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. B

    Euler Angle from Body Frame to Inertial Frame

    Hi, This is not really a homework problem, but a project I'm working on. So, I am trying to build a Simulink model for my quadcopter. I derived the equations of motion using the Newtown-Euler method in the body frame to get transnational and angular acceleration. For the transnational part, I...
  2. L

    Unit solid angle and finite angle

    Homework Statement A point source emits visible light isotropically. Its luminous flux is 0.11 lumen. Find the flux whithin the cone that has half angle of 30 degree from the light source. Homework Equations luminous flux = luminous intensity * solid anlge The Attempt at a Solution I tried...
  3. T

    Angle to lift a body off the surface

    Homework Statement A rectangular box is being pulled by a rope with a force T on a horizontal surface, with a friction coefficient μ. What is the minimum angle α at which it will lift of the surface? See attached image. Homework Equations \begin{equation*} \tau = rF\sin\alpha \end{equation*}...
  4. goonking

    Momentum & Angle: Can Velocity = 0 and Momentum Still Exist?

    Homework Statement Homework Equations p = mv The Attempt at a Solution if an object's velocity at the highest point of a trajectory is 0, how can it still have momentum (since p = mv)? is this question technically correct?
  5. K

    Optimal Dragster Exhuast Pipe Angle

    Homework Statement Top-fuel dragsters can accelerate from rest at a rate of about 5g. If this does not sound impressive, consider that for most automobiles the friction between the ground and the tires produces the acceleration. Since the coefficient of friction between regular treaded tires...
  6. R

    Multiplayer Refraction, Incident Angle

    Homework Statement The figure below shows the path of a beam of light through several layers (n1 = 1.58, n2 = 1.42, n3 = 1.20 and n4 = 1.00) of different indices of refraction. https://loncapa2.physics.sc.edu/res/brookscole/serway/College_Physics_7ed/Chap22/graphics/serw2244.gif a) If θ1 =...
  7. A

    The smallest angle flashlight beam can make with horizontal

    Homework Statement At the aquarium where you work, a fish has gone missing in a 10.5m -deep, 9.45m -diameter cylindrical tank. You shine a flashlight in from the top edge of the tank, hoping to see if the missing fish is on the bottom. What’s the smallest angle your flashlight beam can make...
  8. ShayanJ

    Transformation of solid angle

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  9. H

    Calc Oblique Shock Angle for Supersonic Flow 0-5 Degrees

    Is there an equation to calculate the oblique shock angle for supersonic flow when the given angle of attack is greater than 0, but less than the half angle? In my particular practical experiment, the half angle of the aerofoil is 5 degrees, so want to get a variety of figures between 5 and -5...
  10. E

    Critical angle for a box to start moving on an incline

    Homework Statement A ramp with an angle given by ø (from the horizon) and a box of mass represented by "m" with a given µ=0.55 between the ramp and the box, find the minimum (critical) ø for which the box will begin to move down the ramp. Wether µ is kinetic or static is not given in the...
  11. diracdelta

    Minimal angle of deviation through the prism

    Homework Statement Minimal angle of deviation δm of light after passing through prism is connected with index of refraction n and inner angle of prism Φ: If index of refraction and inner angle of prism are directly measured, determine minimal angle of deviation, n=(1.52 ± 0.04) Φ=(30 ±...
  12. baby_1

    Find theta angle in complex form

    Homework Statement Here is my equation that I want to find theta angle Homework EquationsThe Attempt at a Solution I try to set different value of cos (theta) to find theta but it failed , I want to know the main solving strategy Thanks
  13. T

    Finding a part of an angle with two triangles

    I've never really understood this bit of trig, I think I get it if there are two parallel angles (parallelogram). But, I do not understand how you go about when the triangles aren't in a parallelogram.
  14. A

    Refraction of Light: Is There No Refraction?

