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. AncientOne99

    Change of angle if refractive index changes for 10^-6

    Solution: (delta (ϑ)) = -(minus delta n) /(n*sqrt((n^2-1)))
  2. J

    Trigonometry Help: Calculating the Angle of Light Entry & Exit

    So what I did first was made the face of the triangle flat and calculated the angle the light entered it. This means the light enters the triangle from the base corner angle (so (180-38.8)/2) of 70.6 degrees. 1sin(70.6)=1.47sin(angle) angle=39.915 Now I need to find the angle it exits. But...
  3. M

    Oblique shock waves: how to find the wedge angle for trailing shock?

    Hi, I have a question regarding oblique shockwaves. Question: How can we determine what the wedge angle is for the shockwave in a situation? Context: This problem here shows an oblique shock wave on the trailing edge of the body and it simply states that the wedge angle is 6 degrees. Why is...
  4. J

    Find maxima angle of two interfering waves

    I drew a diagram in the attached files as well, but the the scenario seems to be the same as the double slit experiment, but I don't understand why the answer contains cos instead of sin.
  5. yucheng

    Simmons 7.10 & 7.11: Find Curves Intersecting at Angle pi/4

    >10. Let a family of curves be integral curves of a differential equation ##y^{\prime}=f(x, y) .## Let a second family have the property that at each point ##P=(x, y)## the angle from the curve of the first family through ##P## to the curve of the second family through ##P## is ##\alpha .## Show...
  6. B

    What is the angle between the acceleration and velocity when rotating?

    ##ω = \frac {k} {\sqrt{φ}}## What is the angle between acceleration and velocity after 1spin (2π radians)? First I decided to find out what is the angular acceleration: ##α = \frac {dω} {dt} = \frac {dω} {dt} \frac {dφ} {dφ} = \frac {dω} {dφ} ω \implies ##after integrating ##\implies α = -...
  7. M

    MHB When is the Maximum Angle for Viewing a Tower from an Airplane?

    Hey! :giggle: An aeroplane flies over a tower of height $h> 0$ at height $H> h$. At what distance $x$ is the angle $\alpha$ at which the tower is seen from the aeroplane, maximum? (You can use elementary geometry and that $\arctan'(x)=\frac{1}{1+x^2}$.) From Pythagorean Theorem for the...
  8. Athenian

    Young's Photon Interference - Question on Angle & Voltage

    After conducting the photon interference experiment, below is a sample data of what we got: Time (s) Angle (V) Two-slit Diode (V) 0 0.988 0.203 0.102 0.984 0.297 0.805 0.976 0.398 1.201 0.974 0.5014 1.31 0.968 0.526 The above list goes on for quite a few columns...
  9. I

    Finding the x component of a vector given this angle

    A = |A|cos33.7 A = |A|0.83195
  10. SabeneGeorges

    1" Aluminum Angle 1/16th thick - How much shelf weight?

    I am building a plant rack. Because of size restrictions, I must use angle iron and I want to use aluminum angle because of weight. I am looking at aluminum angle (L shaped) for the shelf brackets. The aluminum angle is 1" and 1/16th thickness, 24" long and screwed into wood. Each angle will...
  11. Euan12345

    Using phase difference to find the angle of a signal

    I want to locate an infrared signal using Angle on arrival (AoA), I have elected to use Phase Interferometry to achieve this, I am however struggling to understand how the phase difference (∆ϑ) is found. Can someone explain how I could find this?
  12. F

    Electron-positron annihilation, photon emission angle

    I consider the laboratory system. The four momentums in this reference system are respectively: ##p^\mu = \big(\sqrt{|p|^2+m^2}, 0, 0, |p| \big)## ##p'^\mu= \big(m, 0, 0, 0 \big)## ##k^\mu = E\big(1, 0, 1, 0\big)## ##k'^\mu = E'\big(1, 0, -\sin \varphi, \cos \varphi \big)## I used conservation...
  13. M

    Rotation angle measurement of pedal with ball and socket joint

    the device that I have is the same as the mirror of this truck.
  14. T

    How the flow angle along the blade would change along the length

    I am not sure how to do this at all or what exactly he is asking me. [Mentor Note -- Two threads on the same problem have been merged into one]
  15. Leo Liu

    The angle of tilt of a gyroscope

    Problem Solution My question For the torque equation, I calculated the torque of the wheel at the point at the upper end of the string L' and wrote ##\dot{\vec L_x}=\tau_x=-Mg(l+L\sin\beta) \text{[the direction of x is out of paper]}## rather than the equation highlighted by green colour...
  16. karush

    MHB Act.ge.5 third angle of triangle

    $\tiny{act.ge.5}$ ok you have 2 seconds to figure this one out:unsure: This question has live answer choices. Select all the answer choices that apply. The correct answer to a question of this type could consist of as few as one, or as many as all five of the answer choices. \item In triangle...
  17. B

    B How to Linearize an R vs θ graph (distance vs angle)

  18. J

    Displacement & Angle Theta: Figuring Out Centripetal Force

    For the displacement, how do I figure out the angle theta between the points? And how does the speed at which the string retracts affect the centripetal force?
  19. W

    MHB Angle at Y-axis Crossing of y=sin(1/x) Graph

    at which angle does the graph y=sin(1/x) cross the y-axis??
  20. M

    I How Does Solid Angle Affect Power Calculation in Radiometry?

