Angle Definition and 1000 Threads

Problem Statement : The statement of the problem again. If ##\tan\dfrac{\theta}{2}=\sqrt{\dfrac{1-e}{1+e}}\tan\dfrac{\phi}{2}##, prove ##\boldsymbol{\cos\phi=\dfrac{\cos\theta-e}{1-e\cos\theta}}##. Attempt : Transposing and squaring what's given, we get...

I can't understand what is going on here. My intuition tells me that the traction pulling on the block should be equal to F. Apparently, however, the problem would have me believe that this is not the case, as it gives me a 30° angle at which the force acts and a 6-8-10 triangle as ways to...

TL;DR Summary: A 10-kW engine drives a solid round steel shaft 1 m long by means of a V belt and pulley at the midpoint of the shaft. At one end of the shaft 7 kW is removed and at the other end 3 kW is removed. The shaft diameter is 15 mm and it operates at 1000 rpm. Assuming that no power is...

y'(t)/x'(t) = cos t/-sin t = -cot t. But as t is the angle, and the derivative is the slope, then isn't the slope supposed to be tan t?

I'm trying to draw a file for a plate that will sit on a piece of 6inch tubing at an angle. I can't quite get the radius right. I've tried R=(.5mM)÷square root of (m squared + M sqaured) m=minor diameter M=major diameter And I've tried R=(H÷2)+(W squared ÷ 8H) H= height of arc W=width of arc...

I've been doing astronomy for Science Olympiad for a few years now and know all the basics about DSOs, HR diagrams, etc. However, I've only recently acquired a telescope since I thought it would be nice to locate some DSOs independently. I understand how RA and D are calculated, but I am not...

I apologize if this is a stupid question but how come we can't just say that for part (a) v_A = -v_1 j hat, and for (b) v_A=v2 sintheta i hat + (-v1-v2cos theta) j hat? i.e. how come we can't just do vector decomposition "normally"? I am especially confused about the given solution in (a) where...

Since I understood that torque = net moment, and as it said angle from the vertical, I used the equation t = F*d*cosx. So, 6 = 40*0.4*cosx, x = 68 degrees. I got a zero out of 5 in this question because the thought process was wrong as well as the answer. I do not understand this problem beyond...

I have tried to use the projectile motion to find Vx and Vy, however since the angle isn't given, I don't think this problem can be solved with only motion formulas (I did solve it with energy formulas).

My final result was $$\tau = IBR\sin{\theta} \int_{0}^{2\pi} {\frac{\sqrt{1+\sin^2{\theta}\cos^2{\gamma}}}{\sqrt{1+\sin^2{\theta}\cos^2{\gamma}}}d\gamma}$$. I think I am supposed to get a simple answer like $$\tau = \vec{\mu} \times \vec{B}$$ where mu=IA. If I take approximations using the...

In geometry, there is a theorem pertaining to whether given an angle, side, and side gives 0, 1, or 2 triangles. See figure. In the figure, if x = 10sin(30) then there is exactly 1 triangle, if x > 10sin(30) then 2 triangles if x < 10sin(30) then no triangles. I think this has a theorem name or...

A few months ago, our teacher gave us a problem regarding cylinder motion. He asked us to calculate the acceleration of a cylinder that's acted upon by a force F at an angle theta due to the x axis. Now, for some reason, he told us that the cylinder would rotate. Now, I'm not sure if he supposed...

Question; My take, I have, then using sine rule; ##\dfrac{x}{x+y} = \dfrac{\sin 20^{\circ}}{\sin 80^{\circ}}## ##\dfrac{x}{x+y} =0.347## ##x=3.47## then ##y=6.53##. then, ##BD^2=3.47^2+10^2-(2×3.47×10×\cos 20^{\circ})## ##BD= 6.842## ... ##10^2=3.47^2+6.842^2-(2×3.47×6.842 ×\cos...

Why are the axes taken as perpendicular to each other rather than at some other angle? Is it just a matter of convention? Is there any mathematical reason behind it? Is there some other reason?

I understand why certain inverse trig functions have two answers. Like for arcsin(0.5), it could be pi/6 or 5pi/6. I know both angles have the same sin value, that they're both on the same horizontal line on a graph of sin, I get all of that, but two questions about it: 1) In cases where...

