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.
Used to play with gravitational attraction simulations ages ago. One thing I noticed it was difficult to get a small object to collide with a bigger spherical one vertically and far more likely to hit at an angle far from 0. Has the math of this been worked out for asteroids entering the Earth's...
Is it like using the sine rule to figure it out:
1.5/sin 68 = x/sin 17 = 0.47 which doesn't seem to be correct. I tried to determine the angle. I though the 5 degree slope means it could be 95 degrees cause the triangle looks like a right angle triangle.
With talk of the Earth's magnetic field slowly moving, (enough to cause navigational issues I've heard) does it effect how the sun's ray hit us? For example, the Northern Lights are solar partials interacts with the magnetic field (I think).
If the poles moves, would it affect the effectiveness...
I am in Algebra 2 and the homework asks a question:
"You and a friend arw driving golf balls at a driving range. If the angle of elevation is 30 degrees and the ball travels 625 feet horizontally, what is the initial velocity of the ball?"
I have a question in my text (Intro Mechanics by Kleppner) and a question is to find the cosine and sine between two vectors.
It gives me the cosine piece: $$\cos(\vec A, \vec B) = \frac{\vec A ⋅\vec B}{|A||B|}$$ which I assume is just from the dot product, but it has no derivation of this, and...
Homework Statement
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Ball with a mass of 0.1 kg travels at a speed of 10 m /s to the boy.
Boy kicks the ball with foot so that it bounces back at an angle of 30 degrees with respect to the horizontal floor. The ball falls back to the ground 20 meters from the boy.
With what average force...
Hi all,
I am a self learner (graduated very long ago and rusty at math) working through the Riley, Hobson and Bence text, chapter 1.
1. Homework Statement
Use the fact that ##sin(\pi/6) = 1/2## to prove that ##tan(π/12) = 2 − \sqrt{3}.##
Homework Equations
##tan(2x) = \frac { 2 tan(x)} {1...
So here's the problem:
A sled slides down a long snow-covered slope that is at an angle θ to the horizontal. Kinetic friction acts on the sled as it slides where the kinetic coefficient of friction between the sled and snow is μk = 0.050. Ignore air-resistance when solving this problem.
If we...
Homework Statement
This is not a direct homework problem. Rather, I modified several that I saw that had different slopes but with the same initial velocity, and the same height answer: An icy, frictionless road slopes upward with angle Θ ° above the horizontal. A snowboarder of mass m...
<< 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...
I am simulating random angles from 0 to 2π with a uniform distribution. However, if I take the differences between random angles, I get a non-uniform (monotonically decreasing) distribution of angles.
In math speek:
Ai = uniform(0,2π)
dA = Ai - Aj
dA is not uniform.
Here is a rough image of...
Hello, I have a question about this optics related problem.
The distance between atomic planes in calcite is 0.30 nm. what is the smallest angle between these planes and an incident beam of 30pm x-rays at which diffracted x-rays can be detected?
Thank you so much for the help guys!
I was reading *Introduction to Nuclear Physics* by Krane and stumbled on the following (page 47):
In Elastic scattering, the initial electron wave function is of the form ##e^{i k_i r}## (free particle of momentum ##p_i = \hbar k_i##). The scattered electron can also be regarded as a free...
Homework Statement
A solid body begins to rotate around a fixed axis with angular acceleration ##\beta=\beta_0\cosφ##, where ##\beta_0## is a constant vector, ##φ##, is the angle of rotation of the body from initial position. Determine the angular velocity of this body as a function of the...
What's the difference between
P = FSin Angle / A
P = FCos Angle / A
Why cannot we use F / A only in both forumlas? I am really confused
When I should use each one of these forumlas ? I just need someone to explain each one of them ... Here's a pic to what I am referring to
, why cannot we...
Homework Statement
A frog jumps at t=0s and follows a projectile motion. The maximum height he reaches is 0.45m. The air resistance can be neglected.
a) What is the initial speed of the frog in y-direction and how long is the total time until he lands on the ground?
b) At which degree should...
Hello,
I am trying to find an analytical expression to determine the solid angle subtended by a disk source onto the face of the cylinder. I will appreciate if someone can provide me directions.
I am aware how to calculate solid angle by a point source to cylinder's face ( omega =...
Homework Statement
What is the ideal speed to take a 70 m radius curve banked at a 30.0° angle?
Homework Equations
tan θ = v2/r g
The Attempt at a Solution
This has me stuck, when I attempted this I came to the equation v= √ g*r* tan Θ
But when I substitute in the variables, I enter then into...
The formula for the angle required for you to launch a projectile with a given velocity, gravity, distance and height difference is, taking g as gravity, v as total velocity, x as total distance on the horizontal plane and y as how high the target is above you (Negative value means the target is...
Hi PF!
Given a 2D plane, the following is a parameterization of a circular arc with contact angle ##\alpha## to the x-axis: $$\left\langle \frac{\sin s}{\sin\alpha},\frac{\cos s - \cos\alpha}{\sin\alpha} \right\rangle : s \in [-\alpha,\alpha]$$
However, I am trying to parameterize a circle...
A space vehicle enters the sensible atmosphere of the Earth (300,000 ft) with a velocity of 25,000 ft/sec at a flight-path angle of -60 degrees. What is its velocity and flight-path angle at an altitude of 100 nautical miles during descent?
(Assuming no drag or perturbations, two body orbital...
Homework Statement
For a physics experiment I need to find the uncertainties and I am using the angle of minimum derivation formula:
The value of A=60° and one of the values of D is 29.7° which has a uncertainty of ±2 (I know it's a very high value)
Homework Equations
How do I calculate the...