    I have a doubt regarding the role of the solid angle when calculating the power(W) with the brightness of the source I'm observing with area Asource. I was given the definition: with A the Aantenna. If now I take as an example the picture below to calculate W, we conisder as solid angle the one...
  21. D

    Engineering Deflection and deflection angle -Unit Load Method (Cantilever beam)

    Please help to check whether I did it correct, thanks
  22. D

    Engineering Determine deflection and deflection angle using Unit Load Method

    relevant equations: My questions: (1)Not sure whether I did correct especially for the deflection angle (2)The limit taken for calculating defection Yc , I didn't understand why is from 0 to L/2 instead of the sum of 0 to L/2 and 0 to L, how is the limit determined? Kindly advise, thanks
  23. J

    Using Equipartition theory to solve the root mean square of a angle.

    For the first question, i believe that mechanical energy is conserved hence we can derive the total energy i think. In regards to the second question, I'm assuming its at room temperature, so helium is monotonic therefore it has 3 degrees of freedom, therefore its internal energy is 3/2KT. I am...
  24. S

    Determining the angle while dealing with friction on an inclined plane

    Hello! So the way I have tried to solve this problem is the following;Since it is an inclined plane and the cofficient of static friction is known, getting to the angle at which the box starts sliding is the following ##μH = \frac {sin (\alpha)} {cos(\alpha)} = μH = tan(\alpha) ## ## \alpha =...
  25. T

    Angle between the hands of a clock (IWTSE)

    I understand this working all the way up until the '2n-1' part, where n is a positive integer. I understand that delta theta is 90 degrees (i.e. pi/2 radians), as the hands are at right angles to each other.. I also understand where the angle equations are derived from and why you have to find...
  26. P

    A What is the meaning of ##d\Omega## in solid angle integration?

    Anyone have any idea how to perform the following two integrals? ##\int d\Omega n_{i}n_{j}## and ##\int d\Omega n_{i}n_{j}n_{k}n_{l}## where the n is a unit vector.
  27. junseok Lee

    I Finding the change in position and angle after moving the rectangle

    I am curious about how to approach the problem mathematically, so I write. There are 4 dots on the square and I know the location. The rectangle moves and the positions and angles of the four points change. I also know the location of the four points that have changed. I don't know the...
  28. DaveC426913

    Boom Angle of Crane: Is High Extension Necessary?

    These boat hauling cranes seem to extend their booms as high as possible. Much higher than necessary for the max height of the boat lifting rig. Does this accomplish something effort or safety-wise? It's not like a simple torque situation - the force applied is gravity - straight down - not...
  29. M

    A Claimed derivation of Weinberg angle, Higgs/W mass ratio

    https://arxiv.org/abs/2010.15621 Superselection of the weak hypercharge and the algebra of the Standard Model Ivan Todorov [Submitted on 29 Oct 2020] I haven't had time to study this paper yet. But a few curiosities: It talks about Clifford algebras. But in fact it builds on work due to...
  30. Jojo-11

    Why does acceleration increase by less as angle of slope increases?

    My only guess is that this is due to air resistance. Below an example of the predicted graph:
  31. andyonassis

    Finding the angle between a plumb line and the Earth's surface.

    From Newton's second law: $$T_{x} = F_{turn}$$ So $$T \sin \theta = ma$$ $$T_{y} = F_{y}$$ so $$T \cos \theta = mg$$ Equate the two equations to get: $$ \frac{T \sin \theta}{a} = \frac{T \cos \alpha}{g} $$ and the angle is given by: $$tan (\theta) = \frac{a}{g} $$ where ##r = \frac{v}{w}## and...
  32. M

    Static Contact Angle (fluids)

    Hi PF! I have an experiment where a wedge about 160mm long is in microgravity. I withdraw silicone oil from the wedge at a relatively slow rate (no turbulence). Since the wedge angle is small, a lubrication approximation is made. Inertia is shown to be low. I want to simulate this flow. When...
  33. K

    Understanding of Wave swing physics

    Yeah, as I said, i have no idea why we can assume beta to be the same for any position at given alpha.
  34. F

    Angle of reflection of a beam light on a moving mirror

    Before to open this topic, I found this there. It's quite similar, if not the same, but I'm a little confused, so I'm here. The situation is represented in this image. From optical geometry, ##\theta_{incident} = \theta_{reflected}## The four-momentum in ##S'## is the following one...
  35. H

    I Where does this solid angle come from?

