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. H

    Min Angle Projectile questions

    Homework Statement whats the minimum angles to the vertical(theta) for a projectile(ball) to be realeased with speed v such that at any point of time the distance to the ball is increasing. Homework Equations Sh=vtsin(theta) Sv=vtcos(theta)-0.5gt^2 The Attempt at a Solution so i used...
  2. D

    What is the relationship between tangential and radial acceleration?

    Homework Statement Homework Equations αt = r α The Attempt at a Solution ωi = 0 rad/s αt = 2.00 rad/s2 r = 112 m θ = ? at a = 6.80 m/s2 I'm not exactly sure where to begin. Help is appreciated.
  3. W

    What Is the Minimum Angle to Keep the Boxes Stationary on an Inclined Plane?

    Homework Statement 9.12) The mass of the box on the left is 30kg and the mass of the box on the right is 40kg. The coefficient of static friction between each box and the inclined plane is μs = 0.2. Determine the minimum angle α for which the boxes will remain stationary. Homework Equations...
  4. Corwin_S

    What is the Jones Matrix of a mirror at an angle?

    Hi, Concerning optical polarization, what is the Jones Matrix of a mirror at a non-zero angle of incidence with respect to incoming light? For a mirror at normal incidence the matrix is (1 0; 0 -1); How do I incorporate the angle?
  5. S

    Find the kinetic friction of an object at an angle

    A box weighing 87 lb is being pulled with a rope that exerts a force of 60. lb at an angle of 15 degrees with the horizontal. If the coefficient of kinetic friction is .35, what is the kinetic friction?
  6. snoopies622

    Seeking a phase angle operator for the QHO

    According to Daniel Gillespie in A Quantum Mechanics Primer (1970), " . . . any observable which in classical mechanics is some well behaved function of position and momentum, f(x,p), is represented in quantum mechanics by the operator f ( \hat{x} , \hat {p} ) . That is, a = f (x,p) . . ...
  7. F

    Calculating angle of ball after collision

    Homework Statement The white ball in the figure has a speed of 1.81 m/s and the yellow ball is at rest prior to an elastic glancing collision. After the collision the white ball has a speed of 1.37 m/s. To the nearest tenth of a degree, measured counterclockwise from east, what angle does it...
  8. R

    At what angle does the normal force go to zero?

    Homework Statement An ice cube is placed on top of an overturned spherical bowl of radius r, as indicated in the figure. If the ice cube slides downward from rest at the top of the bowl, at what angle θdoes it separate from the bowl? In other words, at what angle does the normal force between...
  9. J

    Calculating the torque angle in a free-body diagram

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  10. J

    Estimate diffraction angle - homemade spectrometer

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  11. Alpha123

    At what angle should the bomb be released?

    Homework Statement There is a plane flying at 200 km/h and wants to drop a bomb on a car traveling 130 km/h which is 78.0m below the plane. at what angle should the bomb be released? the answer is 45 degrees. Homework Equations sine law: SinA/a= SinB/b cosine law: a^2=b^2+c^2+bcCosA v=d/t...
  12. Naton

    Resolving angle of parallelogram in 3D space

    Hi there, I'm doing a bit of amateur scale model making as a hobby, building shapes out of flat-cut pieces. Trigonometry is a huge help with this, but I've hit a snag where I'm trying to calculate the angle of a particular parallelogram so it fits with the rest of the geometry. 1...
  13. stewood

    Angle of a semicircle on a ramp

    Homework Statement The semicylinder of mass m and radius r lies on the rough inclined plane for which ϕ = 10∘ and the coefficient of static friction is μs = 0.3. Determine if the semicylinder slides down the plane, and if not, find the angle of tip θ of its base AB Homework Equations f=uN The...
  14. vetgirl1990

    Calculating angle of projectile to hit target

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  15. Einj

    Integral of angular functions over d-dim solid angle

    Hello everyone! I have a question about angular integration in arbitrary d dimensions. The interest comes from the need to use dimensional regularization. Suppose I start with a 2-dimensional integral and then I have to move to d=2-\epsilon dimension to regularize my integral. Now, suppose...
  16. S

    Relationship between angle of twist and temperature gradient

    Homework Statement To derive a formula to find the angle of twist when a torque T is applied and the temperature gradient is ΔT Homework EquationsThe Attempt at a Solution Angle of twist Φ=TL/JG I believe as temperature decreases, torque will increase which means angle of twist is inversely...
  17. S

    Why is air-water contact angle usually assumed to be 0 ?

    I am a Ph.D student currently interested in fluid flow in porous media (rocks in my case). I am currently trying to find the range of values for the contact angle in air-water-sandstone systems at shallow reservoir conditions (say 7.5MPa and 35 degrees C). The only value I have managed to come...
  18. Albert1

    MHB What is the value of Angle BAD in a trapezoid with specific conditions?

    A trapezoid ABCD given : (1)$\overline{AB} // \overline{CD}$ (2)$\overline{BC}\ \perp \overline{AC}$ and $\overline{BC}=\overline{AC}$ (3)$\overline{AB}=\overline{BD}$ find the value of $\angle BAD$
  19. R

    What Happens to a Pendulum's Period at 90 Degrees Inclination?

