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. J

    Power Electronics Rectifier Firing Angle and Overlap Angle

    Homework Statement Homework Equations Since question says the current is always continous, so overlap is always there. So option B is incorrect. Also since firing angle is increased from 0 to 45, the overlap angle will reduce. So it'll be less than 45. So option A is incorrect. The Attempt...
  2. Pushoam

    Calculating angle between velocity and position vector

    Homework Statement Homework EquationsThe Attempt at a Solution I took ## \frac { d\vec r}{dt} = 0 ## . This gives ##t_m = \frac { 1} {\sqrt{ 2}} ## ...(1) To calculate ## \alpha ## , ## \cos{ \alpha } = \frac { \vec v \cdot \vec r}{|\vec v||\vec r|} ## ...(2) Then, magnitude of...
  3. I

    Dynamic contact angle simulation in COMSOL

    I am doing the dynamic process of a water droplet impinging onto a wax substrate in COMSOL, using the Phase Field method for tracking the free surface. I am able to do the simulation for Static Contact Angle(SCA) i.e i am imposing a fixed contact angle throughout the time step in wetted wall...
  4. R

    Projectile motion above ground given only angle and height

    Homework Statement I'm having trouble with part A of this question 1. A ball is fired out at an angle of 30° from the platform of height h = 0.5 m as shown in Figure 1. It is subjected to the gravitational force only thus follows a projectile motion. It falls onto the ground after 0.6...
  5. karush

    MHB 243.12.5.21 acute angle btw vectors

    \tiny{243.12.5.21} $\textsf{Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.}$ $$\textit{$3x+10y+7z=9$ and $7x+ 2y + 9z = 3$}$$ \begin{align*}\displaystyle u&=3x+10y+7z=9\\ v&=7x+2y+9z=3\\ u \cdot...
  6. CAT 2

    The angle and distance of a projection - Grade 11 physics

    Homework Statement A water balloon is fired 34 m/s from a water cannon, which is aimed at an angle of 18° above the ground. The centre of the cannon's target (which has a radius of 1.0m) is painted on the asphalt 42m away from the water cannon. a) Will the balloon hit the target? Justify your...
  7. CAT 2

    Maximum height of a spring toy launched at an angle

    Homework Statement A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. What is the maximum height reached by the spring toy? Homework Equations Δt = 2(V1)Sinθ/(acceleration) ΔD = V1Δt + 1/2(acceleration)(Δt^2) The Attempt at a Solution First I solved for...
  8. C

    B How should I express this angle in words?

    Hi! The diagram above is showing a man swinging a swing (a facility you can find in playgrounds) back and forth. I'm trying to come up with a concise expression in words that describes the angle noted as theta so that I can write a clear and effective research question (theta is the independent...
  9. J

    Current Angle More Than Ninety Degrees

    Hi, I'm studying Sync Generators. In one problem I got Ia as 1.59 angle of -159.9 degrees. How do you calculate power factor for such a current? Book says Ia leads Terminal Voltage by 23.13 degrees. I guess they got that value by 180 - 159.9 But why?
  10. J

    How Much Work Is Done When Pulling a Sled at an Angle?

    Homework Statement A sled is pulled across the barren winter landscape at an angle of 26.0° from the ground with a force of 74 N. If the sled is pulled over a distance of 27 m, how much work was done on the sled? Round your answer to two decimals Homework Equations W = f x s x Cos The...
  11. Z

    Interior and Exterior Angle of a Polygon: Formula not working

    Homework Statement How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle? Homework Equations Interior angle of a polygon: ((n-2) * 180)/n Exterior angle of a polygon: (360)/n The Attempt at a Solution ((n-2) * 180)/n = 8 *...
  12. A

    I Is the Compton scattering angle related to the incident energy?

    The Compton equation determines the shift of the wave-length of the scattered photon as a function of the ##cos\theta## of the scattered photon. It does not depend on the energy of the incident photon. With some manipulation using the equations of conservation of the momentum and energy, one...
  13. K

    B How do astronomers find the "parallax angle" of a star?

    https://www2.jpl.nasa.gov/teachers/attachments/parallax.html It's written that they find the distance by calculating from the parallax angle. But how do astronomers find the parallax angle?
  14. karush

    MHB Angle b/w Velocity $\&$ Acceleration Vectors at $t=0$

    $\tiny{243.13.0113}$ $\textsf{The vector $r(t)$ is the position vector of a particle at time $t$.}]$ $\textsf{Find the angle between the velocity and the acceleration vectors at time $t=0$}\\$ \begin{align*} \displaystyle...
  15. T

    B Eratosthenes angle measurement

    I am writing an article on Eratosthenes and am having a little trouble on how he actual found the angle of the stick. Because as far as I can gather there was no series solutions for any of the trig defin no calculators. All he knew was the length of the shadow and the height of the stick. I...
  16. N

    Linear polarizers: angle between the electric & magnetic fields

    From wikipedia: "An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field." A polarizer is an object that...
  17. L

    MHB Formula for changing a plane intersection angle

    Hello, This is a bit more complex than my previous post, but I don't think it qualifies for university level difficulty. Please move this to the appropriate forum if my assessment is not correct. I have 4 vectors in three space where each vector has its tail at the same point (point B). id...
  18. Anonymous123451234

    How Is the Vertical Force Calculated at the Hinge in a Beam and Sign System?

