Angle Definition and 86 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. junseok Lee

    I Finding the change in position and angle after moving the rectangle

    I am curious about how to approach the problem mathematically, so I write. There are 4 dots on the square and I know the location. The rectangle moves and the positions and angles of the four points change. I also know the location of the four points that have changed. I don't know the...
  2. K

    Understanding of Wave swing physics

    Yeah, as I said, i have no idea why we can assume beta to be the same for any position at given alpha.
  3. F

    Angle of reflection of a beam light on a moving mirror

    Before to open this topic, I found this there. It's quite similar, if not the same, but I'm a little confused, so I'm here. The situation is represented in this image. From optical geometry, ##\theta_{incident} = \theta_{reflected}## The four-momentum in ##S'## is the following one...
  4. DerbisEternal

    Two Charged Balls on Strings

    Given the total angles in the x direction, I set up this: (mg/cos(x))*sin(x)-Fe=0 then isolated for x: mgtan(x)=(kq^2)/(2*sin^2x) sin^2(x)*tan(x)=(kq^2)/(2mg) From here I am stuck. How do I go forward when x is contained in two different trig functions on the left?
  5. Pushies

    CoM reduced by total body height when bending your knee X degrees

    Lets say that a man with a standing height of 185cm bent his knee 30 degrees, how many centimeters will be reduced from his standing height? Assume his femur length is 60cm and his tibia (shin) length is 50cm. Can anyone give me a hint? I've tried to use trigonometry but i dont think i fully...
  6. Michael_0039

    A kid slips off the top of the hill -- find the escape angle

    Hi, This is my try. Are you in agreement with this ? Thanks.
  7. P

    Finding the angle between vectors a and m, knowing the magnitude of m and n

    Summary: Finding angle between vectors a and m, knowing magnitude of m and n, also the angle between m and n with 60 degrees. Using geometry, it looks like the angle is 30 degrees but the answer is suppose to be 54.7 degrees. I'm not sure how to solve this.
  8. nomadreid

    I Tensor calculation, giving|cos A|>1: how to interpret

    On pages 42-43 of the book "Tensors: Mathematics of Differential Geometry and Relativity" by Zafar Ahsan (Delhi, 2018), the calculation for the angle between Ai=(1,0,0,0) (the superscript being tensor, not exponent, notation) and Bi=(√2,0,0,(√3)/c), where c is the speed of light, in the...
  9. Coder Hashtag

    B What is the definition of angle?

  10. G

    How does the release angle of a catapult affect the object's velocity?

    [Moderator: repeated text removed.]
  11. megaly

    Slope Problem

    Im really stuck with this problem ! any help would be much appreciated
  12. QuarkDecay

    Flow (liquid or gas) across a rotating surface's face

    << Mentor Note -- Two threads on the same question merged into one thread >> How does the maximum Power equation change if there's an angle to the way the wind falls into the wind turbine's blades? Example, when it falls vertically to the blades, it's Pmax= 8/27Sρu13 But if there's for...
  13. zehkari

    Double slit intensity question

    Homework Statement Homework Equations (1) Φ = 2π*(dsinθ/λ) (2) Itotal = I0 cos2(Φ/2) (3) Itotal = I0 cos2(πdy/λR) λ = 585 * 10-9 m R = 0.700 m d = 0.320 * 10-3 m y = ? The Attempt at a Solution a) I used eqn (1) and divided the total oscillations by a complete oscillation to find the...
  14. zehkari

    What is the minimum force at this angle that will move the box?

    Homework Statement [/B] 2. Homework Equations Fs = Nμ W = mg Fy = Fsin(θ) Fx = Fcos(θ) The Attempt at a Solution [/B] Hello all at PhysicsForums, I have a question on angled force and static friction. From my attempt below, I think I have found the maximum force required and would need...
  15. archieab

    Converting PyGame 2 axis joystick float to 360 angle

    I would like to convert my joystick's two axis float (horizontal and vertical) to a 360 angle that can be used to set a players direction in my game. From my research, I've found the best route to take is using Atan2. Variables: self.rot = 0 horaxis = joy1.get_axis(0) veraxis = joy1.get_axis(1)...
  16. alexi_b

    Finding the angle in which the resultant force points

    Homework Statement Forces of 11.8N north, 19.2N east, and 15.9N south are simultaneously applied to a 3.93kg mass as it rests on an air table. What is the magnitude of its acceleration? What is the direction of the acceleration in degrees? (Take east to be 0 degrees and counterclockwise to be...
  17. alexi_b

