

    For this problem, The solution is, I don't understand how they got from ##\frac {sin^2\theta_i}{sin2\theta} ## to ##\frac{tan\theta_i}{2}##. Would somebody please show me the immediate steps? I also don't understand is why they say the ignore the trivial case where ##\theta_i = 0~rad##...
  12. Ranku

    I Symbol meaning in CP-violating angle

    I saw this symbol in the statement: 'Effective CP-violating angle θ≅ (10-17). What does the highlighted symbol mean?
  13. Lotto

    B Rope wrapped around a rod - belt friction

    Ideally, it should look circa like this: But in reality, it looks often like this: Is the formula valid also in this case?
  14. chwala

    Finding the angle between two vectors

    This is clear to me; i just wanted to know in which contexts is one allowed to use one rule over the other; or it does not matter. The angle i realise can also be found by; ##\sin θ = \dfrac{||v×w||}{||v||||w||}##=...
  15. M

    A book rests at an angle against one side of a bookshelf...

    1.52cos(31)+Fbsin(Θb) = (0.305)(9.8) Fbsin(Θb) = 1.69 Now for horizontal direction: Fbcos(Θb) = FLsin(ΘL) cos(Θb) = FLsin(ΘL)/Fb cos(Θb) = (1.52 x sin31)/1.69 cosΘb=0.464 Θb = 62.35 I thought to find Fb I would just plug the Θb value into one of the trig functions, but apparently both of my...
  16. A

    Finding velocity for projectile given distances and launch angle

    i used t=d/v for the x direction using the formula t=250/vcos55 and subbed that into the formula for the y direction d = (v) (t) + (0.5) (a) (t)^2 35 = (vsin55) (250/vcos55) - (4.9) (250/vcos55)^2 canceled out the first two v 35 = sin55 (250/cos55) - (306250/v^2cos3025) 35 = 357 -...
  17. shivajikobardan

    JavaScript How to reflect the ball at an angle?

    Here's the full code: When a ball collides with bat or walls, I want the ball to be reflected with an angle, how do I do it? I suspect there's lots of physics to it. So, should I stop this project here? I'd have to probably build a part of game engine…Can anyone help here?
  18. G

    Angle of the principal axes

    Statement figure: My attempt at a solution: FIGURE 1 ##\rightarrow A=a^2## CG ##\rightarrow \overline{x}=-a/2, y=-a/2## $$\overline{Ix}_1=\dfrac{bh^3}{12}=\overline{Iy}_1=\dfrac{a^4}{12}$$ $$Ix_1=\overline{Ix}_1+\overline{y}^2A=\dfrac{a^4}{12}+\dfrac{a^4}{4}=\dfrac13 a^4\...
  19. S

    Angle between normal force and radial line for cylindrical coordinates

    so I was wondering. there is this normal force on the can from the path. And there's this formula to find the angle between the radial line and the tangent or also between the normal force and either the radial or theta axis. the formula is ##\psi = r/dr/d\theta##. The thing is that here they...
  20. abdulbadii

    The angle grinder flange pair in UNF

    Does anyone happen to know if there's a grinder flange pair, i.e. its spacer and fastener flanges, with 3/8" x 24UNF thread instead of M10 x 1.5?
  21. S

    B Graphical representation of the weak mixing angle

    The graphical pattern of particles in the weak hypercharge and weak isospin plane, visible in this wiki page, shows the mixing angle between the Yw and Q axes. Actually , from the weak hypercharge (-2) of a right-handed electron and its electric charge (-1), one obtains an angle Pi/3, not the...
  22. C

    Angle between proton velocity and B-field

    For this problem, The solution is, However, this may seem like a silly question, but do we need both angles? Many thanks!
  23. Leo Liu

    The choice of sweep angle (low speed) and its impact on C_L, C_D, C_M

    My school's group project is to design a powered model flying wing that can fly for as long as possible. To make it stable in the longitudinal direction, we either have to use a swept wing design or an airfoil with reflex (like BR1). We are forced to use wing sweep because the airfoil with...
  24. J

    Downwash reducing angle of attack of a wing?

