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. S

    The relationship between angle and static coefficient

    I know you find the static friction of an incline by raising it until it begins to move and then measure the tangent of that angle, but I'm not sure how I'm supposed to show a relationship or create a procedure based off that.
  2. S

    Angle observed in rest frame related to relativity

    My answer is (A) since I think the motion of the spacecraft will alter the length of the spacecraft (length contraction) but not changing the orientation so the angle will stay the same But my teacher said my answer is wrong. What is my mistake? Thanks
  3. R

    Mechanics: calculating launch angle of projectile

    I am trying to find the launch angle ##\theta## using the relationship: ##\theta=\arctan(\frac{v_{y}}{v_{x}})## So, ignoring attenuation due to air resistance, we have a constant horizontal velocity: ##v_x = d_x/t = 95m/4.5s \approx 21 m/s## But what value do we use for ##v_y## which is not...
  4. neilparker62

    I Maximum Angle of Deflection for Colliding Particles

    When a heavier mass (or nucleus say) collides with a lighter one, it deflects through a certain angle which has a theoretical maximum. There are numerous derivations for this maximum angle of deflection ##(\sin\theta_{d_{max}}=m/M)## where m is the small mass and M the larger but none seem to...
  5. ayans2495

    Relationship between horizontal range and angle of launch

    I would like to conduct an experiment asking the question "how does the angle at which a projectile is launched vary with respect to the horizontal range it covers?" Ultimately, I'd like to prove that the horizontal range is directly proportional to sin(2(theta)). This will be done with the aid...
  6. R

    A Optimum profile of light pipe exit for narrow beam angle

    I am trying to design an acrylic light pipe that has a 3W power red LED input with 60 degree beam angle. I need a reasonably collimated exit light beam or at least a narrow angle output. What I'd like to know is - what is the optimum shape of the exit end of the light pipe to produce the...
  7. wnvl2

    I Absolute meaning of spatial deviaton angle of light around the sun

    Einstein first calculated the bending of light rays that are touching the sun as 1.75 arc-sec. For the calculation I refer e.g. to https://www.mathpages.com/rr/s8-09/8-09.htm I know that spatial angles in general relativity don’t have an intrinsic value (are not invariant). They are dependent...
  8. S

    I How does sound reflect from an interface at an angle?

    How does sound reflect from interface at an angle? The propagation of light is determined by a single factor - index of refraction. Sound is affected by two factors - speed and acoustic impedance. Take the case of two substances with identical acoustic impedance but different sound speeds - one...
  9. U

    Vectors in yz and xz plane dot product, cross product, and angle

    I tried to find the components of the vectors. ##a_y =2.60 sin 63.0 = 2.32## and assuming the z axis would behave the same as an x-axis ##a_z =2.60 cos 63.0 = 1.18## ##b_z =1.30 sin 51.0 = 1.01## making the same assumption ##b_x =1.3 cos 51.0 = 0.82## I now think I should have switched these...
  10. mncyapntsi

    Calculating Tension in a Pulley System at an Angle

    Hi! I really can't figure this one out... I have a = (F-cos(36.1)g) = a and from that I get T = mB1 a = 6.3 (20.3736) = 128 N. Could someone please help? Thanks!
  11. M

    Geometric Construction (bisecting an angle with a compass and straightedge)

    In discussing flight mechanics with a (15 years younger) co-worker with a doctorate in Aerospace Engineering. We examined some angles and I happened to mention bisecting an angle. I told him in High School in the early 1970's we learned how to bisect an angle with compass, and straightedge...
  12. D

    Finding the Magnitude and Angle of a Problem: Two Solutions

    Hello, I solved this problem two ways and got the same value for the magnitude but different values for the angle. I am wondering which is correct. I showed my work, so I hope someone can tell me if one method is just invalid.
  13. ayans2495

    2 Dimensional Motion: Net force at an angle

  14. B

    MHB What is the Angle Between Vectors Using the Dot Product Formula?

    Find the angle between the vectors v=-5\sqrt{3}i+5j and w=5i
  15. M

    MHB Find $\angle B$ for Triangle $ABC$ with Bisectors $AD,BE$

    Let $ABC$ be a triangle with $\angle A= 60^{\circ},$ and $AD,BE$ are bisectors of $A,B$ respectively where $D\in BC, E\in AC.$ Find the measure of $B$ if $AB+BD=AE+BE.$
  16. chwala

    Find angle B in the trigonometry problem

    Now i was just doing some random study and i saw this problem on the internet. The problem was to find angle ##B## now there were several responses, let me screen shot one that i think was a bit straightforward... my question is, "is there a much simpler way to find the angle ##B##"?
  17. M

    I Formula For Calculating Field Angle (Beam Angle) of Light?