Homework Statement
I would like to understand why alpha particles experience large angle deflections and if this is the same thing as recoil of alpha particles? Do large angle deflections occur near the end of the alpha particle track or can they occur at any point along the trajectory...
I am looking for an optical piece that can act as a mirror when the angle of incidence is close to normal (90 degrees) but acts as a see-through glass when the angle of incidence is less than 60 degrees?
Alternatively it can be a filter placed in front of a mirror that passes a lot of light at...
Homework Statement
ABC is a triangle
The angle A = 30 degrees
AB = 7cm
BC = 5 cm
C is an acute angle. Find the size of angle C?
Homework Equations
I need to use the cosine rule here Cos C = (a^2 + b^2 - c^2) / 2ac
The Attempt at a Solution
The problem is I do not know the size of side b?
So...
Homework Statement
If the plane 3x+y+2z+6=0 is parallel to the line (3x-1)/2b = 3-y = (z-1)/a then 3a+3b is?
Homework Equations
angle between two lines=90 degree when l1l2+m1m2+n1n2=0 where l,m,n are direction ratios...(i)
The Attempt at a Solution
First I divided x/3 and 3-y by -1 to get the...
I seem to have come across a new problem
I am trying to programm a sloping pipe system to match an array of vector points.
I thought I had it all sorted out until I tested with a very high slope angle. With a normal slope of around 2% everything looks fine. If I increase the slope to 30% there...
Triangle ABC has area 25*sqrt(3). if Angle BAC=30 degrees, find |AC|=|BC|=?
the answer I got was 10*4th root(3)
Is this correct?
I am asking because someone other than my professor wrote the study guid for us for the final and I am not 100% sure what |AC|=|BC| means as my professor never...
Homework Statement
[/B]
Homework Equations
Drawing a diagram for the forces is the easy part. I am not sure I am doing the equation of the sum of the torques well.
The Attempt at a Solution
This is my attempt for the forces[/B]
And this for the torques:
How do I determine the degrees of an angle if I three X and Y coordinates? I honestly just need a formula to plug into some code. Thank you in advance.
Homework Statement
Tarzan runs at 6 m/s and grabs a vertical vine (negligible mass) of length 4.1 m which is tied to a branch at the top. Tarzan then swings up.
Determine the maximum height Tarzan will swing up and the maximum angle the vine will make with respect to vertical.
Homework...
Tomorrow is my math test and I'm going over the study guide:
I have vector U=<1, 3> and vector V=<5, 2>
It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)?
I already know how to find the missing angle for cos(theta) but we never covered how...
Hello, I was struggling with solving a specific integral. I know that I can rewrite the exponential matrices and the range of the three Euler angles. However, I am not sure I should I write in terms those three Euler angles.
MY apologies that I don't think this is particularly advanced; my algebra and trigonometry is quite good, but all seems to fall apart once i move from 2D to 3D environments.
Johnson Solid J2 is a pentagonal pyramid consisting of five equilateral triangles on a pentagonal pase, meeting at the...
Homework Statement
We shot a projectile with mass ##m## and velocity ##v_0## with angle ##\phi## it collide with a box with mass ##M## at the maximum height of its path. Then, they both start to move with another speed. (We define ##t=0## at this time) (Completely Inelastic Collision). The box...
Elliptically polarized light strikes a glass surface (in air) with refraction index n at Brewster's angle.
What is the polarization of the reflected ray?
How does it change if now the glass surface is partially submerged in water?
And if the glass surface is fully submerged in water?
How...
Hello,
what is the length of x in the attached?
I tried the following:
of course BE = 5, and also the point D must be the center of internal circle that is tangent to triangle and from there i came up with some equations together with the side ratio formulas of angle bisectors but it didnt...
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...
Hi all,
This is not exactly a homework question, more like for my own safety
So I have a project going on and I need to use an angle grinder without the safety guard which will be enclosed in a box (made from plastic most probably).
So I decided to check if the plastic box would be able to...
Hi,
I am trying to 'size' my first motor to drive a system. I am trying to make a feeder where a PVC pipe is fed as shown. There are 2 vertical rollers, on connected to the motor as shown and an other coupled to a pneumatic piston to keep the pipe under pressure. the frictional force will be...
Homework Statement
Tarzan who weighs 688 N swings from a cliff at the end of a vine 18 m long. From the top of the cliff to the bottom of the swing he descends by 3.2 m. The vine will break if the force exceeds 700 N. Find the angle with the vertical at which the vine breaks.
Homework...
Homework Statement
An archer launches an arrow from coordinates ##(0, 0)## at an angle ##\alpha## and with an initial velocity ##v_0##. There's a target located ahead of the archer and the center of that target is at coordinates ##(d, h)##. At what ##v_0## and at what angle ##\alpha## does...
Homework Statement
In double slit interference , the angle between the center bright fringe and the path length (aka the angle used to find the path length difference) can be approximate as a small angle. However, we cannot assume the angles of bright fringes due to diffraction gratings are...
Hello everyone,
Does anyone know what the slip angle is in relation to rubber tires? What is its effect? Is it a positive or negative effect?
My basic understanding is that when a tire is cornering, the tire does not point directly along the curved direction of motion but is slightly twisted...
Homework Statement
Over a completely flat surface a thermal detonator (Star Wars) is thrown by a Wookiee (a member of the rebel alliance) towards a group of imperial stormtroopers. The thermal detonator always leaves the Wookiee’s hand with a speed of 100m/s and the thermal detonator has a mass...
Homework Statement
A fish floats in water with its eye at the centre of an opaque walled full tank of water of circular cross section. When the fish look upwards, it can see a fish-eye view of the surrounding scene i.e. it is able to view the hemisphere of the scene above the water surface, and...