Angle Definition and 1000 Threads

I've never really understood this bit of trig, I think I get it if there are two parallel angles (parallelogram). But, I do not understand how you go about when the triangles aren't in a parallelogram.

I understand that when light goes between air and water, refraction occurs (either towards or away from the normal). If the light going between air and water is already going in the same direction as the normal, is there no refraction (or a refraction angle of 0 degrees)? Thank you.

Hi there, I have a question I'm unable to get properly started on: A cylinder of radius R and mass m is lodged between cross pieces that make an angle θ with each other, as shown in the diagram below. The cross pieces of negligible mass are connected in point C, with lengths AC = BC = 2R and...

Homework Statement So the full problem is the following: "On the top of a truck, there is a cubic container with a side-lenght of 1,00 m and it's filled with 500 liters of water. The truck accelerates with 2.0 m/s2 in the x-direction during the whole experiment. When the watersurface has...

Homework Statement Sin2x-cosx=1 Solve for all x values between [0,2pi) Homework Equations Sin2x=2sinxcosx The Attempt at a Solution [/B] 2sinxcosx-cosx=1 cosx(2sinx-1)=1 I don't know what to do after this. It doesn't equal 0 so I can't set each factor equal to 0

I kind of understand what to do with this when there are no numbers in front of the expressions, I also kind of understand that you can rewrite 4Sine(4x) as 4Sine(2x+2x) hat do I do with the 4 and 8? In an algebra problem you could divide the 4 into the -8, then simplify that expression, am I...

Hey all, I'm stuck on this problem and not sure how to proceed/if I'm in the right direction. Problem: One reference frame N sits at the origin (inertial frame) while another frame, B, describes a disk rolling on a circular ring about the other frame. Picture below (A) find the direction...

MODERATOR NOTE: THIS THREAD WAS ORIGINALLY IN ANOTHER FORUM, SO THERE IS NO TEMPLATE. I have a hollow shaft made of a titanium alloy, Shear Modulus "G". The shaft has a wall thickness of 3.2mm and an inner diameter of 20mm. The shaft looks as show in the attached image. A torque T of 232 Nmm...

I am trying to design a material transfer system ( the system at duration 0:57 to 1:34 ). The general layout is http://i.imgur.com/ajQ05qy.png It was suggested that angle be 5 degree. The reason is for hauling effect so the tray can revolve back. can you explain this? why 5 degrees? supporting...

I don't need the solution solved for me, but I need help with the method to find the solution. 1. Homework Statement A projectile is launched from an unknown angle and expected to hit a target at a lower altitude. The values given are the initial velocity, and the distance of the target from...

Question: The height of the given vessel is h,and the width of the given vessel is b (as given in the diagram). The density of the liquid is r.Find the force exerted by the liquid on the slant wall. Relevant formulae : P = F/A F = Vdg An attempt at the solution...

Assume a 2D problem. Given a linear antenna array, let's say 3 antennas distributed around the z axis, how could we extract the incidence angle of the received wave? Having 3 antennas equally spaced by λ/2 in the z axis and connected to each other, the result gain would be a function of ϑ (angle...

Homework Statement Find the angle made by the two tangents to the curve ##x=\sin2t## and ##y=\sin(2t)\cos(2t)## at the point ##(0,0)## Homework Equations ##\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}## (Derivative of a parametric equation) The Attempt at a Solution ## x = \sin(2t) = 0...

Hi all, I was wondering if anyone could help me with calculating the angle of lean on a motorbike on a banked curve (with friction). If possible proofs would be very useful. Thanks Lee

I ran across a project at the Univ. of Tennessee that has deployed a network of frequency meters around the power grid in the US. see http://fnetpublic.utk.edu/anglecontour.html I understand the frequency excursions may indicate unexpected events like generator trips or loss of load. What do...

Homework Statement A person is dragging a packing crate of mass 100 kg across a rough floor where the coefficient of kinetic friction is 0.400. He exerts a force F just sufficient to keep the crate moving at a constant velocity. At what angle above the horizontal should his pulling force F be...

This was a homework problem; after five tries, I still did not get it, and I can't figure out how to get at the answer the assignment gave me. I could not find the answer anywhere that didn't get into angular velocity, which we are not at yet (and also did not give me the answer!). 1. Problem...