    Finding Vector Angle using cosine law

    Homework Statement Vectors A and B have equal magnitudes of 4.93. If the sum of A and B is the vector 6.79j, determine the angle between A and B Homework Equations c^2 = a^2 + b^2 -2abcos(theta) The Attempt at a Solution I just rearranged the formula above so that I could solve for the...
  18. alexi_b

    Map question involving vectors (find the angle)

    Homework Statement Instructions for finding a buried treasure include the following: Go 66.0 paces at 256deg, turn to 140deg and walk 125 paces, then travel 100 paces at 169deg. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant...
  19. alexi_b

    Vector Addition Question: find angle (A+B & A-B)

    Homework Statement Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be 65 times greater than the magnitude of A - B, what must be the angle between them? Homework Equations The Attempt at a Solution I tried using the dot product and solving for the angle but...
  20. alexi_b

    River question (looking for angles and headings)

    Homework Statement A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.35km/h. The child is 0.505km from shore and 0.780km upstream of a boat landing when a rescue boat sets out. If the boat proceeds at its maximum speed of 18.8km/h relative...
  21. Muhammad Danish

    Resultant Vector

    According to my understanding, option D is the only possible value of R. I don't understand how options A, B and C are included. Please explain this question. Thanks. (regards)
  22. Ventrella

    A Binary fractal tree with equidistant leaves on a circle

    Does there exist a binary fractal tree… (reference: ) …whose leaves (endpoints) lie on a circle and are equidistant? Consider a binary fractal tree with branches decreasing in length by a scaling factor r (0 < r < 1) for...
  23. C

    Constraint of Two blocks on an inclined plane

    Hello, I have an issue regarding a constraint related to an angle: Suppose I have masses 'A' and 'B' on an inclined plane ( of mass 'C') attached by a pulley. I place my origin as shown and I want to find a constraint relating angle β. so, I saw my classmate writing as follows to find...
  24. Curiose

    Is it all in the angle?

    For one of my current projects in computer vision (which really is a study in point clustering and tracking in a data stream of n-dimensional data), I have come up with a way to very quickly index a 2D angle between two points or the angle of a vector. Doing a little bit of investigation, and...
  25. O

    Pulling an object at an angle with friction -- find the Kinetic Energy

    Homework Statement A boy pulls a sled (mass m=59.2 kg) along the ground using a force of magnitude F = 586 N inclined at an angle of θ=37.3° to the horizontal. There is friction between the sled and the ground with a coefficient of µk = 0.205. If the sled starts at rest, how much kinetic energy...
  26. S

    Coulomb's Law, Three Charges, X Y Components, Angle

    Homework Statement This is finding net force on Q3. I was taught by my Physics teacher to always get angle from the Positive side of x-axis (+X-Axis). For example in the above situation, if the angle is -30deg from the +x-axis (assuming the Q3 is the origin), Why is F31 x-component = 140...
  27. O

    Projection at an angle - throwing stones

    Hello everyone. I have this problem: 1. The problem statement, all variables and given/known d I throw stone from height h at an angle α, then at an angle β (so I know h, α, β). I throw it with same velocity v. The stones fall in same distance d. The question is: find the d (distance) and v...
  28. J

    I Calculation of the hour angle of the Sun

    Hi all, According to the sunrise equation, the hour angle of the sun at sunset is: cos H = -tan(a)tan(d) where H = the hour angle, a = latitude and d = solar declination angle. This equation says that H at sunset = -H at sunrise. Now, I have a few questions concerning that: 1) I was...
  29. Const@ntine

    Refraction in Cylinder.

    Homework Statement A non-transclucent container in the form of a cylinder, has a diameter of 3.00 m, has its top part open, and is filled with water. When the sun created a 28.0 degree angle with the horizontal, the light doesn't illuminate the bottom of the container. What's the depth of the...
  30. R

    If air drag is a factor, how will it affect a projectile?

