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. A

    Component forces on angle bracket

    Homework Statement See photo attachment Homework EquationsThe Attempt at a Solution Ive begun by defining an x and y axis, followed by find the sum of x-components of the forces, and y-components. Followed by the magnitude of the resultant force. The only method i could think of was to find...
  2. M

    MHB Which is the velocity and the angle?

    Hey! :o If a particle of mass $m$ has velocity $v$, its momentum is $p=mv$. In a game with balls, one ball of mass $2g$ springs with velocity $2m/s$, it hits two balls, both of which have mass $1g$, and stops. The one ball get soared with velocity $3m/s$ and with angle $45^{\circ}$ to the...
  3. K

    Angles in a Static Equilibrium

    Homework Statement I have 3 masses (Fα, Fβ & Fg) with 2 pulleys, and a wind variable which is in static equilibrium. I have already calculated the appropriate forces for the 3 masses by multiplying it with 9.81m/s² (gravity). Fwind = 60N Fα = 313.9N Fβ = 619N Fg = 882.9N I'm required to find...
  4. Q

    Finding Angle of String with Two Charged Balls

    Homework Statement http://loncapa.vcu.edu/res/vcu/phys202/zzImages/Ch25_TB.jpg A charged ball with charge Q1 = 0.1 μC and mass 0.05 kg is suspended from a ceiling with a thin massless string as shown in the figure. The second charged ball has a net charge Q2 = -0.5 μC and it is located d = 0.3...
  5. E

    Why does magnetic field depend on angle?

    In addition, why is there no magnetic field along the line of motion of a charge? If length contraction occurs along this line of motion, I don't see why there is no magnetic field created along this line of motion for other charges to interact to. I get magnetism is fundamental, but at least...
  6. F

    Releasing a rod tied to a string which was held at an angle

    Homework Statement "Find the tension in the right string, when the left string is cut, if the mass of the rod is ##m## and its length is ##l##, and ##\sin \theta = 3/5##. The rod is initially horizontal." Please refer the diagram below (sorry for its clumsiness!). Homework Equations $$I_{rod}...
  7. evinda

    MHB Calculating the Angle between Ship and Rock

    Hello! (Wave) A ship that is at the position $(1,0)$ of a chart ( with the north at the positive direction $y$) "sees" a rock at the position $(2,4)$. Which is the vector that connects the ship with the rock? What angle $\theta$ does this vector form with the direction of the north? I have...
  8. F

    Ball bounce angle on inclined surface

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  9. L

    How to show how speed varies with incline, and with Gear ratio

    Hey guys, I'm having difficulty with my university project which is to build an electric bike. My design is to have a friction wheel attached to the shaft of my 800W 2800rpm electric motor which is rated at 2.8Nm. I have two issues with my spreadsheets at the moment. Can someone please help...
  10. C

    What is the optimum angle to hit a golf ball the furthest?

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  11. Neeps

    Sailboat rudder physics, and water flow estimate

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  12. B

    Ultrasound - Doppler angle vs. beam steering angle

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  13. J

    Given: parallelogram and right angle; Prove: parallelogram

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  14. B

    Find angle with given distance and height

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  15. Cosmophile

    Kleppner/Kolenkow: Conical Pendulum & Angle with Vertical

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  16. G

    Why light can't penetrate the prism with 45 degree angle

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  17. B

    Angle of electric field line heading to infinity

    Homework Statement Charges 2q and -q are located on the x-axis at x=0 and x=a respectively. (a) Find the point on the x-axis where the electric field is zero, and make a rough sketch of some field lines. (b) You should find that some of the field lines that start on the 2q charge end up on...
  18. DaveC426913

    What is the optimal support angle for a steel clothing rack?

    I'm building a clothing rack that swings out of the way. It's ideally made of 7/8" (or possibly 1") stainless steel tube, with 1/16" thickness and will sit on a 3" bearing (lazy susan) that supports 200lb. The top is firmly attached to a stud in the sloped ceiling. It needs to hold up something...
  19. K

    I How to Write Vectors in Spherical Coordinates for Scalar Product Evaluation

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  20. samjohnny

    Brewster Angle through Glass Slab

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  21. K

    Conservation of Angular Momentum; angle of rotation

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  22. Priyadarshini

    What is the Angle Made by a Pendulum Using Parallel Lines?

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  23. J

    Proving Vector Bisector Theorem: Simplifying Dot Products

    Homework Statement Show that vector C = (BA + AB) / (A + B) is an angle bisector of A and B. Where vectors are represented by bold font, and magnitudes are regular font. Homework Equations A ⋅ C = A C cos(θ) ⇒ cos(θ) = (A ⋅ C) / (A C) B ⋅ C = B C cos(θ) ⇒ cos(θ) = (B ⋅ C) / (B C)The...
  24. M

    Lab investigating angle of descent and velocity help

    Homework Statement I have to do a high school report investigating the relationship between the angle of descent and the velocity of a ball rolling across a horizontal surface after it has gone through a ramp. I have collected the data already with the use of photo gates that measured the...
  25. N

    Stator inlet angle in turbomachine?

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  26. E

    Field frequency and angle of incidence in optical waveguides

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  27. L

    What is the Angle of a Vector with x, y, and z Axes?

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  28. x2017

    At What Angle Will This Box Begin to Slide?