    I found this paper https://arxiv.org/abs/quant-ph/0412216 We have an interferometer with to arms. The firsr has a couple of HWP's inclened by an angle theta and the second has the crossed couple. A mixed state is in input. i look to the figure withe the Bloch sphere. i see 2 paths on it. one...
  36. Andrei0408

    Inclination angle of a banked turn in a road for a maximum speed

    I know the solution is based on velocity and the sliding friction coefficient, and I believe I should put the condition Fcf smaller than Ff, but I just don't understand how to include μ in the solution, to find the angle. Even if you don't solve the problem, I just need to understand the...
  37. A

    Need help finding the launch angle of a ball

    the mass is 0.8kg speed is 50m/s distance is 100m
  38. cwill53

    Using the solid angle to simplify an integral when deriving Gauss' Law

    I'm a bit confused on the derivation above. I understand what the goal of the derivation is, as it derives Gauss's Law using the solid angle, but i was wondering if someone could kind of fill in the steps the author skipped and explain the use of the solid angle.
  39. A

    Minimum value of an angle

    I tried to do it by derivative but there are two variables, so I don't know how to proceed. Does anyone know how I can solve it? Remembering that you don't need to find the value of ##\theta##. I just need to find a relationship between ##\theta_1## and ##\theta_2##
  40. kspex2

    Two mirrors meet at a 135 degree angle.... (light ray question)

    I tried to use complementary angles and the law of reflection but I still have no idea how to find the angle.
  41. T

    A ball thrown at an angle above an inclined plane

    I understand how the diagram below determined the ##x## and ##y## axis for the velocity vectors but I don't understand the gravity vectors. What I don't understand about the gravity vectors is why is ##-mg## in the ##y-##axis equal to ##-mg\cos\theta## and the ##x-##axis is equal to...
  42. K

    Calculating Angle Between E-Field and Current Vectors in Anisotropic Mat.

    In a certain anisotropic conductive material, the relationship between the current density ##\vec j## and the electric field ##\vec E## is given by: ##\vec j = \sigma_0\vec E + \sigma_1\vec n(\vec n\cdot\vec E)## where ##\vec n## is a constant unit vector. i) Calculate the angle between the...
  43. AN630078

    Trigonometry: finding an angle, area and length of sector of a circle

    1. Using the formula for the arc length; s= θr I have endeavoured to find the angle AOB sine both the arc length and radius are known; 11= θ*8 θ=11/8=1.375 rad I actually do not think that this can be correct as it seem to simplistic a response. Have I misinterpreted the question or used the...
  44. M

    A Exploring Cabibbo Angle Anomaly: Modified Neutrino Couplings

    These days, most particle physics anomalies (meaning, observations suggesting beyond-standard-model physics) eventually disappear under closer scrutiny. This one caught my eye because it can be attributed to the neutrino sector, which we understand least and which therefore has the most room for...
  45. S

    Mechanics: Find the minimum initial velocity and angle of this projectile

    Attempt at solution in attachment.
  46. Ozen

    Minute Of Angle Linear Adjustment Help

    I am working on developing a micro reflex sight and finally got the optical science of it sorted out, but now I reached a new impasse (hopefully the last really difficult one!). The device has to have an adjustment mechanism so the user can align the reticle with the bullet impact point, which...
  47. GreenOlive

    Change in acceleration with change of angle of applied force

    Let ##μ_k## = 0.5 ##F_a## = 10 Newtons ##\theta## is the angel of the Applied force. How will the acceleration of the block change if the angle of the applied force is increase by ##5^o##? Write Increase, Decrease or Stay the same. Recently we were discussing a question similar to this in...
  48. Amit1011

    Why am I getting this weird equation between angle and time?

    I tried solving this, the equation coming up is given by: θ≈4 cot^(-1)(e^(-3.1305 sqrt(1/R) t)). However, this is not correct as can be seen when plotted: enter image description here Can somebody please let me know, why is this equation not valid.?
  49. TheSurfers12

    I Lorentz Factor Variant: Derivation & Angle Dependence

    I made a derivation of a general transform of the lorentz factor but i still looking in books that the lorentz factor is 1/sqrt(1-v^^2/c^^2) and my derivation is perfectly correct, my result is 1/(sqrt(1-v^^2*sin(a)/c^^2)+v*cos(a)), if we put here 90 degrees we get the classical lorentz factor...
  50. F

    Shooting in a π/4 Angle: Is it Possible?

    So the statement says that in r(0)=0, so it departs from the origin. And it also says that v_y0 = 0, thus meaning thar it´´´ s position in the y direction is Constant. Is shooting in a π / 4 angle still plausible? or there´ s no way that can happen? So far I´ ve thought since there´ s no...
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