    There is theory in aerodynamics for 3D wing (finite span) that say : quoted Douglas Mclean book: "wing is flying through air that is already moving generally downward between wingtips.Thus the wing can be thought of as flying downdraft, or downwash, of its own making. 3D downwash can thus be...
  25. Spocktastic

    Trying to Figure out Tension force angle on Arm

    I already solved for part a, setting the sum of the Torques of the arms and deltoid equal to 0 and subbing in values which lead to a tension force of 870N in the deltoid. For part b, I remembered the law of static equilibrium, so the summation x and y components of all the forces in the system...
  26. J

    A Why does the free end refraction occur after Brewster's angle in TM?

    Thanks for reading my question, and i’m really sorry about my poor english. What i am wondering about is why does the free end occur after the incidence angle overcome the Brewster angle in TM wave? (The ray incident from vacuum to glass(dense medium)) i tried to interpret this phenomenon with...
  27. S

    Maximum angle reached by a cube placed inside a spinning cylinder

    I am trying to solve a problem where we have to find the maximum angle before a cube starts sliding when said cube is placed inside a spinning hollow cylinder (the cylinder is placed horizontally). The radius of the cylinder is 0.4 m, the coefficient of static friction between the cube and the...
  28. Philip Koeck

    A Fast electrons passing a beam of slow electrons at a right angle

    I'm wondering what happens when fast electrons (100 - 300 keV) interact with a beam (diameter 1 to 10 μm) of slower electrons (1 to 10 keV), which is at right angles to the trajectories of the fast electrons. The beam of slower electrons is relatively dense with 1 to 10 electrons per μm line...
  29. Leo Liu

    Why doesn't aircraft weight affect descent angle in a gliding flight

    It's a homework question, but I feel like it fits better in this forum. The solution fails to convince me because C_D and C_L can be both written in terms of weight: $$C_L=\frac{2W}{\rho v^2 S}$$ $$C_D=C_{D0}+k_1 C_L(W)+K_2 C_L(W)^2$$ Question: Solution: Any insight will be appreciated.
  30. J

    Ideal car rear roofline angle and shape for low drag?

    What is ideal rear roofline(rear window and trunk) angle and shape(straight line, curve ..etc) for lower drag? Keep in mind if you increase angle, you reduce butt area / wake, but induce low pressure at rear window/trunk , if you decrease angle you increase butt/wake but increase pressure at...
  31. A

    B Understanding the Doppler Effect at an Angle

    hello everyone How is the sound Doppler effect formula in the case where the movement of the source and the observer is at an angle?
  32. G

    I What is the angle of the Sun on June 21 & Dec 21 at US Zip Code 37129?

    What is angle of Sun June 21 & Dec 21 at zip code 37129. I need lowest angle & highest angle and probably angle of sun about Feb 20. Google word search shows nothing. I am probably need using correct word search to find what I want. Several years ago I accidently found a calendar that showed...
  33. FEAnalyst

    Gear teeth force from the rotation angle

    Hi, in books about machine design fundamentals, one may easily find the formulas for forces acting on the teeth of paired spur gears. They require torque as input. For example, for the tangential force: $$F=\frac{2T}{d}$$ where: ##T## - torque applied to the driven gear, ##d## - pitch diameter...
  34. jevans123

    Pulling a crate across the floor with a rope at an angle

    I drew out a motion diagram and used 115N sin(26.7 degrees) = 51.7 N but It turns out to be wrong.
  35. Ahmed1029

    I What's the definition of angle in a curved space embedded in a higher Eucledian space?

    I don't want to post this in a math forum because it's very basic and I just want a straightforward answer, not something math heavy . What's the definition of angle in a cuved space embedded in a higher eucledian space? Like when I have a spherical surface in 3d eucledian space and want to work...
  36. Jan Berkhout

    Calculate the best angle for maximum light dispersion through a medium

    I first thought that the angle would have to be maximum when it is closest to the critical angle for total internal reflection. From my lectures the equation for the critical angle is ##\theta _1>\ sin ^{-1} \left( \frac {n_2} {n_1} \right),## so as ##n_2 = 1##, we have ##\theta _1=\sin...
  37. chwala

    Calculate angle AEC and ADC

    Question; Text Solution; My reasoning; ##∠ABC= 180^0 -(32^0+60^0)## =##88^0## ##∠ABC=∠ACF=88^0## (Alternate segment theorem). ##∠EBC=92^0## i.e angles lying on a straight line and ##∠BCE=180^0 -(88^0+60^0)=32^0## therefore; ##∠BEC=180^0 -(32^0+92^0)=56^0##...
  38. babaliaris

