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.

View More On Wikipedia.org
Recent contents Top users
  1. D

    What is the Power Dissipated in a Bulb with a Set Firing Angle?

    Homework Statement If the firing angle is set to ##\alpha = \frac{\pi}{3}## estimate the power dissipated in the bulb if it is rated at ##100w## and the voltage source is ##230V## @ ##50Hz## Homework Equations [/B] ##Vpeak = \frac{230}{0.707}## = 325V ##Vload = 325\sqrt\frac{\left(2\pi...
  2. Toby_phys

    Special relativity - transformation of angle

    Homework Statement Homework Equations Gamma factor: $$\gamma = \frac{1}{\sqrt{1-\beta^2}} $$ Lorentz contraction $$l'=\frac{l}{\gamma}$$ Trig: $$ cos\theta = \frac{adjacent}{hypotenuse}$$ The Attempt at a Solution I have all the quantities but the algebra doesn't seem to work out...
  3. T

    Find new location -- 2-wheeled car/robot

    Hello, everyone! Now I'm trying to develop 2 wheels robot, which travels along the line simulator. The robot can turn only by increasing velocities of each wheel. The conditions are below: - I know velocities of 2 wheels - I know radius between wheels The task is next: How to find new location...
  4. Andy Resnick

    Insights New High Performance Ultra-wide Angle Lenses - Comments

    Andy Resnick submitted a new PF Insights post New High Performance Ultra-wide Angle Lenses Continue reading the Original PF Insights Post.
  5. S

    I Can Camera Distance Affect Angle of Foreshortening in Video Measurements?

    Hi. I was wondering if anyone could help me with the following problem. I am doing a independent lab at the moment. I am using video footage to measure displacement of a ball. I have cameras set up on the x and y-axis where a ball is in line with the centre of both cameras. I have 1cm grids on...
  6. F

    Chief Ray Angle and Field of View

    Hi all! I was studying the datasheet of a CMOS sensor when I bumped into a graph which defined the CRA (Chief Ray Angle) of a lens as function of the FoV (Field of View). cdn.sparkfun.com/datasheets/Dev/RaspberryPi/ov5647_full.pdf page 134 I've understood what is the CRA, and I've got the...
  7. danielhep

    MasteringPhysics: Find the angle between the point charges.

    Homework Statement Two m = 4.0 g point charges on 1.0-m-long threads repel each other after being charged to q = 80 nC , as shown in the figure. What is the angle θ? You can assume that θ is a small angle. Homework Equations Fe=kq2/r2 F=ma Fg=mg The Attempt at a Solution Equation 1:[/B] r =...
  8. K

    Calculating components of a force applied at an angle

    1. The problem statement, all variables, and given/known data Attached is a diagram of what I am trying to solve. I need to calculate the X and Y components for both F1 and F2. The results will then be used in a later problem that I've already solved but I am coming up with an error and I was...
  9. C

    How to find the optimum angle for takeoff for ski jump using

    Homework Statement I need to find how to find the optimum angle for take off on the ski flying hill using projectile motion. and why? Homework Equations The Attempt at a Solution [/B] I'm just confused, because would I just use all the formulas above to solve the problem? or do I have to...
  10. K

    B Average angle made by a curve with the ##x-axis##

    The average angle made by a curve ##f(x)## between ##x=a## and ##x=b## is: $$\alpha=\frac{\int_a^b\tan^{-1}{(f'(x))}}{b-a}$$ I don't think there should be any questions on that. Since ##f'(x)## is the value of ##\tan{\theta}## at every point, so ##tan^{-1}{(f'(x))}##, should be the angle made by...
  11. S

    A Weinberg angle in terms of Higgs mass

    The Weinberg angle ##\Theta_{W}## is commonly expressed as $$\cos\Theta_{W} = M_{W}/M_{Z}.$$ Can the Weinberg angle ##\Theta_{W}## be expressed in terms of the Higgs mass and the mass of the W boson as $$\sin^{2}\Theta_{W}= m_{H}/M_{W}?$$
  12. EthanVandals

    How long does it take to push this block at an angle?

    Homework Statement A 100 kg block is pushed across a level frictionless surface at a 60 degree angle, with a force of 20 Newtons. How many seconds does it take to go 100 meters? m = 100kg Mu = 0Homework Equations F = MA The Attempt at a Solution I sketched out the problem on my paper here...
  13. G

    What is causing the reflected beam's s oscillations at Brewster's angle?