    A shop sign weighing 215 N hangs from the end of a uniform 155-N beam. Tension in supporting wire= 642 N Horizontal force exerted by the hinge= 526N Find the vertical force exerted by the hinge on the beam at the wall Fy= Fhy + Ft * sin() - mg - Mg =0 My attempt: Fhy= -(Ft *sin() - mg -...
  19. P

    I Determining The Inclination Angle of A Stellar Binary System

    I am a Physics undergraduate at the University of Texas at Arlington. I am currently taking an Astrophysics class in which my professor talked about the inclination angle of the orbital plane of the binary star system and how it is impossible to determine that angle. I was wondering why is it...
  20. A

    Elastic Collision Angle Proof

    Homework Statement Prove that in the elastic collision of two objects of identical mass, with one being a target initially at rest, the angle between their final velocity vectors is always 90 degrees. Homework Equations m1v1+m2v2 = m1v1'+m2v2' 1/2m1v1^2 +1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2...
  21. L

    Pulley at an Angle Problem - Newton Forces

    Homework Statement Homework Equations Friction Force = normal force * static coefficient for friction Fnet = ma The Attempt at a Solution So i drew the free-body diagrams for both the objects...[/B] Im trying to figure out the tension in the 2nd free body diagram and i know that it's...
  22. ubergewehr273

    Problem about an elastic collision between a rod and a ball at an angle

    Homework Statement Homework Equations Conservation of linear momentum Conservation of angular momentum ##\frac{-v_{relative after collision}} {v_{relative before collision}}=e## where e is coefficient of restitution The Attempt at a Solution Components of velocity given as...
  23. R

    Intuition for why escape velocity doesn't depend on angle

    Homework Statement solve for escape velocity from Earth's surface Homework Equations just either use the line integral, and the tangential term disappears, or just use the energy equations The Attempt at a Solution I've solved it, but I'm having some trouble just coming to grips with this...
  24. A

    How is the minimum work needed to push a car up an inclined plane calculated?

    Homework Statement What is the minimum work needed to push a 1000-kg car 300 m up a 17.5 degree incline? A. Ignore friction B. Assume the coefficient of friction is 0.25 Homework Equations W = F*d Net force = ma The Attempt at a Solution At first I did: Work = F*300*cos17.6 but I later...
  25. S

    How to find the maximum angle of a pendulum after a mass collides with it

    Homework Statement A 10g ball is fired at 6 m/s into a 280g pendulum. What maximum angle will the pendulum swing to if the effective radius of the pendulum is 28cm? Homework Equations How to find theta? The Attempt at a Solution I converted 28cm to 0.28m; 10g to 0.010kg; and 280g to 0.280kg...
  26. E

    Projectile Motion: Determining Launch Angle

    Homework Statement A hunter aims a high velocity semi-automatic rifle at a moose that is 500.0 m away in a direct line of sight. The moose stands 40.0 m below the horizontal in a depression with a bog at the bottom. The muzzle velocity is 2500.0 feet per second and the sight on the rifle is...
  27. A

    How to calculate projectile off cliff when angle is below th

    Homework Statement Cliff is 50 m tall Stone thrown downwards with velocity of 12 m/s and 22 degrees below horizontal What is the time it will take to hit the ground? Homework Equations V=d/t D= Vi t + 1/2at^2The Attempt at a Solution Vx1= cos (22)(12) = +11.12620625 Vy1= sin (22) (12) =...
  28. A

    Finding the direction of an angle in the unit circle

    Homework Statement I'm having trouble understanding how to find the angle of a vector. Here we are given the x and y component to help us find the direction of vector C. In this case, both x and y component is negative, so it should be in the third quadrant. I know that since we have both the x...
  29. patrykh18

    ∆KE if angle between force and displacement varies

    Homework Statement A string is attached to a block that can slide along a frictionless horizontal surface aligned along the x axis. The left end of the string is pulled over a pulley of negligible mass and friction at a height of 1.3m so that the block slides from x1=3m to x2=1m. The tension...
  30. C

    How Does Angle of Force Application Affect Acceleration on a Frictional Surface?

    Homework Statement A force is applied to an initially stationary block of mass 2.65 kg that sits on a horizontal floor as shown. The 81.0 N force is applied at θ = 50° angle to the vertical. The coefficients of friction between the floor and the block are μs = 0.895 and μk = 0.665. What is the...
  31. 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...
  32. A

    I Angle of projection for maximum range

    Hi, I can't seem to work out how angle of projection for maximum range comes out to be (pi/4 - Beta/2) This happens when the projectile is protected up the inclined plane. Similarly, I couldn't understand how the angle comes out to be (pi/4 + Beta/2) when the projectile is protected down the...
  33. N

    Conduction Angle of a Diode Circuit

    Homework Statement I am trying to prove that the diode conducts between the expressions shown here: Homework Equations I know that Vo = Vpsin(wt) and the only information i know about the diode is it has a turn on voltage of Von. The Attempt at a Solution I have tried to plug the variables...
  34. A

    Elastic collision and angle of deflection problem

    1. 2. The equations are the equations of conservation of momentum: m1v = m1v1cosθ1 + m2v2cosθ2 0 = m1v1sinθ1 + m2v2sinθ2 3. I tried to solve it using the above equations and also tried using kinetic energy conservation since it's an elastic collision. But I can't work out the...
  35. 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...
  36. 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...
  37. X

    How convert a point on an X and Y grid to a angle degree?