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  29. A

    Angle of deflection of electron

    Homework Statement 2 parallel plates of length 4.0 cm are arranged horizontally in a vacuum. The upper plate is positively charged and the lower plate is negatively charged. An electron is projected horizontally with an initial velocity of 6.0 x 106 ms-1 and experiences a constant electric...
  30. T

    Observing wavelength at an angle

    I recently came across an equation stating that ## \lambda_{ob} = \frac{\lambda}{cos(\alpha)} ## if ##\alpha## is the angle the observer is relative to the wave's direction of propagation. I guess I can kind of understand that a person perpendicular (i.e. ##\alpha = 1##) would see the normal...
  31. N

    MHB Solve for frequency & angle in dispersion equation

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  32. Bdhillon1994

    The End of the Ski Jump - Optimizing Launch Angle

    Homework Statement A ski jumper leaves the ski track moving in the horizontal direction with a speed of 25.0 m/s as shown in Figure 4.14. The landing incline below her falls off with a slope of 35.0°. Where does she land on the incline? I've attached an image of the problem, my work is below...
  33. O

    Simple Harmonic Motion - Determine quadrant for phase angle.

    Homework Statement When completing this problem I am able to find a value for the phase angle but am unsure of how to find the quadrant for the phase angle therefore unable to get the correct phase angle. Homework Equations Provided in the question: x = xmcos(wt+ phi) The Attempt at a...
  34. I

    Loss cone opening angle

    Homework Statement Hi! I need to find the opening angle of the loss cone at a given altitude, when the magnetic latitude is 65 deg. Homework Equations See below The Attempt at a Solution First, I used the following equation to calculate the magnetic field at a given altitude...
  35. F

    Satellite angle, remote sensing

    Homework Statement You have a geostationary satellite (location 0◦N 0◦E, 36000 km above geoid). Assume the Earth to be spherical with a radius of REarth = 6372km When observing a region centered at 60◦N 0◦E: What is the incidence angle of the satellite’s line of sight (at pixel center...
  36. S

    Circulation of a Mag field around a wire, what is the angle?

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  37. R

    Astrophysics - Hour angle calculation

    Homework Statement At midnight (local time) on Dec 21st 2015, the Local Sidereal Time at Palomar Observatory, California, was 6h 27m. Palomar Observatory has latitude 33◦ 210 2100 N, and longitude 116deg 51arcmin 60arcsecW. a) What was the approximate Local Hour Angle of the Sun at 23:00 local...
  38. nilfound

    How to find the Eg of an object thrown at an angle?

    Homework Statement Four identical balls are thrown from the top of a cliff, each with the same speed. The first is thrown straight up, the second is thrown at 30° above the horizontal, the third at 30° below he horizontal, and the fourth straight down. How do the speeds and kinetic energies of...
  39. I

    Charged particle hitting electric field at angle?

    If I have an electric field between a cathode and an anode, are there electric field lines between the plates? If yes, what happens if a charged particle enters the field at an angle? Is the force acting on the particle reduced?
  40. J

    Given two waves, find phase angle

    Homework Statement Given two waves characterized by y1(t) = 3 cos wt; y2(t) = 3 sin(wt + 60deg); does y2(t) lead or lag y1(t) and by what phase angle? Homework Equations y1(t) = 3 cos wt; y2(t) = 3 sin(wt + 60deg) The formula I'm given in my book Fundamentals of Applied Electromagnetics is...
  41. D

    What Angle Should the Goose Fly to Head Directly Southward?

    Homework Statement Canada geese migrate essentially along a north-south direction for well over a thousand kilometers in some cases, traveling at speeds up to about 100 km/h. The one goose is flying at 100 km/h relative to the air but a 38 km/h -km/h wind is blowing from west to east. At what...
  42. J

    Angle of Refraction through a Prism

    Hello everyone, I am trying to figure out how to explain an aspect of this question to my students, but cannot seem to recall the geometry that explains the textbook's approach. In the figure below, for part (b) of the question, we are using the angles of refraction at the left boundary to...
  43. J

    How to find initial velocity with height, distance and angle

    Homework Statement We need to fin the initial velocity of a water fountain. The data I have collected is: Height (bottom to apex)= 0.042 m Distance (from spout to end on the stream)= 0.112 m Time (it takes to travel)= .25 seconds Angle the water shoots from= 50 degrees Here is more if it...
  44. S

    Relation between cross section, scattering angle and KE?

    I'm trying to figure our the relation between cross section, scattering angle and KE? I'm doing a few exercises where I've been given kientic energy and scattering angle and have to calculate the cross section. Cross section is in units of Barns (m2), and KE is 1/2 kg*m2*s-2, but I can't seem...
  45. R

    Calculating Archerfish's Line of Sight Angle in Relation to Squirt Angle

    Homework Statement An archerfish hunts by dislodging an unsuspecting insect from its resting place with a stream of water expelled from the fish's mouth. Suppose the archerfish squirts water with a speed of 2.00 m/s at an angle of 50 degrees above the horizontal, and aims for a beetle on a...
  46. L

    MHB Calculate the sides of a triangle knowing its area, perimeter and angle A.

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  47. Albert1

    MHB Find $\angle ADB$ in a Plane

    In a plane we have :$\overline {AB}=\overline {BC}=\overline {CA}=\overline {CD}=10$ and $\overline {AD}=11$ find :$\angle ADB=?$
  48. carllacan

    What determines the Compton scattering angle?

    Hi. I've been reading about Compton scattering and I don't understand what determines the angle at which the electron and photon are scattered. Is it a quantum process, and therefore the value of the angle is "random"? If it is a quantum process, is there any theory that gives the probability...
  49. R

    Angle made by arms with horizontal

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  50. A

    Ball thrown from ISS to earth at right angle to it's path

    Suppose I am on ISS and Earth is exactly below (at the right angle to the ISS's line of path). Now if I throw one ball below towards Earth from window at exactly 90 degrees to the line of path of ISS and one ball upwards at right angle to the line of path of ISS. **Assume normal human strength...
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