    Homework Statement What would the period be if the pendulum had been inclined to 90 degrees? What value of g does this correspond to? theta=90degrees. Just as a side note, theta=0degrees when the arm is facing vertically downwards towards the ground. g=9.8m/s^2 Effective length=0.275m. The...
  20. Icaro Lorran

    Rotating the angular momentum eigenket by an arbitrary angle

    Homework Statement What is the best way to evaluate the rotation of a angular momentum eigenket (## | l,m \rangle ##) around an Cartesian axis? 2. The attempt at a solution I've tried to use the method in...
  21. 9

    Statistics - Finding standard deviation of an angle

    Homework Statement Find the formula for the standard deviation (s_h) of heading angle, given the north and east standard deviation of position of two points (s_n1, s_e2, s_n2, s_e2), each point's north-east covariance (s_cov_ne_1, s_cov_ne_2) and the north and east distance between them (d_n...
  22. I

    Loop-de-Loop with function of angle

    Homework Statement Task: [/B] On a friction free loop de loop, a object (m=600kg with passengers) moves with a velocity of vu = 120km/h at the lowest point of the loop. The loop has a radius of r=15m. The position of the object is given with the angle α. Derive the formula for the velocity...
  23. Q

    B Prove Bisecting Angle Theorem - 5 Min Exercise

    Hi, guys, i made an exercise, can you prove this? m(∠EAD)=[m(∠ABC)-m(∠ACB)]/2 If you have 5 free minutes, try it, i hope you'll like it! It's my first own exercise, so I would like some feedback, too. AD= bisecting(splits angle in 2 equal sides)
  24. G

    Angle of the slope when the object start moving

    Homework Statement when the object is moving , why the theta is larger than the theta(s) when the object is started moving ? I was told that when the object is moving , the Fk will become smaller than Fs , right ? so, IMO , the theta should be larger than the theta(s) , am i right ...
  25. A

    What would the angle φ be for this deflected laser beam?

    Homework Statement The mirror in the image below deflects a horizontal laser by angle θ. What is the angle φ if θ = 60°. Homework Equations θi=θr The Attempt at a Solution So I know that, if I draw a line normal to the mirror, that will make it so that the incident angle and the reflected...
  26. trinkleb

    Rotational Kinematics - angle between force and velocity

    Here is the problem I am working on. I have found answers for all of them except part (f), which is the one I need help with. I will report the answers I have so far: A classic 1957 Chevrolet Corvette of mass 1240 kg starts from rest and speeds up with a constant tangential acceleration of 2.00...
  27. M

    Specify force magnitude and angle

    Homework Statement See picture. Homework EquationsThe Attempt at a Solution I tried drawing a parallelogram, but it didn't help, so I'm stuck. I'd need an idea in the right direction, if possible.
  28. R

    Tension of a pole attached to a wall at an angle

    Homework Statement A rod extends from a vertical wall at an angle of 27º from the horizontal. A 2.5-kg lamp is mounted at the end of the rod. After John throws his 300-g winter coat over the lamp, what is the magnitude of the tension in the rod? The answers choices are: A) 30N B) 70N C) 27N D)...
  29. vetgirl1990

    Finding launch angle from vertical and horizontal distance

    Homework Statement The mountain rescue officers trigger the avalanche by firing a gun at a distant mountain slope. The muzzle velcoity of the gun is 225m/s. The horizontal and vertical distance from the gun to the slope is x=1,072m and y=538m respectively. Find the lowest angle between the...
  30. Driverfury

    Angle between two vectors (Only by having their lengths)

    Homework Statement Ok guys, I'm studying Physics and I started, of course, by learning about vectors. So I have this problem: There are two vectors: A (its length is 3 m) and B (its length is 4 m). I have not other informations about them. I want to know how I can dispose them to get a vector...
  31. X

    Contour Integration: Action Angle Variables (Mechanics)

    I only really need help evaluating the contour integral. I added more detail for completeness. 1. Homework Statement A particle of mass ##m## is constrained to move on the ##x## axis subject to the following potential. V(x)=a \sec^2\left( \frac{x}{l} \right) Find the action angle variables...
  32. Mr Davis 97

    Finding an angle with Newton's Second Law

    Homework Statement Given the free-body diagram below, and that the body is in equilibrium, find θ. Homework Equations F = ma The Attempt at a Solution [/B] Basically, I used Newton's second law in the y direction. Here is my work: This does not seem like the correct answer, because the...
  33. hawkeye1029

    Projectile Launched at an Angle: Velocity

    Homework Statement A bridge rises 321 m above the water. Supposed Jack kicks the rock horizontally off the bridge. The magnitude of the rock's horizontal displacement is 45.0 m. Find the speed at which the rock was kicked. Homework Equations Kinematics I think? v = vo + at Δx = vot + 0.5at2 v2...
  34. T

    Physical meaning of field components in "angle" directions

    This has been in the back of my head during a course in Mathematical Physics. In for example cylindrical or spherical coordinates, we have one or two unit vectors describing position (er, for example), their directions in a Cartesian system the function of three variables. But we also have e.g...
  35. faiziqb12

    Calculating Force on a Ball at an Angle

    Homework Statement a mass of 100g strikes the wall with speed 5 m/s at an angle of 60 degrees to the wall and it rebounds with the same speed. if the contact time is 2 * 10^ -3 , what is the force applied by the wall and in what direction? The Attempt at a SolutionI tried solving the question...
  36. C

    Calculating Velocity and Angle - Normal & Tangential Accel.