I tried posting this on the physicsstackexchange, but wasn't making any progress in understanding what's going on. Suppose the axes in two coordinate systems S, S' are parallel. Now, suppose I rotate S through some angle ##\theta## and also rotate S' through the same angle ##\theta## It's not...

Attempt one: 1sin(35.8) = n2sin(90) n2=0.58 1.33sin(𝜃)=0.58sin(90) 𝜃_c=25.8 Attempt two: n1=n2/sin𝜃_c n1=1/sin(35.8) n1 = 1.7 sin𝜃_c = 1.33 / 1.7 𝜃_c = 51.57

I also tried to solve for T when the centripetal force is equal to the tension in the x-dir, but I got 2.174s and that's not the right answer either. I'm not sure what I'm doing wrong exactly.

I was just wondering if I needed to set up this double integral or not. I've never seen anywhere people setting up double integrals for calculating the work.

A ball is thrown with an initial speed vi at an angle 𝜃i with the horizontal. The horizontal range of the ball is R, and the ball reaches a maximum height R/8. In terms of R and g, find the following. (a) the time interval during which the ball is in motion: Sroot(R/g) Correct (b) the ball's...

My take, ##5 \cos 0 = 10 \cos θ## ##\cos θ = 0.5## ##⇒θ = 60^0## and ##X= 10 \cos (90^0-θ)=\cos 30^0= 8.66## (to two decimal places). ...insight welcome

I'm doing special relativity in undergrad and I have the following problem: Let a particle of mass M travelling at speed ##\beta = 1/2## (##\gamma = 2/\sqrt 3 \ \ c=1##) decay in to two photons: ##A \rightarrow 1+2## 1) Calculate energy and moment of the photons in the reference frame of the...

Is angle Vag 180 since the vector is a straight line pointing left? Also you can add 30 degrees with 150 which will be 180?

I've been told that the infinitesimal change in coordinates x and y as you rotate along a hyperbola that fits the equation b(dy)^2-a(dx)^2=r takes the form δx=bwy and δy=awx, where w is a function of the angle of rotation (I'm pretty sure it's something like sinh(theta) but it wasn't clarified...

Hi, so I have no clue how to solve this problem but I started off by rewriting the issue as a dot product to find the angle. So; cos(θ)= RSC⋅RSun / ∣RSC∣⋅∣RSun∣ Where Rsc = space crafts position vector. Rsun is the Suns position vector. ∣RSC∣ is the length of the spacecrafts position...

I can't find the angle between F(Big arrow in my drawing) and the y-axis! I am terrible in geometry, what book do you suggest to me as Mechanical Engineer to get better at geometry?? This is my attempt to solution and the figure:

Why it said that angle between r and F is 30? I guess it should be 120 degrees... Am I wrong?

I have been taught that in order to find the angle made by a liquid in a container with the horizontal, we use the fact that the free surface is perpendicular to the net force vector acting on the fluid (including the pseudo force vector for an accelerating container), however, if say the...

The above question is adopted from the exercise of Preskill's quantum information lecture note My attempt: (a) From the condition, ## p(\theta)\propto \sin^{(2N-4)}\theta \cos\theta ##. Normalizing the probability distribution would give the answer. This is because the weight of the phase of...

My take: I got ##BC=10.25## cm, using cosine rule...no issue there. For part (b) ##BK=3cm## using sine rule i.e ##\sin 30^0 =\dfrac{BK}{6}## Thus it follows that ##∠BDK=48.59^0## ...⇒##∠ADB=131.4^0## correct...any other approach? Also: ##∠ADB=48.59^0## when BD is on the other side of the...

Hello. For a project I am working on I need to draw a template of a "curve of intersection" of a plane (B) intersecting a cylinder at a "compound angle".. I do not know the correct terminology so I added a sketch of what I wish to achieve. If it is not understandable please say so and I will...

Good morning , I managed to simplify the physics of my car with only the centrifugal and traction forces. If I'm in control of it, the realism is acceptable for a city builder. On the other hand, I encounter a problem when the car follows an array of points. The path of the car on my graph...