    For a Pendulum: Knowing Acceleration Find Maximum Angle

    PS: By the way today I had exams in Physics and this problem was the first one I had to solve :p (unlucky) The question was to find the maximum angle θ that the pendulum can reach if we know that the magnitude of the acceleration is the same when the mass is located in the highest and the lowest...
  39. D

    Designing a spiral with a certain angle relative to movement direction

    I have a disk traveling on the inner blue track (let's say the blue part is the center of the disk). I want to push the disk outside (as the disk is traveling in a circle) to the outer track. The black part is the wall separating the tracks To that end, I've made some calculations, but I...
  40. tbn032

    B Confusion about the angle between two vectors in a cross product

    The magnitude of cross product is defined of vector A⃗ and B⃗ as |A⃗×B⃗|=|A⃗||B⃗|sinθ where θ is defined as the angle between the two vector and 0≤θ≤π.the domain of θ is defined 0≤θ≤π so that the value of sinθ remains positive and thus the value of the magnitude |A⃗||B⃗|sinθ also remain positive...
  41. X

    I Why do droplets of condensation run at an angle on a plastic sheet?

    I think the picture says it all! As the droplets of condensation reached a certain size they begin to run down the plastic sheet, but rather than just running straight down, they veer off to the left or right. Most of the tracks are at fairly much parallel, with some exceptions, and the pattern...
  42. Benjies

    Subsonic airbreathing engines and inlet blade angle

    Hello! My background in propulsion is extremely lackluster with airbreathing engines, so any help is appreciated with the following questions. I understand blade pitch is highly variable for turbofans which operate near the speed of sound, to avoid any localities on the blades reaching the speed...
  43. M

    MHB Angle of diagonals

    Two angles of a square with side protrude beyond a strip of width with parallel edges. The sides of the square intersect the edges of the strip at four points. Prove that the diagonals of the quadrilateral whose vertices are these points intersect at an angle of degrees.
  44. S

    Initial velocity and angle when a ball is kicked over a 3m fence

    Hello there, I don't understand what I'm doing wrong I don't get the correct answer, but have done the same analysis 3x already and still get the same... Some input would be appreciated thanks in advance. Note: y-axis is upwards and x-axis is to the right. 3 unkowns i.e. 3eqs. ##x = x_0 +...
  45. M

    MHB Find the angle in the triangle

    I've tried: BC || EF How to find angle GDC? I think GDC=7x but why? I have an answer but how to solve this?
  46. S

    Calculations for swinging on a rope out over a lake (max. tension, final angle, etc.)

    Please tell me if I need to post my solution for this.., but I just have a question more or less 'conceptual' question about (c). so I know that from Newton's 2nd law for centripetal acceleration --> ##F_{rope} - mgcos(\theta) = ma_n## where ##a_n = \frac {v^2}{R}## such that where the normal...
  47. S

    The angle at which a skier will leave the sphere

    Back here again.. but I am sorry guys, only the parameters are on my paper so wouldn't be of much help to show. I basically have no clue on how to start solving this problem at all. I stopped yesterday and let it sit overnight but still have no clue on how to approach the problem basically...
  48. dejavu333

    Projectile launch angle

    if the target is lower than me, the formula is below, but if it's higher as in the task, a whole different formula is required I think. a = 9.8 * distance^2 / velocity^2 phi = Arctan(distance / height_diff) angle_if_elevation = ( Arccos((a - height_diff) / Sqroot(height_diff^2) + distance^2)) +...
  49. G

    Find v_1 for projectile using start position, final position and angle

    I have attempted the problem a few times, and have posted my work below. I thought to check my work using ## v_x t = v_1 \times \cos\theta \times t = \Delta x## to see if I get back expected results, and I did for the horizontal motion (the substitutions are from the numbered steps below): ##...
  50. N

    I Lens angle of coverage/image circle

    Hello, I was wondering what parameters determine the angle of coverage/size of the image circle of a lens. For example, for a fixed focal length, aperture and flange focal distance of a camera, what can a lens designer do to change the size of the image circle. I'd also like to know how the...