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. Tali

    In mechanics: doea the length of the wire affects the angle?

    Homework Statement general question: if I give a ball velocity (He is tied to a wire (tension)) and consider that the wire has no mass. Does the length of the wire affects the angle? If I solve this with energy tools then I get that the longer the wire the smaller the angle. it does not settle...
  2. A

    Investigate one factor that affects the angle of refraction

    Statement: I need a suitable method and factor to investigate ONE factor that affects the angle of refraction. It has to be related to the context of everyday life and glasses, i.e. how glasses are used to focus light and the light focused is that of a refracted ray. Therefore factors such as...
  3. T

    Angle of Impact: Calculating with Velocity & Distance

    Homework Statement A ball rolls off a table at speed v and impacts the floor at distance d. What is the angle between the path of the ball and a vertical line drawn at the moment of impact. Homework Equations I have derived from basic projectile motion formulae: Time of impact t =...
  4. A

    Find the Angle Theta for E Field in Glass Below Boundary | E Field Problem

    Problem statement: The E field measured just above a glass plate is equal to 2 V/m in magnitude and is direct at 45° away from the boundary, as shown in the figure. The magnitude of the E field measured just below the boundary is equal to 3 V/m. Find the angle theta for the field in the glass...
  5. T

    Solving trigonometric equations using compound angle formula

    Hello. I find this whole topic of compound angle formula really confusing. I've been doing equations like cos(60+x) = sinx using the co function identities so far, yet this one seems to be impossible to do using cofunction identities so I need to know how to do it using compound angle formula...
  6. C

    Elastic collison at an angle

    Homework Statement A racquet ball with mass m = 0.224 kg is moving toward the wall at v = 15.1 m/s and at an angle of θ = 28° with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the...
  7. Samurai44

    Calculating Critical Angle: Relative vs. Absolute Refractive Index

    Greetings, Do we use Absloute refractive index when finding crtical angle ? if it was two mediums ( not vacuum or air) how would i calculate the critical angle ? I mean i get confused when I find relative refractive index because sometimes i get sine inverse greater than 1 which give no...
  8. R

    Torsion, angle of twist, diameter, load, momentum and find G

    http://www.upload.ee/image/4760492/DSC_0002.JPG Homework Statement I have given angle of twist, diameter, uniform load, and length of the beam. I need to find the G.The load gives me some trouble and i don't know if i should solve it by using integration or? :) Homework EquationsThe Attempt...
  9. B

    Calculate intial angle of a refracted wave

    Please see attached image for problem and brief description of attempted solution.
  10. W

    Calculate angle of swing in a carousel

    Hello, this problem has given me headaches for days 1. Homework Statement The diameter of a carousel is 15 m and it rotates 8,0 rounds per minute. Calculate how large of an angle is formed with respect to the vertical plane by the swing that hangs by the ropes fixed to the edge of carousel...
  11. Eoraptor

    Angle determination of Sum-Frequency Generation in BBO

    Hi, 1. Homework Statement I have difficulties to get the correct angles for a third-order autocorrelator and I hope you can help me. In my setup are two BBO Crystalls, the first for SHG (Second-harmonic Generation) and the second for SFG (Sum-Frequency Generation). The Laser is a...
  12. Dyatlov

    Need help with a triangle's length side/ angle relation.

    Hello. I am trying to wrap my head around where from did he got the x = sin of theta equation at the 32:44 mark of the video: . Isn't sine of theta x over the hypotenuse in the diagram ? Thanks in advance!
  13. S

    How do two light beams combine at a shear angle?