    <Moderator's note: Moved from a technical forum and thus no template.> Hello Forum, This post is a spin-off from this post: https://www.physicsforums.com/threads/how-much-would-time-pass-between-watching-the-sun-set.925257/#post-5840279 If I have an X and Y point on a grid that represents...
  38. F

    Projectile Motion: Angle & Range with Air Resistance and Wind

    Homework Statement A projectile is launched at an angle to the horizontal and rises upwards to a peak while moving horizontally. What is the angle of maximum range and how it is dependent on initial velocity if we include air resistance and if the wind is blowing in the horizontal direction of...
  39. S

    Find angle between displacement and velocity vector

    Homework Statement A stone is thrown at 25m/s and at 37 degrees above the horizontal from a 20m high building. Take g=10m/s2 Let D be the displacement vector from launch point on top of the building to landing point on the ground, and v be the velocity vector on impact, what is the angle...
  40. alphaj

    Organic chem: draw this in line angle structure

    Homework Statement Draw this formula in line angle structure. CH3CH2OC(O)CH2CC(CH2)3CH(CN)CHO. Homework Equations None. The Attempt at a Solution I'm confused with the CC(CH2)3 part of the condensed formula. I knew I got it wrong the first time I drew it because I couldn't just tag three...
  41. A

    Relationship between Launch Angle & Horizontal Distance

    Homework Statement How to prove the correlation between launch angle (<45°) and horizontal displacement. Independent Variable: Horizontal distance Dependent Variable: Launch Angle (Important) Controlled Variable: Firing velocity [90 m/s] Another problem is, with the data that I have...
  42. M

    What is the angle and displacement of the plane?

    Homework Statement In the figure below, a radar station detects an airplane approaching directly from the east. At first observation, the range to the plane is d1 = 412 m at 40° above the horizon. The airplane is tracked for another 123° in the vertical east–west plane, the range at final...
  43. jlmccart03

    Finding Angle Theta in Relativistic Skydiving Scenario

    Homework Statement A skydiver is strapped to a rocket and shot into outer space. There is no air resistance so he is able to make his arms into a 45° angle with respect to his body and pretend they are "wings." To a stationary observer on the Moon (we will consider the Moon stationary for our...
  44. C

    Shooting a bullet at an angle from a given height

    Homework Statement A sniper standing on a 70 meter-tall tower fires his rifle at 30 degrees upwards with the initial velocity of 1000 m/s. What is the range of the bullet and how much time will pass before it hits the ground? Assume no air-resistance. 2. The attempt at a solution I divided...
  45. F

    Induction motor - calculating rotor flux angle

    Hello. I'm trying to write my own soft for Field Oriented Control of induction motor. I have finished hardware - 3ph 3kW inverter, controlled by STM32F4, and V/F open loop algorithm to control ACIM - it works. Now I'm trying to implement FOC algorithm. As we know we need to do Clark&Park...
  46. F

    What is the Maximum Angle of Deflection in a Particle Collision?

    Homework Statement A particle of mass ##M## and speed ##v_1## bumps a particle of mass ##m##, ##(M >m)##, at rest. Find the maximum angle of deflection of ##M## after the bump.The Attempt at a Solution I would like to solve this problem in the reference frame of the center of mass, because it...
  47. Q

    Plane wave angle of incidence calculation

    Good afternoon! Please help me figure out the mathematics of this simple plane wave question! 1. Homework Statement 2. Homework Equations n1*sin(theta1)=n2*sin(theta2) The Attempt at a Solution I need help calculating the angle of incidence. I found the propagation vector for incidence...
  48. H

    The force required to raise a bridge/lever to an angle?

    Homework Statement Tower bridge in London is an example of a bascule bridge (moveable bridge) where each part that is raised up is called a ‘span’. In this photo, the two spans are raised to an angle of 38° to let two tug boats through. Each span is 30.5 m long and weighs 1 x 108 kg (you can...
  49. E

    Angle between a Point on a Ellipse and its Center

    1. The problem statement, aall variables, and given/known data I need to find the angle between a point on the ellipse and the ellipse's center shown in the figure below: The known variables are 'd', the distance between point O (the center of the ellipse) and point A, and 'a', the angle...
  50. Z

    Angle between 2 charged spheres hanging from string

    Homework Statement Two positively charged metal spheres are suspended from the same hook by light strings of equal length, making an angle of 10.0◦ with each other. The charges carried by the spheres are as shown in the diagram. After that, the spheres are brought in contact briefly, then...
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