    I understand that when light goes between air and water, refraction occurs (either towards or away from the normal). If the light going between air and water is already going in the same direction as the normal, is there no refraction (or a refraction angle of 0 degrees)? Thank you.
  15. C

    MHB Find Tension in Horizontal Rope DE | Cylinder Mass & Angle θ

    Hi there, I have a question I'm unable to get properly started on: A cylinder of radius R and mass m is lodged between cross pieces that make an angle θ with each other, as shown in the diagram below. The cross pieces of negligible mass are connected in point C, with lengths AC = BC = 2R and...
  16. Alettix

    Angle of Inclination of a Water Surface

    Homework Statement So the full problem is the following: "On the top of a truck, there is a cubic container with a side-lenght of 1,00 m and it's filled with 500 liters of water. The truck accelerates with 2.0 m/s2 in the x-direction during the whole experiment. When the watersurface has...
  17. F

    Double Angle Trig: Solving Sin2x-cosx=1 for x in [0,2pi)

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  18. T

    4Sine(4X) = -8Sin(2x) Double angle identity

    I kind of understand what to do with this when there are no numbers in front of the expressions, I also kind of understand that you can rewrite 4Sine(4x) as 4Sine(2x+2x) hat do I do with the 4 and 8? In an algebra problem you could divide the 4 into the -8, then simplify that expression, am I...
  19. Q

    Direction cosine matrix of rolling disk on circular ring

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  20. S

    Finding the shear stress and angle of twist in hollow shaft

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  21. physicsodyssey

    Optimizing Angle for Material Transfer System Efficiency

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  22. H

    Find unknown angle of Projectile

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  23. A

    Calculation of the force exerted by a liquid

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  24. synMehdi

    Antenna theory detection of angle of incidence

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  25. Calpalned

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  26. L

    Engineering Calculating angle of lean on a motorbike on a banked curve

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  27. P

    What does a leading/lagging angle mean on the grid?

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  28. Yam

    Frictional forces and the angle for minimum frictional force

    Homework Statement A person is dragging a packing crate of mass 100 kg across a rough floor where the coefficient of kinetic friction is 0.400. He exerts a force F just sufficient to keep the crate moving at a constant velocity. At what angle above the horizontal should his pulling force F be...
  29. E

    Circular motion: find velocity with angle, mass, and radius

    This was a homework problem; after five tries, I still did not get it, and I can't figure out how to get at the answer the assignment gave me. I could not find the answer anywhere that didn't get into angular velocity, which we are not at yet (and also did not give me the answer!). 1. Problem...
  30. W

    Calculate the Pitch of a projectile with moving destination

    Hi all. I am not quite sure if this is the right forum to place this question but for me there are several forums that would fit with my situation :D I am making a game where I have to throw/shoot a projectile through a 3 dimensional space which has to land on a specific object. There are...
  31. T

    Length of a missing side no angle given :(

    I'm given an irregular shaped plot with 3 sides, and have been asked to find the fourth missing side, no other detail is given. Is it possible to find the missing side? If so, then how? Here is what it looks like roughly:
  32. M

    Why use 0 degrees for one of two forces acting at an angle?

    1. Two forces, 80N and 100N, acting at an angle of 60deg with each other, pull on an object. a) what single force would replace the two forces? r^2=(x^2 + y^2)^2 , sinΘ, cosΘThe Attempt at a Solution I actually got the correct answer by using an angle of 0 degrees for 80N and 60 degrees for...
  33. T

    Angle of total acceleration of an object in circular motion

    Homework Statement A train slows down as it rounds a sharp horizontal turn, slowing from 90 km/h to 50 km/h in the 15 s that it takes to round the bend. The radius of the curve is 150 m. Compute the total acceleration at the moment the train speed reaches 50 km/h Homework Equations a =...
  34. T

    Why is the change in angle of precession equal to dL/L?

    If a rapidly rotating gyroscope attached to a perch is released in a horizontal position -- that is, so that the axis of the gyroscope is horizontal -- the gyroscope will precess around it's perch. Let L represent its angular momentum. Let dL represent a small change in that momentum. Let dA...
  35. E

    Angle of Bob in a Moving Train

    Homework Statement A bob of mass m is suspended from the ceiling of a train moving with an acceleration g/√3 (a) If an observer is sitting inside the train, what angle with the vertical will he observe? (b) If an observer is standing on the platform, what angle will he observe? Homework...
  36. A

    Does the coefficient of friction change with the angle?

