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. Heisenberg7

    Applying Force on a Cylinder at an Angle

    A few months ago, our teacher gave us a problem regarding cylinder motion. He asked us to calculate the acceleration of a cylinder that's acted upon by a force F at an angle theta due to the x axis. Now, for some reason, he told us that the cylinder would rotate. Now, I'm not sure if he supposed...
  2. chwala

    Find angle ADB in this isoceles triangle given some extra information

    Question; My take, I have, then using sine rule; ##\dfrac{x}{x+y} = \dfrac{\sin 20^{\circ}}{\sin 80^{\circ}}## ##\dfrac{x}{x+y} =0.347## ##x=3.47## then ##y=6.53##. then, ##BD^2=3.47^2+10^2-(2×3.47×10×\cos 20^{\circ})## ##BD= 6.842## ... ##10^2=3.47^2+6.842^2-(2×3.47×6.842 ×\cos...
  3. murshid_islam

    B Why are the axes taken as perpendicular to each other?

    Why are the axes taken as perpendicular to each other rather than at some other angle? Is it just a matter of convention? Is there any mathematical reason behind it? Is there some other reason?
  4. A

    How to Determine Correct Inverse Trig Angle?

    I understand why certain inverse trig functions have two answers. Like for arcsin(0.5), it could be pi/6 or 5pi/6. I know both angles have the same sin value, that they're both on the same horizontal line on a graph of sin, I get all of that, but two questions about it: 1) In cases where...
  5. U

    I Why are rotated parallel axes still parallel?

    I tried posting this on the physicsstackexchange, but wasn't making any progress in understanding what's going on. Suppose the axes in two coordinate systems S, S' are parallel. Now, suppose I rotate S through some angle ##\theta## and also rotate S' through the same angle ##\theta## It's not...
  6. vwoods316

    Finding critical angle: not sure which one is correct

    Attempt one: 1sin(35.8) = n2sin(90) n2=0.58 1.33sin(𝜃)=0.58sin(90) 𝜃_c=25.8 Attempt two: n1=n2/sin𝜃_c n1=1/sin(35.8) n1 = 1.7 sin𝜃_c = 1.33 / 1.7 𝜃_c = 51.57
  7. daisy7777

    Uniform Circular Motion: A plum-bob makes a 70 degree angle...

    I also tried to solve for T when the centripetal force is equal to the tension in the x-dir, but I got 2.174s and that's not the right answer either. I'm not sure what I'm doing wrong exactly.
  8. C

    I Work done by a non constant force over a non constant angle

    I was just wondering if I needed to set up this double integral or not. I've never seen anywhere people setting up double integrals for calculating the work.
  9. R

    A ball is thrown w/initial speed vi at an angle 𝜃i with the horizontal

    A ball is thrown with an initial speed vi at an angle 𝜃i with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/8. In terms of R and g, find the following. (a) the time interval during which the ball is in motion: Sroot(R/g) Correct (b) the ball's...
  10. chwala

    Calculate the value of ##θ## and ##X##

    My take, ##5 \cos 0 = 10 \cos θ## ##\cos θ = 0.5## ##⇒θ = 60^0## and ##X= 10 \cos (90^0-θ)=\cos 30^0= 8.66## (to two decimal places). ...insight welcome
  11. lambdadandbda

    How Does Special Relativity Affect Photon Emission Angles?

    I'm doing special relativity in undergrad and I have the following problem: Let a particle of mass M travelling at speed ##\beta = 1/2## (##\gamma = 2/\sqrt 3 \ \ c=1##) decay in to two photons: ##A \rightarrow 1+2## 1) Calculate energy and moment of the photons in the reference frame of the...
  12. Ineedhelpwithphysics

    Vector addition, trying to find the angle

    Is angle Vag 180 since the vector is a straight line pointing left? Also you can add 30 degrees with 150 which will be 180?
  13. Sciencemaster

    B How to find the infinitesimal coordinate transform along a hyperbola?

    I've been told that the infinitesimal change in coordinates x and y as you rotate along a hyperbola that fits the equation b(dy)^2-a(dx)^2=r takes the form δx=bwy and δy=awx, where w is a function of the angle of rotation (I'm pretty sure it's something like sinh(theta) but it wasn't clarified...
  14. K

    Engineering Calculate angle between spacecraft & Sun vectors

    Hi, so I have no clue how to solve this problem but I started off by rewriting the issue as a dot product to find the angle. So; cos(θ)= RSC⋅RSun / ∣RSC∣⋅∣RSun∣ Where Rsc = space crafts position vector. Rsun is the Suns position vector. ∣RSC∣ is the length of the spacecrafts position...
  15. Mohmmad Maaitah

    Engineering Improving Geometry Skills for Mechanical Engineers: A Recommended Book List

    I can't find the angle between F(Big arrow in my drawing) and the y-axis! I am terrible in geometry, what book do you suggest to me as Mechanical Engineer to get better at geometry?? This is my attempt to solution and the figure:
  16. MatinSAR

    Calculate the torque that is produced by this force on a cylinder

    Why it said that angle between r and F is 30? I guess it should be 120 degrees... Am I wrong?
  17. brochesspro

    B Finding Angle Between Fluid & Horizontal: Clarified

    I have been taught that in order to find the angle made by a liquid in a container with the horizontal, we use the fact that the free surface is perpendicular to the net force vector acting on the fluid (including the pseudo force vector for an accelerating container), however, if say the...
  18. NeophyteinPhysics

    The increase of Fidelity after non-selective measurement

    The above question is adopted from the exercise of Preskill's quantum information lecture note My attempt: (a) From the condition, ## p(\theta)\propto \sin^{(2N-4)}\theta \cos\theta ##. Normalizing the probability distribution would give the answer. This is because the weight of the phase of...
  19. chwala

    Find the possible values of angle ##∠ADB##

    My take: I got ##BC=10.25## cm, using cosine rule...no issue there. For part (b) ##BK=3cm## using sine rule i.e ##\sin 30^0 =\dfrac{BK}{6}## Thus it follows that ##∠BDK=48.59^0## ...⇒##∠ADB=131.4^0## correct...any other approach? Also: ##∠ADB=48.59^0## when BD is on the other side of the...
  20. 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...
  21. 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...
  22. 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...
  23. L

    Rearrange formula and work out phase angle

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

    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...
  25. M

    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...
  26. 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...
  27. 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?
  28. M

    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!
  29. M

    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##...
  30. 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?
  31. 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?
  32. 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||}##=...
  33. 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...
  34. 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 -...
  35. 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?
  36. G

    Is Moment of Inertia Dependent on Surface Movement Away from Axis?

    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\...
  37. 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...
  38. 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?
  39. 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...
  40. M

    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!
  41. 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...
  42. 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...
  43. Spocktastic

    What is the Correct Angle for Tension Force in Arm Mechanics?

    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...
  44. 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...
  45. 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...
  46. 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...
  47. 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.
  48. 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...
  49. 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?