    Ive been reading about reflections and transmission at Air water surface. I get the idea that at the Brewster's angle dipoles aligned at the surface can not emit p-oscillations in the reflected direction as the dipole is aligned parallel to this direction. What I don't get is that if the...
  14. hdp12

    How to find the angle of a pinned rod at a certain depth

    Homework Statement The uniform 5 m-long round wooden rod (ρ = 800 kg/m3 ) is tied to the bottom by a string with length 1 m. Determine the inclination angle θ if the water level is 3.5 m. What if the water level is 7m? Homework Equations Fb = ρgV The Attempt at a Solution So I'm really...
  15. mh_99

    What Angle Maximizes Air Time for a 34.6m Football Punt?

    Homework Statement A football punter can punt a maximum range of 40.8 m. If he instead wants to punt only 34.6 m, but maximize the time the ball is in the air, at what angle from the horizontal should he kick the ball, and how long will it stay in the air if he hits it perfectly? (neglect air...
  16. J

    Magnitude and angle of an electric field vector

    Homework Statement The electric potential at points in an xy plane is given by V = (1.5 V/m2)x2 -(2.9 V/m2)y2. What are (a) the magnitude of the electric field at the point (3.9 m, 2.9 m) and (b) the angle that the field there makes with the positive x direction. Homework EquationsThe Attempt...
  17. I

    Newton's 2nd Law Problem, Angle exerted on block by surface

    Homework Statement Problem: A 12.0-kg block is pushed to the left across a rough horizontal surface by a force that is angled 30.0◦ below the horizontal. The magnitude of the force is 75.0 N and the acceleration of the block as it is pushed is 3.20 m/s^2 . What angle does the force exerted on...
  18. sampsont

    I Angle between two vectors with many dimensions

    The angle between two ℝ2 or ℝ3 vectors makes sense. I have a vector like [0 0.707 1 0.707 0 -.707 -1 -.707]T (Actually my vector is A/D conversions of a sine wave from the wall power outlet. The sample rate is 4800 so there are 80 samples, separated by 1/Fs for a 60Hz sine wave. If I...
  19. C

    How to calculate the gravity on a hill?

    The question is about a box with no movement standing on a hill. The hill has an angle of 25 degrees. The box has a mass of 40 kg. 1. Calculte the gravity This I still get: F= M x A = 40 x 9,81 = 3,9 x 10^2 The next question tough: 2. Calculate the component Fgravity,x off the gravity...
  20. Prof. 27

    Angle between vector and tangent vector

    Homework Statement My problem is: For the logarithmic spiral R(t) = (e^t cost, e^t sint), show that the angle between R(t) and the tangent vector at R(t) is independent of t. Homework Equations N/A The Attempt at a Solution The tangent vector is just the vector that you get when you take the...
  21. D

    MHB Calculating the Length of an Angle Bisector: Is My Solution Correct?

    How to find the length of an angle bisector (BK) in a triangle A(1;4), B(7;8), C(9;2). I calc BK: \frac{x-7}{\frac{1+\frac{\sqrt{13}}{\sqrt{10}} \cdot 9}{1+\frac{\sqrt{13}}{\sqrt{10}}} - 7} - \frac{y-8}{\frac{4+\frac{\sqrt{13}}{\sqrt{10}} \cdot 2}{1+\frac{\sqrt{13}}{\sqrt{10}}} - 8}=0 Is it right?
  22. karush

    MHB 231.12.3.19 angle between vectors

    $\tiny{231.12.3.19}$ $\textsf{Given $v=-7i-j$ and $w=-i-7j$}\\$ $\textsf{find the angle between v and w}\\$ $\displaystyle \frac{\left(-7, -1, 0\right)\cdot\left(-1, -7, 0\right)} {\sqrt{50}\cdot \sqrt{50}} =\frac{14}{50}\approx 0.28$ $\arccos(0.28)\approx 73.74^o$ $\textit{not sure if this is...
  23. S

    Angle of pitch and heel for a boat snagged on the side wall

    Hi everyone, this is a real world problem following the sinking of a narrowboat in 2014. The boat caught on the side of the lock as the water level dropped, and the resultant combination of pitch and heel resulted in the boat taking on water at the stern and sinking - luckily with no loss of...
  24. F

    Angle of rotation in fixed end of beam

    Homework Statement In the first photo , i was told that the fixed end moment is zero when the far end is pinned or roller supported . Why in the example in the second and third photo( both end are fixed) , the angle is zero ? Homework EquationsThe Attempt at a Solution I think it's wrong ...
  25. J

    What is tangent of power factor angle for an alternator?