    How do two light beams combine at a shear angle? Two electromagnetic beams cross at a shear angle. They have equal phase, intensity and polarization. The angle is shear enough, so that in region in which they intersect, there is less than a quarter wave difference in phase over the...
  14. C

    Circular Aperture Diffraction, Angle of First Minimum

    Homework Statement A helium-neon laser ( ##\lambda =633nm##), is built with a glass tube of inside diameter 1.0mm. One mirror is partially transmitting to allow laser light out. From an optical perspective, the laser beam is a light wave that diffracts through a 1.0mm diameter circular...
  15. G

    Calculate Refraction Angle of Light Falling to Aquarium Water

    Homework Statement I need to calculate refraction angle of light, if light ray is falling to the surface of aquarium water from the bottom in the angle of 60 degrees, n for water = 1,33 Homework Equations sinφ2=(n1×sinφ1) /n2 The Attempt at a Solution So i get sinφ2=1,33*0,866( meant as...
  16. D

    Angle Elevation of King's Chamber in Pyramid: Get Answer Here

    I have posted this question in other forums and received nothing for an answer, So it's worth a shot here :-) What is the angle elevation of the king's chamber in reference to the base of the X,Y,Z center of the pyramid? Or should I ask the question this way? Measuring from the center of the...
  17. A

    Calculate turning angle - 2 wheels car

    i am looking for a function for calculating the turning angle, using the difference between two wheels speed. i have a model car , with 2 engines and 2 wheels, without steering. thanks.
  18. C

    Speed limitations of pot & arduino for angle measurement?

    If I am using a continuous rotation potentiometer on a pulley, and I want to use an Arduino to convert this reading into an angle as part of an angle control system, then what are the limitations for how fast the pulley can turn? Specifically, if the pulley is turning at 450RPM, will a...
  19. saadhusayn

    Length contraction at an angle

    Hi, My question concerns the following problem from chapter 4 of Special Relativity by A.P. French. A statement of the problem: 4-15 A flash of light is emitted at point O and is later reabsorbed at point P. In frame S, the line OP has a length l and makes an angle θ with the x axis. In a...
  20. Shahab Mirza

    Diffraction Grating Problem ?

    Hi, 1. Homework Statement Q : A diffraction grating with 10000 lines per CM is illuminated by yellow light of wavelength 589 nm, At what angles is the 2nd order bright fringes seen ?Homework Equations From my textbook , I got this equation , d sin theta = m (λ) The Attempt at a Solution Ok so...
  21. lulzury

    Small Angle Approximation in Single Slit Interference

    Homework Statement A monochromatic light source is used with a double slit to create an interference pattern on a screen that is 2.00 meters away. If the 2nd bright spot is observed 8.73 mm above the central maximum, can the small angle approximation be used? Show and/or explain your reasoning...
  22. moenste

    Stone thrown off a cliff: height and angle

    Homework Statement A stone thrown horizontally from the top of a vertical cliff with velocity 15 m s-1 is observed to strike the (horizontal) ground at a distance of 45 m from the base of the cliff. What is (a) the height of the cliff, (b) the angle the path of the stone makes with the ground...
  23. A

    Where is my calculation of sun angle incorrect?

    Hi there, I hope this is the right place for this question and furthermore doesn't appear rude that my first post is a question! If so, I do apologise, I haven't been able to find an appropriate place to ask this. I'm working on calculating the position of the sun at a given day of the year for...
  24. A

    The greatest angle at which a ladder won't slip

    [EDIT: Never mind about this problem, I found my mistake.] 1. Homework Statement A uniform ladder of mass m and length L rests against a wall. The coefficients of static friction between the floor and the ladder and between the wall and the ladder are equal to each other (μ). What is the...
  25. K

    Angle of Deflection of Laser Given Tilted Mirror

    Hi Everyone, A question in my latest Physics I lab wishes for a proof showing that if a laser beam is incident on a mirror that is then rotated an angle θ the beam is deflected an angle 2θ. I attempted to prove this geometrically below. In the diagram the angle γ, is the angle of deflection...
  26. 1

    Computing Cherenkov angle when only knowing n?