I don't know the correct works search to find this info online. I have been doing word searches since about Dec 15, 2022 but not finding what I want.??????? Some where there much be a chart by date and zip code for sun angle. I built a sun dial in the yard to learn the angle of the sun on...

Vix=Vcosθ Vix=0.76604*V Xf=Vixt Xf=0.77604V*2 V=Xf/1.55208

so far i think Ip = 10 f = 1000hz struggling with the phase angle

For this I am trying to prove that angle theta between PQ and QO is equal to theta highlighted so that I know I can use theta is the path difference formula. I assume that the rays ##r_1## and ##r_2## are parallel since ##L >> d## My proof gives that the two thetas are equal, however I am...

The data collected from the experiment is, The first column is the polarizer angle measured in degrees. The second column is recorded intensity measured in lux. The third column is the transmitted intensity measured in lux. This is equal to the recorded lux - ambient lux The fourth column is...

I'm assuming the boat is traveling north at an 8 m/s and the river is flowing east at a 2 m/s. For the boat to move in a straight line, it has to aim at an upstream angle given by #theta#. Using SOH CAH TOA, ##v_r = 2m/s##, ##v_b = 8m/s## $$\theta =\sin^{-1} \frac{v_r}{v_b}$$ $$\theta = 14...

My textbook introduces this angle concept really early on and I still don't understand it. It just shows that a normal to a line and some other random angle shown is the same. I don't see any transversal angles or anything. Where did they get the secondary line to form theta for the normal line?

For (c), Solution is Can someone please explain how they calculated that angle? I thought they would do ##arc\tan (\frac {32}{3.35})## Many thanks!

For this problem, The solution is, I don't understand how they got from ##\frac {sin^2\theta_i}{sin2\theta} ## to ##\frac{tan\theta_i}{2}##. Would somebody please show me the immediate steps? I also don't understand is why they say the ignore the trivial case where ##\theta_i = 0~rad##...

I saw this symbol in the statement: 'Effective CP-violating angle θ≅ (10-17). What does the highlighted symbol mean?

Ideally, it should look circa like this: But in reality, it looks often like this: Is the formula valid also in this case?

This is clear to me; i just wanted to know in which contexts is one allowed to use one rule over the other; or it does not matter. The angle i realise can also be found by; ##\sin θ = \dfrac{||v×w||}{||v||||w||}##=...

1.52cos(31)+Fbsin(Θb) = (0.305)(9.8) Fbsin(Θb) = 1.69 Now for horizontal direction: Fbcos(Θb) = FLsin(ΘL) cos(Θb) = FLsin(ΘL)/Fb cos(Θb) = (1.52 x sin31)/1.69 cosΘb=0.464 Θb = 62.35 I thought to find Fb I would just plug the Θb value into one of the trig functions, but apparently both of my...

i used t=d/v for the x direction using the formula t=250/vcos55 and subbed that into the formula for the y direction d = (v) (t) + (0.5) (a) (t)^2 35 = (vsin55) (250/vcos55) - (4.9) (250/vcos55)^2 canceled out the first two v 35 = sin55 (250/cos55) - (306250/v^2cos3025) 35 = 357 -...

Here's the full code: When a ball collides with bat or walls, I want the ball to be reflected with an angle, how do I do it? I suspect there's lots of physics to it. So, should I stop this project here? I'd have to probably build a part of game engine…Can anyone help here?

Statement figure: My attempt at a solution: FIGURE 1 ##\rightarrow A=a^2## CG ##\rightarrow \overline{x}=-a/2, y=-a/2## $$\overline{Ix}_1=\dfrac{bh^3}{12}=\overline{Iy}_1=\dfrac{a^4}{12}$$ $$Ix_1=\overline{Ix}_1+\overline{y}^2A=\dfrac{a^4}{12}+\dfrac{a^4}{4}=\dfrac13 a^4\...

so I was wondering. there is this normal force on the can from the path. And there's this formula to find the angle between the radial line and the tangent or also between the normal force and either the radial or theta axis. the formula is ##\psi = r/dr/d\theta##. The thing is that here they...