Hi all. I am not quite sure if this is the right forum to place this question but for me there are several forums that would fit with my situation :D I am making a game where I have to throw/shoot a projectile through a 3 dimensional space which has to land on a specific object. There are...

I'm given an irregular shaped plot with 3 sides, and have been asked to find the fourth missing side, no other detail is given. Is it possible to find the missing side? If so, then how? Here is what it looks like roughly:

1. Two forces, 80N and 100N, acting at an angle of 60deg with each other, pull on an object. a) what single force would replace the two forces? r^2=(x^2 + y^2)^2 , sinΘ, cosΘThe Attempt at a Solution I actually got the correct answer by using an angle of 0 degrees for 80N and 60 degrees for...

Homework Statement A train slows down as it rounds a sharp horizontal turn, slowing from 90 km/h to 50 km/h in the 15 s that it takes to round the bend. The radius of the curve is 150 m. Compute the total acceleration at the moment the train speed reaches 50 km/h Homework Equations a =...

If a rapidly rotating gyroscope attached to a perch is released in a horizontal position -- that is, so that the axis of the gyroscope is horizontal -- the gyroscope will precess around it's perch. Let L represent its angular momentum. Let dL represent a small change in that momentum. Let dA...

Homework Statement A bob of mass m is suspended from the ceiling of a train moving with an acceleration g/√3 (a) If an observer is sitting inside the train, what angle with the vertical will he observe? (b) If an observer is standing on the platform, what angle will he observe? Homework...

I said stay the same, the definition of co efficient is here http://simple.wikipedia.org/wiki/Coefficient_of_friction but the main part i saw not only here was "The coefficient of friction is dimensionless, meaning it does not have any units. It is a...

1. Problem Statement: Consider the scattering of an alpha particle from the positively charged part of the Thomson plum-pudding model. Let the kinetic energy of the α particle be K (nonrelativistic) and let the atomic radius be R. (a) Assuming that the maximum transverse Coulomb force acts on...

Homework Statement "Show that particles hitting a plane boundary have traveled a distance 2λ/3 perpendicular to the plane since their last collision, on average."Homework Equations (Root mean path squared) <x> = 2^(.5)λ λ = ( 2^(.5) * n * sigma )^(-1) ANSWER: The Attempt at a Solution...

Homework Statement Assume two stars are in circular orbit around a mutual center of mass and are separated by d = a. Assume angle of inclination is i and stellar radii are r1 and r2. Find an expression for the smallest angle of inclination that will just barely produce an eclipse. Homework...

If I had a block that I pushed with a force F along a horizontal path and then removed the force before an incline, would the angle of the incline matter on how far above the ground the block would travel? I am assuming a frictionless surface.

My understanding is that the seasonal variation in temperature, amongst many other things, is a reflection of the Earth's tilt. Simply put, at the equator, sun rays fall "straight down" (100% vertical), and all of their energy hits the surface of the Earth. At different latitudes, these rays...

I've attached an image of part a of the question to this thread. My question is this (the solution to these former homework problems are posted to help us study for exam, which is why know this already): The angle between the two velocity vectors is determined to be pi/2. How? I know that dot...

At first this sounds like a very popular and often asked/solved question but it has a twist - I need help with the twist please. 1. Homework Statement A cannon is at Point A in a 3d environment. There is a wall at Point B which sits between the cannon and a castle, at Point C. Write a...

Homework Statement Please see attachment for circuit and parameters. Homework Equations i --> 90 phase angle for inductor so Z of inductor = 0.5<90 sum of voltages = 0 #<40 = #*cos(40) + i*sin(40)*# The Attempt at a Solution shteii01 - 100 + 0.5<90 + V2<theta = 0 --> 100 + 0.5*cos(90) +...

What is the notation for the angular distance traveled by an object moving in circular motion? s is for regular distance (m,ft,inches, etc.). What I want is some x to be the distance in either degrees or radians. How should I call that x?

Homework Statement An inductive load is connected to a 120V (rms), 60Hz AC source. The load draws 5.0 kW at a power factor of 0.81 (lagging). You need to improve your power factor to 0.96 (lagging) by adding a capacitor. What is the Capacitance needed (in uF)? Homework Equations P/|S| =...