    I said stay the same, the definition of co efficient is here http://simple.wikipedia.org/wiki/Coefficient_of_friction but the main part i saw not only here was "The coefficient of friction is dimensionless, meaning it does not have any units. It is a...
  37. J

    Max Scattering Angle from Thompson Plum Pudding Model

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  38. K

    Finding average angle in kinetic theory of gases

    Homework Statement "Show that particles hitting a plane boundary have traveled a distance 2λ/3 perpendicular to the plane since their last collision, on average."Homework Equations (Root mean path squared) <x> = 2^(.5)λ λ = ( 2^(.5) * n * sigma )^(-1) ANSWER: The Attempt at a Solution...
  39. L

    Smallest angle of inclination between two stars for eclipse

    Homework Statement Assume two stars are in circular orbit around a mutual center of mass and are separated by d = a. Assume angle of inclination is i and stellar radii are r1 and r2. Find an expression for the smallest angle of inclination that will just barely produce an eclipse. Homework...
  40. S

    Conservation of Energy and the angle of the incline

    If I had a block that I pushed with a force F along a horizontal path and then removed the force before an incline, would the angle of the incline matter on how far above the ground the block would travel? I am assuming a frictionless surface.
  41. itchybrain

    Question about solar energy: angle of incidence

    My understanding is that the seasonal variation in temperature, amongst many other things, is a reflection of the Earth's tilt. Simply put, at the equator, sun rays fall "straight down" (100% vertical), and all of their energy hits the surface of the Earth. At different latitudes, these rays...
  42. C

    Dot product in uniform circular motion question -- Finding angle?

    I've attached an image of part a of the question to this thread. My question is this (the solution to these former homework problems are posted to help us study for exam, which is why know this already): The angle between the two velocity vectors is determined to be pi/2. How? I know that dot...
  43. T

    Find velocity & angle to fire cannonball through *Two* points

    At first this sounds like a very popular and often asked/solved question but it has a twist - I need help with the twist please. 1. Homework Statement A cannon is at Point A in a 3d environment. There is a wall at Point B which sits between the cannon and a castle, at Point C. Write a...
  44. D

    Find phase angle of RLC network

    Homework Statement Please see attachment for circuit and parameters. Homework Equations i --> 90 phase angle for inductor so Z of inductor = 0.5<90 sum of voltages = 0 #<40 = #*cos(40) + i*sin(40)*# The Attempt at a Solution shteii01 - 100 + 0.5<90 + V2<theta = 0 --> 100 + 0.5*cos(90) +...
  45. A

    What is the notation for angular distance travelled?

    What is the notation for the angular distance traveled by an object moving in circular motion? s is for regular distance (m,ft,inches, etc.). What I want is some x to be the distance in either degrees or radians. How should I call that x?
  46. D

    Capacitor needed for phase angle change (RLC network)

    Homework Statement An inductive load is connected to a 120V (rms), 60Hz AC source. The load draws 5.0 kW at a power factor of 0.81 (lagging). You need to improve your power factor to 0.96 (lagging) by adding a capacitor. What is the Capacitance needed (in uF)? Homework Equations P/|S| =...
  47. J

    Stone being tossed from mountain Uni Physics with Calc

    Homework Statement A stone is thrown horizontally from the top of a 20-m high hill. It strikes the ground at an angle of 45◦ . With what speed was it thrown? Homework Equations g=9.8 projectile motion is symmetric The Attempt at a Solution I got the answer 277.539 by treating this is a...
  48. 1

    Angle of photon emission from particle decay (Particle Phys)

    Homework Statement a) Particle A decays at rest into two photons. Calculate, in terms of the rest mass of A, the energy and momentum of each photon. b) In a different reference frame, particle A is initially in motion such that its kinetic energy is equal to its rest energy. Find the momentum...
  49. R

    Calc Angle of Incidence & Reflection to Solve Determining Angle Homework

    Homework Statement Suppose a solid body approaches a sphere of radius one and height z, how do I calculate the angle ##\theta## at which the body bounces off the sphere? An image is attached: Homework Equations Angle of incidence, reflection and velocityThe Attempt at a Solution I was...
  50. F

    What is the angle between the two emerging beams of light?

    Homework Statement Light consisting of a mixture of red and blue light enters a 40°, 70°, 70° prism along a line parallel to the side opposite the 40° vertex. The index of refraction of the prism material for blue light is 1.530, and for red light it is 1.525. What is the angle between the two...
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