    My book had these two solved examples that gave contradictory replies. The power output of an alternator is 100 kW. Now if the tangent of pf angle is 0.8 lagging, the KVAR rating must be -80KVAR. I drew phasor and got this. I took it that since tangent is negative. Now tangent is opposite...
  26. karush

    MHB S4.854.13.5.47 Find symmetric equations, angle between the planes

    $\tiny{s4.854.13.5.47}$ $\textsf{a. Find symmeteric equations for the line of intersection of planes}\\$ $\textsf{b. Find the angle between the planes}\\$ \begin{align}\displaystyle j+y-z&=2 \\ 3x-4y+5z &=6 \end{align} \begin{align}\displaystyle n_1&=\langle 1,1,-1\rangle\\ n_2&=\langle...
  27. C

    Deducing Bragg angle for G_220 Bragg peak for LiF

    Homework Statement Calculate the reciprocal lattice vectors for LiF. Given the lattice parameter ##a = 0.402 nm## calculate the magnitude of the ##\textbf{G_{220}}## reciprocal lattice vector for LiF and thus deduce the Bragg angle for the (2,2,0) Bragg peak for incoming wavelength of ##0.9...
  28. F

    Angle of twist of a gear relative to another

    Homework Statement why we need to consider 2 moment caused by the 85Nm in this question ? The question ask for the determine the angle of twist of gear A relative to D . Homework EquationsThe Attempt at a Solution Why shouldn't the angle of twist = (85)(0.4) / ( (0.5pi)( 0.015^4-...
  29. D

    Angle of electron in an electric field

    Homework Statement https://imgur.com/zEoCpc0 I am trying to figure put the angle and my attempt is tanx=sy/sx (I have calculated a value for the distances) But my book is saying: tanx =vy/vx I don't understand why my way of solving it is wrong... I don't get the same answer for x :/
  30. F

    Angle of twist / stress of thin wall having closed section

    Homework Statement why the mean area enclosed within the boundary of the centerline of tube thickness is (0.035)(0.057) ? Is it wrong ? Second question , why for the ds it's 2(57) and 2(35) respctively ? what is ds actually ? Homework EquationsThe Attempt at a Solution for the first...
  31. R

    Angle for Static Position of Block 1 and Movement of Block 2

    Homework Statement what is the angle the force should apply in order to be box number 1 in static position and box number 2 move Homework Equations F=ma The Attempt at a Solution
  32. M

    MHB Prove Equal Area Triangle & Parallelogram, $\angle ADC=90^{\circ}$

    Workings $\triangle ADE \cong \triangle CFE \left(AAS\right)$ $\angle AED = \angle CEF $( vertically opposite angles ) $\angle CFE= \angle EDA $( alternate angles ) $AE=EC $( E midpoint ) $ii.$ADCF is a parallelogram because diagonals bisect each other. Where is help needed How should...
  33. T

    Pressure Gradients along an angle pipe

    I have a high pressure volume coupled with a low pressure volume by a pipe and valve . If the pipe was straight I would expect the isobars of the pressure gradient to be parallel to the pressure differences and perpendicular to the pipe , I would expect a reaction force (red arrow) on the wall...
  34. F

    Sign of angle in mohr's circle

    Homework Statement In this question , how could the $$\theta_p$$ and $$\theta_s$$ has the same sign ? For $$\theta_p$$ , it is to be rotated clockwise to horizontal axis , right ? For $$\theta_s$$ , it is to be rotated anticlockwise to vertical axis , right ? They are in different...
  35. K

    MHB Deriving expressions using double angle formula?

    How do I use the double angle identity in order to derive this expression: cos6(u)?
  36. karush

    MHB S6.12.3.17 Find the angle between the vectors

    $\tiny{s6.12.3.17}\\$ $\textsf{ Find the angle between the vectors $a$ and $b$}\\$ \begin{align} \displaystyle a&=\langle 3,-1,5\rangle &b&=\langle -2,4,3\rangle\\ \\ \cos\left({\theta}\right)&=\frac{(3\cdot -2)+(-1\cdot4)+(5\cdot3)} {|\sqrt{35}|\cdot|\sqrt{29}|}\\ &\approx 0.1569 \\...
  37. F

    Angle of principal stress vs maximum shear stress

    Homework Statement I'm having problem with the angle of $$theta_s1$$ . My ans is +35 (as in my working) , but the ans provided is $$theta_s1$$ = -55[/B] Homework EquationsThe Attempt at a Solution As in the picture posted
  38. F

    Calculating Stresses at an Angle: Why Does it Matter?