Homework Statement A stone is thrown horizontally from the top of a 20-m high hill. It strikes the ground at an angle of 45◦ . With what speed was it thrown? Homework Equations g=9.8 projectile motion is symmetric The Attempt at a Solution I got the answer 277.539 by treating this is a...

Homework Statement a) Particle A decays at rest into two photons. Calculate, in terms of the rest mass of A, the energy and momentum of each photon. b) In a different reference frame, particle A is initially in motion such that its kinetic energy is equal to its rest energy. Find the momentum...

Homework Statement Suppose a solid body approaches a sphere of radius one and height z, how do I calculate the angle ##\theta## at which the body bounces off the sphere? An image is attached: Homework Equations Angle of incidence, reflection and velocityThe Attempt at a Solution I was...

Homework Statement Light consisting of a mixture of red and blue light enters a 40°, 70°, 70° prism along a line parallel to the side opposite the 40° vertex. The index of refraction of the prism material for blue light is 1.530, and for red light it is 1.525. What is the angle between the two...

How would I go about creating something like a hatch, that could be arrested at any instance. I am looking for a solution for a 0-90, 90-180, and 0-180 degree range. A 360 degree solution such as a whiteboard, would work just as well. If you know how this can be made, or know a link that...

I need to calculate the angle of a rigid body under constant angular velocity as a function of time. The RPM of the body is known, so the angular velocity is ω=2πf. Therefore θ=ωt=[RPM]2πt/60. How can I calculate the angle so that it 'resets' after a full rotation?

Homework Statement So we have a force of unknown magnitude acting on these struts at an angle θ measured from strut AB. The component of the force acting along AB is 600lb, and the magnitude of the force acting along BC is 500lb. If Φ = 60°, what is the magnitude of F and the angle θ...

I am trying to write a java code where the user inputs the height at which a solid body approaches a sphere of radius R and outputs the angle ##\theta## at which the body bounces off the sphere. I have all my code written is just that I don't know how to derive the equation that calculates the...

Which will produce consistently faster lap times, when landing a 4 wheel drive race car at speed: - front wheels first - rear wheels first - front and back simultaneously Given a 4 wheel drive race vehicle traveling at racing speed, suspended in the air, after driving off a jump or drop off...

Homework Statement If c = |a|b + |b|a, where a, b, and c are all nonzero vectors, show that c bisects the angle between a and b. Homework Equations Angle between a & b is cos-1(a dot b)/(|a||b|) Angle between a & c is cos-1(a dot c)/(|a||c|) Angle AC is half of angle AB The Attempt at a...

Homework Statement Find the values of x such that the angle between the vectors <2, 1, -1>, and <1, x, 0> is 45 degrees. Homework Equations <2, 1, -1> dot <1, x, 0> = 2 + x |first vector| = (6)0.5 |2nd vector| = (1 + x2)1/2 Angle = cos-1(a dot b)/(|a||b|) Cosine of 45 is the root of two...

Homework Statement A heavy uniform cylindrical drum is placed, with its axis horizontal, on a slope inclined at an angle α to the horizontal. It is prevented from sliding or rolling down the slope by a triangular wedge. The weight of the wedge is negligible compared with the weight of the drum...

Homework Statement Find the slope of the tangent line to the give polar curve at the point specified by the value of theta R = 1/θ, θ = π Homework Equations Slope of a polar equation is (dR/dθsinθ+Rcosθ/dR/dθcosθ-Rsinθ) The Attempt at a Solution Using my calculator, I plugged π for θ, -.101...

Homework Statement Two Forces are acting concurrently and their resultant is 500 N as shown in figure on the right. Determine P and the angle P makes with the x-axis? 2. The attempt at a solution Is my answer correct?[/B]

I am trying to symbolically resolve the angle of rope that suspends a load (rectangle) between two pulleys given the length of rope that is let out over the pulleys. See attached image. the load is not intended to move horizontally, only vertically. so you can imagine each pulley must have an...

Homework Statement Find the angle that makes with the positive x axis: (Consider vectors above the x-axis to make positive angles and vectors below the x-axis to make negative angles.) Homework Equations pheta = arctan (Ex/Ey) tan(pheta) = Ex/Ey The Attempt at a Solution I already found that...