    Homework Statement...
  37. bigsmile

    Pendulum - Maximum Angle in 2nd half of swing

    A simple pendulum, 2.0 m in length, is released by a push when the support string is at an angle of 25° from the vertical. If the initial speed of the suspended mass is 1.2 m/s when at the release point, to what maximum angle will it move in the second half of its swing? Let h1 be the...
  38. K

    Finding the coefficient of Kinetic force with an angle

    Homework Statement A 1000N crate is being pushes across a level floor at a constant speed by a force (F) of 300N at an angle of 20 degrees below the horizontal, what is the coefficient of kinetic force? Homework Equations Fk= uk*N uk= Fk/N[/B] Fk=F2 The Attempt at a Solution in the back of...
  39. JulienB

    Determine components of a vector without knowing the angle

    Homework Statement (I roughly translate the problem statement from German) Given the vectors a = (1,-2,3) and b = (1,1,1), divide the vector a in two components a1 (parallel to b) and a2 (perpendicular to b). Homework Equations In a previous question of the problem, I found that: a.b = 2 a x...
  40. W

    Finding angle for specific moment

    Homework Statement i have question with part B my working is 13.2 cos tetha (0.86x10^-3)+ 13.2 sin tetha (1.22x10^-3) = 1.95 i gt stucked here. how to proceed? i only have one equation , how to solve two unknown ? Homework EquationsThe Attempt at a Solution
  41. J

    Find tension and angle from second rope

    Hi, I am having a seemingly hard time trying to find the tension in this rope. I've looked everywhere for a problem with these given variables but I found none. Here we are given: T1, T1 angle, mass of man and that is all. I included the picture here.The Attempt at a Solution I found, t1y, which...
  42. L

    Reflected Light at 3D Angle: Shift in Polarization

    I've searched high and low for answers to this, and a friend of mine finally pointed me in the right direction. I decided to write a post about it so hopefully others who have the same question will find the answer more easily. When linearly polarized light is reflected at a 3D angle, the...
  43. spareine

    Birefringence deviation angle?

    The best known effect of birefringence is the lateral displacement of the extraordinary image. Why is this effect rarely quantified? I couldn't find a table of materials specifying the deviation angle δ of the extraordinary ray (say, for an angle of incidence equal to zero). Birefringence seems...
  44. Matterwave

    Finding the sine of the angle between 2 rays

    Hello, say you are on the unit sphere and you have 2 rays intersecting it from the origin. You know the spherical coordinates of where these 2 rays intersect the sphere ##(\theta_1,\phi_1),(\theta_2,\phi_2)##. Now, because we know the dot product of two vectors, it is simple to get that the...
  45. R

    MHB Angle between the tangents to the circle

    Hi everyone, I need further explanations about the answer of this problem. The answer is angle T = 87.9 degrees. Thanks.
  46. F

    Finding launch angle and velocity

    Homework Statement You are an invading army who wants to launch a rock over the enemy castle’s wall. The wall is 12 meters high and there is a moat surrounding the wall which forces you to launch from a distance of 17 meters away. What angle and velocity should you shoot at in order to just...
  47. J

    Calc BC derivative problem with trig and double angle -- Help please

    Homework Statement Find f'(x) if f(x) = 8^(sin^2(3x)) Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it. Homework Equations if y=a^u then y' = ln a * a^u * du sin(2x) = 2sinxcosx The Attempt at a Solution We're...
  48. Marcin H

    Finding Initial Angle for a Projectile to Hit a Target 10,000 ft Away

    Homework Statement : [/B] Find two elevation angles that will enable a shell, fired from ground level with a muzzle speed of 800 ft/s, to hit a groundlevel target 10,000 ft away. Homework Equations Look at attached picture The Attempt at a Solution Look at attached picture ***I get to...
  49. S

    Force with friction problem(determine a force by the angle)

    Homework Statement A block of mass m rests on a horizontal table. The block is pulled by a massless rope with a force F at an angle θ. The coefficient of static friction is 0.60. The minimum value of the force needed to move the block depends on the angle θ a)Discuss qualitatively how you would...
  50. M

    What is the Inverse Cosine of a Squared Angle?

    Not sure if I'm doing this right. I have an angle theta to find but the cosine has been squared. I brought over inverse cosine to multiply to leave theta on its own. I was told the answer should be closer to 37 degrees? Am I doing something wrong here?
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