    There are actually several questions. The formula for calculating the "beam angle" of light (emitted from lights bulbs, flashlights etc) is - α = 2 arcCos ( 1 - Lm ÷ ( 2 π Cd )) Where, α = beam angle in degrees Lm = luminous flux (Lumens) Cd = luminous intensity (Candela) The above formula...
  18. baby_1

    Phase velocity in oblique Angle propagation (Plane wave)

    Hello, Regarding the wave oblique angle propagation and based on Balanis "Advanced engineering Electromagnetic" book on page 136 ( it has been attached) I need to know why the phase velocity in x direction is not important to keep in step with a constant phase plane( Just equation 4-23). I...
  19. B

    Solid angle in an optics problem (artificial irradiance of the Earth)

    The actual problem can be found as #2 on this link: https://ocw.mit.edu/courses/mechanical-engineering/2-71-optics-spring-2009/assignments/MIT2_71S09_ups1.pdf I rewrote the problem above with the solar irradiance data that they give. My interpretation is of a square 1 m x 1 m plane sitting...
  20. T

    Using virtual work to find the angle of a bar supported by two planes

    I imagined the bar slipping along a virtual displacement, with the top and the bottom slipping by equal amounts. Since the planes are orthogonal, I took the components of these displacements: the lower end is displaced Lsinα in the direction of the right plane and by Lcosα in the direction of...
  21. jonas_28

    How to determine Refractive Index without using the Refractive Angle?

  22. sam0916

    Engineering Angle of Wrap (Belt Friction)

    Attached is the picture of the belt. The angle of wrap seems to be >180 degrees.
  23. S

    Finding the lower and upper limits for angle of elevation

    distance (metres) Angle of elevation (degree) 950 7 1500 12 1800 15 3300 20 I think I don't need to use information about 900 metres because the path starts from elevation of 1000 metres. I imagine the distance will be the hypotenuse of a triangle and the height of a certain location...
  24. F

    I Calculate m (slope) of a line given the angle in degrees

    Hi, I want calculate the m = slope of a linear line WHEN I already know the angle in degrees of the line. Here is an example: I calculate with Excel the angle with the following function: =+DEGREES(ATAN(0.0874887)) and I get as result the angle of 5%. But how do I calculate the value...
  25. FEAnalyst

    Angle of twist from in-plane displacements in FEA

    Hi, solid elements used in FEA don't have rotational DOFs so normally it's not possible to read the angle of twist from simulation involving torsion. Some programs allow the transformation of results to cylindrical coordinate system but it's not always the case. From what I've heard, it's...
  26. jmao15

    Rod in equilibrium, and find its angle to the vertical plane

    Literally, don't know how to start.
  27. Mikkel

    Ultra high energy cosmic ray deflection angle causes by magnetic field

    I'm given an ultra-high energy cosmic ray with energy 10^20 eV. It is coming from a source 10 Mpc away with an extragalactic magnetic field with strength B = 10^-9 G. I am to determine the maximum angular deflection of this cosmic ray, so it hits Earth. I don't have an attempt of the solution...
  28. T

    The order of Euler Angle rotations for a top

    Good Morning All. I have asked this before, but my post was not clear (my fault: I apologize). I hope this is more clear (please be patient as I try to get to the core of my confusion). In the first figure, below, the spinning top precesses as shown (well, it is not a animated jpg, but it...
  29. agnimusayoti

    Calculating the Solid Angle of a Nebula from Earth

    If I assume the nebula is a circle, than the length of arc viewed from Earth is a half of the circumference. So, here $$l = \frac{1}{2} \pi D$$ From the problem, ##D = 125 000 ly##. Because the distance of nebula is much larger than the diameter; I try to approximate R with the distance of...
  30. karush

    MHB ASVAB Find Angle CAD: Using Alternate Interior Angles

    OK wanted to see how a transparent image would look like here:unsure: well first $\angle{BAC}=57^o$ by alternate interior angle are equal and then...
  31. X

    MHB Optimizing Profit with Three Points: A Scientific Approach

    Hey guys, I'm struggling trying to figure this out and need some assistance. Not sure if I'm in the right category or needing the angle or what. But the goal is to prove Ex.1 is much smaller of an angle than Ex.2 and to be able to use the formula on a universal scale. Ex1: A=190, B=222, C=195...
  32. E

    Angle of incidence and total internal reflection

    the angle of incidence at A is 40°, then why did the answer key say "angle of incidence at A is just less than 90°". it is obvious that 40° is quite far from 90° right?
  33. N

    How Do I Calculate Angle BAC if Angle CBA is 69 Degrees?