    Homework Statement Why can't i use the equation to determine the normal stress and shear stress ? Is my concept wrong ? I use the method in the link to do this question. The question said the stress on a plane making angle 30 degree anticlockwise from plane AD . Homework EquationsThe Attempt...
  39. E

    Dielectric slab and angle of incidence

    Hello! Let's consider a plane wave represented by a ray, propagating in a 2D dielectric slab. It has a medium with refractive index n_1 as its core and a medium with refractive index n_2, n_2 < n_1, as its cladding. In order for this ray to represent a mode, it must satisfy two conditions: -...
  40. P

    Directional Acceleration at Relativistic Speeds

    Homework Statement A particle flies along in the positive +x direction. It has a constant force F applied 30º clockwise to the x-axis. It is moving at .6 c. What is the angle of acceleration? Homework Equations a = F/(mγ3) The Attempt at a Solution [/B] I'm pretty sure I know how to do...
  41. N

    Measure angle in Ansys Workbench

    Hello, I want to ask how I want to make a rotation using angle in Ansys Workbench ? I already read some suggestions that it can be done by using local coordinate system but unfortunately I can't done it right. Is there any youtube video or tutorials that I can refer ? I hope someone can help...
  42. S

    Angle between vector and z-axis

    1. Homework Statement I am looking at problem 2.2 pictured above. I have solved all portions of the question except the last part, which asks for the angle between the normal vector to the surface and the z-axis. I am aware that the normal vector is simply equal to the gradient of the surface...
  43. C

    MHB Finding Angle at $\gamma$ - Help Requested

    Hi, could someone please tell me what theorem I need to be looking at to work out the angle at $\gamma$ please? I've worked out the rest but can't find a theorem for this one. Thanks
  44. V

    B Compute Angle Between Multiple 3d Vectors

    Imagine a point with n vectors (all with equal magnitude) coming out from that point that equally cancel each other out in magnitude. How would you calculate the equal angle between n vectors? For example: 2 vectors (equal magnitudes) coming from one point that cancel each others magnitude...
  45. A

    I Angle at which cardioid hits the x-axis

    How can we find the angle at which the curve of equation : r=b + acosθ hits the x-axis. I want a fast way or method since I only need it to plot the graph well. I'm only asked to plot the curve well and pay attention to the angle at which the curve hits the x-axis and not to calculate and...
  46. Z

    What is the exterior angle of a triangle?

    Homework Statement It looks as if 50 degrees is an external angle of the triangle.So it should be greater than the two opposite interior angles (i.e x and the other one). But book tells a different answer. Somebody please guide me.Zulfi. Homework Equations No eq. Rule: Exterior angle of a...
  47. G

    B Why I think radians should *not* be dimensionless

    As most know and rest can find out, radians are a dimensionless unit. Actually, it's even worse: angle in general is a dimensionless quantity. That stems from it being defined as a ratio of the arc versus the radius. I now present my opinion of disagreement to this concept. In the strict...
  48. V

    Simplifying Double Angle Formula: Cos^2 8x - Sin^2x

    Homework Statement Simplify cos^2 8x - sin^2x Homework EquationsThe Attempt at a Solution I thought it would be in the format of cos2x But I can't seem to figure it out I tried cos (4 * 2x) And I tried to change the sin^2x into 1-cos^2x and I could get any farther. Not sure how else to...
  49. A

    Engineering Free Exercises on Right Angle Projections & Cross Section Views

    I am looking for free solved exercises about: right angle projections, (cross) section views Here are some pictures of my book so you can understand what I am looking for http://1.1m.yt/3cNNDl-.jpg http://1.1m.yt/FekMn6x.jpg http://1.1m.yt/1t3KEer.jpg http://1.1m.yt/urA5V2_.jpg...
  50. Adriano25

    Find angle of the sphere losing contact with the surface

    Homework Statement A solid sphere rolls down a hemisphere from rest. Find the angle at which the sphere loses contact with the surface. R = radius of hemisphere a = radius of sphere Homework Equations ΣFr = Macm,r N-mgcosθ = -mVcm2/(R+a) N = mgcosθ - mvcm2/(R+a) eq. (1) Conservation in...
Back
Top