    Homework Statement If all we know is that the media is 1.001, how can we compute the Cherenkov angle and threshold momentum of electrons,muons, pions, and kaons?Homework Equations I know that cos(theta_c) = 1/beta*n, where beta = v_p/c and n=c/v_em, where v_p is the particle velocity and v_em...
  27. W

    Predicting angle of deflection of light

    Hello, I was recently reading relativity the general and special theory by Albert Einstein. When I came across the equation to calculate the angle of deflection for light as it approaches a massive body. I was just wondering if someone could explain why this works and also what "1.7 seconds of...
  28. K

    Force required to hold a pendulum at an angle

    What is the minimum horizontal force "F" required to hold a simple pendulum (mass "m") with string of length "l" at an angle of 60 degrees with the vertical. [ given answer = mg/√(3) , veracity uncertain ]This at first seemed simple enough, standard mechanics apply, leading to ...
  29. gracy

    Angular magnification what is angle subtended?

    In case of simple microscope .we take angular magnification I know The angular magnification of an instrument is the ratio of the angle subtended at the eye when using the instrument divided by the angular size without the instrument But what I am not getting is how this subtended angle is...
  30. Mr Davis 97

    Does the angle of a ramp with the ground affect velocity?

    I have a question. If a put a marble at the top of a ramp, will the angle that ramp makes with the horizontal affect the velocity of the marble when it arrives at the bottom of the ramp? I am suspecting no, since the gravitation potential energy does not change as we change the angle of the...
  31. Harry Atkinson

    Compton Scattering: Find scatter angle of electron & Vf

    Homework Statement http://oi58.tinypic.com/2zitybl.jpg Homework Equations As above The Attempt at a Solution [/B] Rearranging the above equations to remove unknowns, finally substituting new equations into the compton effect equation. Will post up next page as I fill it, - is it acceptable...
  32. A

    MATLAB Matlab: Finding the right angle

    Hi! I have a question about an assignment. It is about throwing a rock which should land 20 meters away from the "shooter". My job is to find the angle "a" which makes the rock land 20 meters away. The motion is given by a multivariable, second order differential equation which I have already...
  33. Z

    Double Slit Diffraction:Finding Greatest Angle for Minimum

    I'm at wits end. I hate WileyPlus. Part A, B and C are correct. I cannot figure out what Part D is -- all of the answers I am getting are wrong. Homework Statement Homework EquationsThe Attempt at a Solution
  34. O

    How Can I Improve the Viewing Angle on a Basic LCD?

    I'm in need of some help understanding the viewing angle of a basic LCD. I am replicating a product that contains a backlit LCD from a similar product. The original product has an orange display that is clearly viewable at most angles. The similar product has a blue display that has poor...
  35. Y

    Self Locking in Worm Drive with lead angle of about 8

    Hi I have built a gear drive for robotic arm that uses a worm set (worm gear +worm) at stage one. Worm (wheel) is of bronze and worm gear is steel haing a lead angle of appx 8 deg. This set is further coupled to a spur gear set that further increases the torque such that the over all gear ratio...
  36. dwn

    How to Calculate RLC Phase Angle in Multisim

    Homework Statement This is actually a lab I'm performing on Multisim. I've recreated a circuit that I build in lab class , but I'm not getting the output I need. I am trying to calculate the V and phase angle across each component. I already have the measurements found form the class lab. In...
  37. S

    Electric Field Angle at Origin: 209 deg

    Homework Statement A +20nC point charge is placed on the x-axis at x = 2.0 m, and a -25 nC point charge is placed on the y-axis at y= -3.0 m. What is the angle that the direction of the electric field at the origin makes with the x-axis. (a) 209 (deg) (b) 61 (deg) (c) 29 (deg) (d) 241(deg) (e)...
  38. YearnToLearn

    Finding max acceleration with force at angle incl friction

    Homework Statement Hey. I was doing some exam practice questions, but I hit a snag with this one and can't quite work out how to proceed. A 6kg block at rest is pulled along a horizontal surface by force F→ at angle θ. Given that the coefficient of kinetic friction is 0.15, find the optimal...
  39. K

    Which have smallest bond angle? NH3 or N(CH3)3?