    Please see attached drawing which I have written my work (in colour). Despite spending 1h on it I still can’t understand how to find angle BAC.
  34. J

    Solving Destructive Interference: Angle vs Wavelength

    The destructive interference equation for small angles is angle=wavelength/(2a), where a is the width. I assume it means destructive interference since its talking about areas where no light is present. Using the equation after changing degrees into radians I get the answer of 2491 nm when the...
  35. ILoveParticlePhysics

    Does anyone know the formula to find the angle after a collision?

    I think it has to do with conversation of momentum and projectile motion.
  36. S

    MHB Forces of 8N: Find Angle & Mass of Particle

    Two forces each of size 8N, have a resultant of 13N. a) Find the angle between the forces b) The two given forces of magnitude 8N act on a particle of mass m kg, which remains at rest on a horizontal surface with no friction. The normal contact force between the surface and the particle has...
  37. Z

    Comp Sci Solving the ballistic trajectory equation for Launch Angle

    In a process of writing a game. Effectively need to know how to angle the barrel for the projectile to hit the selected target. So for the equation y = h + x * tan(α) - g * x² / 2 * V₀² * cos²(α) Everything except α is known. Could anyone more wise in the ways of science than me help me solve...
  38. H

    Calculating Rotation Rate from Change of Angle

    If we know the change of angle is twice the incident angle, then the rate of rotation is 2*100 rpm = 200 rpm. Is there a better explanation of it?
  39. ddedeasx

    How do you read the Brewster angle formula / equation?

    So far all I know is that n1 and n2 represent the refractive indices of the two media, and so is theta (I think). Please help
  40. flyparnape

    Finding the Velocity of a Projectile knowing only Launch Angle and Flight Time

    I don't know the distance or the horizontal velocity so I can't find any logical solution
  41. rbh

    Body thrown at an angle to the horizontal

    The answer says t = Vb - Va/g. Shouldn't it be Va + V(from highest point to point b)/g ?
  42. Purpleshinyrock

    Pulling a sled across snow with a rope at an angle

    Hello. Can someone tell me what area of phisics should I study to better understand this exercise and also what should I do to solve this exercise please? A man pulls a small sledge with a force F ⃗ of intensity equal to 50.0 N and that makes an angle with the horizontal θ = 30º (see figure)...
  43. L

    Elastic collision considering the angle of impact

    https://www.plasmaphysics.org.uk/collision2d.htm This is the only one I found, but when I plug in the numbers of his example I get a wrong result. Do you know any others who solved it i.e. considering the angle of impact? Angle of impact I name the angle that is shaped between the initial dx...
  44. jskrzypi

    Angle on ramp with cart and weights on rope at end

    I believe the nx, Ty, and (fs)y are all 0. I could solve for theta if I could figure out (fs)x or ny. edit: Track is frictionless, so delete (fs) forces.
  45. B

    I Dimension of an Angle: Clarifying the SI Standard

    Quickly estimate the value of this expression: sin(1.57). If your answer was about 1, then you assumed that 1.57 was a radian value. If your answer was about 0, you assumed that 1.57 was degrees. If you said that you can’t determine an answer, then you were expecting to see an angle...
  46. DaveC426913

    B Angle of the diagonal of a cube

    I've looked for this in a hundred places but I keep finding the unit length of the diagonal (root 3). I want to find the angle. i.e. the angle between the cube's diagonal and its three edges at a vertex (all three angles will be identical, of course). I guess I hoping to figure it out without...
  47. jjson775

    What is the expression for Compton scattering angle in terms of t?

  48. G

    Critical angle (symmetry of refraction) confusion

    Refraction has a symmetry; on going from glass to air light at the glass air surfaces refracts away from the normal. If you turn the light source around and make the former refracted beam the incident beam then its refracted angle will be the former incident angle. So at critical angle, do the...
  49. J

    Work done on an Object - Pulling a wagon while lifting up at an angle

    Juri is tugging her wagon behind her on the way to... wherever her wagon needs to go. The wagon repair shop. She has a trek ahead of her--five kilometers--and she's pulling with a force of 200 Newtons. If she's pulling at an angle of 35 degrees to the horizontal, what work will be exerted on the...
  50. B

    Find the tension in the wire from this mass hanging at an angle

    I do not understand how this type of exercise is solved because I have not had a solution to such an example. I would ask you to show me the solution of this exercise step by step, so that I understand how to solve it. I appreciate your help. Thank you.
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