    If air drag is a factor, how will it affect a projectile’s trajectory qualitatively? Its velocity? Its acceleration?
  31. andylatham82

    I Angle between vectors via scalar product vs vector product

    Hello, I have a question about why I can't determine the angle between two vectors using their cross product. Say there are two vectors in the XY-plane that we want to find the angle between: A = -2.00i + 6.00j B = 2.00i - 3.00j The method to do this would be to work out the scalar product of...
  32. 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...
  33. 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...
  34. 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...
  35. 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...
  36. 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...
  37. A

    Find the time of movement

    Homework Statement A particle is thrown in the angle pi/3 radian with speed 10m/S. Find the time of movement if the maximal height is equal to the distance of fall. Homework Equations v^2-voy^2=2gh The Attempt at a Solution 0-10^2*3/4=2*10*hmax hmax=3.75 v0x*2t=3.75 v0*cos60*2t=3.75...
  38. A

    Solving for Launch Angle Using Vo

    Homework Statement Find the angle at which the projectile is launched. (Hint: use tan^2+1=sec^2) Initial Net Velocity=430 m/s The projectile lands perfectly on the edge of a cliff 80 meters high and 175 meters away. Homework Equations tan^2+1=sec^2 Kinematics, i.e.- v=vo+gt...
  39. H

    Speed of box from ramp to floor

    Hey, so I just finished taking a physic's test and one of the question was interesting to me. I thought it was pretty simple but my friend did the problem a different way, so I'm wondering what's the correct way to do this problem. So a box is moving down a frictionless ramp and onto the floor...
  40. T

    Really quick Droop control question

    Hi, I just want to double check my understanding of Power angle. Say you have a large network, and you have a bus with a small generator and a larger load on it. For power to be going into that bus from the rest of the network there has to be power angle between the bus and a bus(s) which power...
  41. C

    B For oscillations, why do we use angles in waves and oscillat

    For example, the term angular frequency, it units is radian per second. For phase, it is also measured in radians or degrees, why is that? Why is the math the same when you use angles to describe oscillations?
  42. D

    Inclined Plane Find Theta

    Homework Statement This problem asks for the angle on an inclined plane-- I have attached the problem below. Homework Equations fnet=ma The Attempt at a Solution I honestly have no idea what to do. I found the vector components for gravity and made a FBD for the box, but I can't really figure...
  43. C

    Find if the boat will see the flare, what angle will they?

    Homework Statement You have been stranded on a deserted island. Fortunately, you managed to bring a flare gun. You can see a ship 300. m off shore. Unfortunately, because of the daylight the ship cannot see your flare unless it is within 100. m of the ship. A.) If you fire the flare gun from...
  44. C

    What angle will the vine break and what's the max tension?

    Homework Statement You come to a river and you see a vine you will use to swing across. Your mass is 75.0 kg, the vine is 18.0 m long, and the vine breaks when under 655 N of tension. a) at what angle from the vertical will the vine break? b) what should be the maximum tension supported by the...
  45. StarWarsNerd

    Angle of Deflection in Elastic Collision

    This is the problem I am looking to solve: given two objects of different mass, find the angle of deflection after an elastic collision for each object. For both objects we know: m : Mass in Kilograms θi : Initial Angle in Degrees si : Initial Speed in Units per Second sf : Final Speed in...
  46. B

    Question about Centripetal Force

    Homework Statement Question 2.b. from this paper - Homework Equations let theta = x Tcosx = mg Tsinx = 2.5 (2.5 is the centripetal force) The Attempt at a Solution I rearranged the above equations and got 52 degrees as my answer. The...
  47. Jonski

    Angle of twist

    Homework Statement What is the angle of twist at gear A relative to the motor? (Round to the closest 6th decimal) Homework Equations I know to find the angle its θ = ∑ (TL/JG) but it can also be θ = Lτ/Gr The Attempt at a Solution So i used both these equations, and I got...
  48. Blockade

    Can someone help me find the angle between two forces?

    Can someone help me relearn finding the angle between two forces when solving for work of each forces (gravity, tension, fF, normal)? I remember that cos(90°-α) = sin(α) but what I don't understand is when the angle in between is "90°-α" or when it's just "α". I tried doing this on my own and...
  49. Z

    L Bar Structural Question

    Hi All. Given a 20 inch L bar with 1" sides. If 6 inches of this bar is buried in a concrete wall horizontally, which orientation would render the most downward force strength? 1. A V orientation with the tip of the V pointing down. 2. A V orientation with the tip of the V pointing up. 3...
  50. ckyborg4

    Is there any relationship between light intensity and angle

    Homework Statement I'm working on a project right now, which uses laser beams and part of the project requires me to find a mathematical model which relates angle of projection to the intensity of the light. Does anyone know of an equation(s) which relates the intensity and angle together...