    Hi guys, which of nh3 and N(CH3)3 have the smallest bond angle? My answer is NH3, because H is smaller than CH3. so lone pair electron of N can easily push the H and make the bond smaller. Is this right?
  40. X

    Finding the phase angle of current through a capacitor?

    Homework Statement Calculate the current in the capacitor shown in the figure below if the voltage input is V(t) = 29cos(377t-30) V, C = 1 micro Farad Homework Equations i = C dv/dt The Attempt at a Solution I essentially differntiate V(t) and multiply by 1 * 10^-6. I then get a negative...
  41. A

    Horizontal & vertical angle of antenna beams & UE position

    Hi this is my first post here. Sorry for this naive question xD I want to calculate antenna gain for which I need the horizontal Φ and vertical θ angle of an antenna beam. The formula for gain is. is it ok to convert the rectangular coordinates of antenna into spherical coordinates and compute...
  42. S

    Statics: find tension/wrap angle for pulley

    Homework Statement Given: T(sub-B) plus T(sub-B) prime = 36. Both T(sub-C) values are 0. T (sub-D) =36 and T (sub-D) prime = 12. Find values of T (sub-B) and T (sub-B) prime[/B]Homework Equations OK, so we need to find the wrap angle, which should be 180 + 30 -22, which comes to 188...
  43. F

    Astronomy: Sun azimuth from altitude, hour angle, and declination

    Homework Statement Hi everybody, I am trying to do a numerical aplication of change of coordinate system to another; the objective is to calculate the azimut of the sun knowing the altitude, hour angle and declination . Homework Equations Cosh * Sina = Cosδ * Sin H where a is the azimut h is...
  44. F

    Doubt About Hour Angle: How Can It Change So Little?

    Hi everybody, I was messing arround with the program stellarium; I decided to check the hour angle of the sun at 10 am on August 12; it was 19h 53 min; then I did the same for september 4th and it was 20h 0 min. As far as I know it takes 23h 56 minutes to the sun to cross the same point in the...
  45. I

    Unsure about angle inside Mohr's circle?

    Can someone explain why the angle inside the triangle inside Mohr's circle is θP2 rather than θP1 ? I understand everything else but just this small point is frustrating me. Thanks
  46. T

    Confusion about EM Transmission coefficient - critical angle

    Hi, The reflection coefficient (R) of an EM wave is, as far as I know, 1 if there is total reflection and -1 if there is total reflection AND the phase changes by 180º. However, we also know that the transmission coefficient is given by T = R + 1 (or by its own formula, which should give the...
  47. R

    How do I calculate the angle of rotation?

    Homework Statement We consider Rectangle Parallelepiped on a board and a=1m ; b=2m and c=3m. The face a and b is considered touching the board. there’s no sliding; we tilt the board so a is horizontal. Q: Starting from which angle we can see a rotation? Homework Equations I want to know how...
  48. Y

    The distribution of energy and angle of backscattered SEs?

    What is the distribution of energy and angle of backscattered electrons from a few MeV heavy ions beam? Someone telled me the energy obeys landau distribution, but I don't know what's the most probable energy.
  49. Philosophaie

    Between -180 and 180 degrees (convert a larger angle)

    I need a formula to put an angle between -180 and 180 and recycle if not in the range. I can do it between 0 and 360: angle = deg - 360 * floor(deg / 360) just not between -180 and 180 Oh and what is the name of this function?
  50. G

    At what angle of force is Kinetic friction least?

    Homework Statement The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction Uk is least when the force is applied at an angle theta such that a.sin(theta) = Uk. b.cos(theta) = Uk. c.tan(theta) = Uk. d.cot(theta) = Uk. e.sec(theta) = Uk...
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