Velocity Definition and 1000 Threads

In this question, the particles are constantly transmitting their momentum to the rocket. The force required to keep the rocket stable can be express as ##\vec F=(\vec v-\vec u)\dot m##. However, when I tried to solve this question using the Newton's 2nd law, I found that the infinitesimal...

Why the velocity in spherical coordinates equal to ## v^2 = v \dot{} v = \dot{r}^2 + \dot{r}^2\dot{\theta}^2## maybe ## v^2 = v \dot{} v = (\hat{ \theta } \dot{ \theta } r +\hat{r} \dot{r} + \hat{ \phi } \dot{\phi } r \sin{ \theta}) \dot{} (\hat{ \theta } \dot{ \theta } r +\hat{r} \dot{r} +...

Let the vertex of the cone be ##O##, the contact point on the cone all the way to the right be ##D## touching ground. Then ##v_{\text{D relative to the table}} = v_{D/table} =0## since it rolls without slipping. Due to relative motion $$\vec v_{P/table} = \vec v_{P/D} + \vec v_{D/table} = \vec...

I have some troubles with this relatively simple problem My idea was to find the acceleration by F = ma and then integrate the graph and then find the velocity to t = 10 s + start velocity The graph will be - 2x And integrated -x¨^2 But this seems wrong Thanks in regards

I'm a parent and have no idea, just looking for help please

this expression : ##a(t) = −ω^2 (C_1 \cos θ + C_2 \sin θ)## I´ve never seen it before, where is it from? It kinda looks like centripetal acceleration, but what exactly are ##C_1## and ##C_2##? Can we calculate its velocity and position? If I´ve got two initial conditions ##x(0)=x_0## and...

The Wikipedia page for angular velocity makes a big fuss over "spin" and "orbital" angular velocities, but I have checked through Gregory and Morin's textbooks on classical mechanics and haven't found any reference to them at all. They just work with a single quantity, the angular velocity...

Say that all the engines of a boeing 737 failed while it was 12.496km in the air and fell into freefall, what would its terminal velocity be and how long would it take to hit the ground

This problem was from the chapter on Work and Energy so, I thought of using the principle of conservation of mechanical energy. Clearly, the potential energy of the block decreases by mgh (assuming the block has mass m). This energy should have been converted to kinetic energy, but it clearly...

Question 1: A pendulum 2.2m long has a mass of 8.5kg suspended from it. The pendulum is initially in a vertical position and is moved to new position 35 degrees from the vertical. (a) How much work is required to move the pendulum to its new position? (b) If the pendulum swings from this...

Someone know how to derive v = √(T/μ) for waves traveling? (without being by dimensional analyse)

Hello, I have completed the question below. I am just unsure on whether i am correct or not. I am unsure on Mechanical Advantage. As i have seen a few different equations. Question: Answer: a) Velocity Ratio = $$\frac{\text{Distance Moved By Effort}}{\text{Distance Moved By Load}}$$...

At time t=0 , a car moving along the + x -axis passes through x=0 with a constant velocity of magnitude v0 . At some time later, t1 , it starts to slow down. The acceleration of the car as a function of time is given by: a(t)= 0 0≤t≤t1 -c(t−t1) t1<t2 where c is a positive constants in...

Good Morning When we derive the Euler Lagrange equations using Hamilton's Principle, we make a point of varying the velocity and the position at the same time, (despite the fact that, normally, they are related through a derivative). I do understand that this is allowed: we are trying to find...

My solutions (attempts) : a> w=v/r | r=6.35x10^6m | therefore V=7.04x10^-5 m/s b> speed of rotation is faster at the equator than the pole as w=v/r. As w remains constant, as r increases towards the pole V has to decrease. c> F = W - R d> Stuck here. I presume that I have to use the equation...

Angular velocity is the degrees by which something rotates over a time period. If I have an angular velocity in one direction and I resolve it into its components, its components would obviously be of lesser value. Here's what I don't get. When I imagine this scenario, I see that the thing...

Could I please ask for any help with the following question: Here's my attempt: (i and j are unit vectors in the directions of east and north respectively) (apologies that LaTeX is simply not working for me, I'll label the angles in each case T and P as shown in my diagram) Let the...

Answers are the following : (i) v=(2cost)i - (2sint)j -(1/2)k (ii)2.06m/s (iii)2m/s^2 horizontally towards the vertical axis, making an angle of pi/4 with both the I and j axes.

Further given: - every beam is infinite stiff - pulleys are massless - cables don't stretch, no slip, and frictionless. -Every pulley has a diameter D except pulley Q. Pulley Q has diameter 0.5*D So what I don't understand is how to calculate/determine the velocity at R and S. Can someone help...

In graphene system, the velocity operator sometimes is v= ∂H/ħ∂p, and its matrix element is calculated as <ψ|v|ψ>, i.e., v_x = v_F cos(θ) and v_y = v_F sin(θ) [the results are the same with Eq. 25] for intraband velocity. Recently, I see a new way to calculate the velocity matrix (Mikhailov...

When calculating the dV available from a rocket booster, the below calculation is used: (ISP . g) . ln(Mass when full/Mass when empty) Is 'g' always equal to 9.81 in this equation, or do you use the actual gravitational acceleration that the booster will experience, at it's given altitude, to...

I'm reading a text on special relativity (Core Principles of Special and General Relativity), in which we start with the equation for composition of velocities in non-standard configuration. Frame ##S'## velocity w.r.t. ##S## is ##\vec v##, and the velocity of some particle in ##S'## is ##\vec...

Top example- How do I get to 31.7 m/s from 30.8 and 7.7? This is way over my head and need help. Thanks in advance Dean

This question came in NEET Exam 2018.Now my first query is that in the question,the mass of one Oxygen molecule is given wrong.Its exactly half it's true value.I don't think anybody has noticed this before because I couldn't find any change in the printed question on so many different books...

Below are equations/formulas/text from https://en.wikipedia.org/wiki/Schwarzschild_geodesics https://hepweb.ucsd.edu/ph110b/110b_notes/node75.html I apologize for not remembering the source for the "v=" equation, or for my inability to find it again. For a circular orbit, the distance r and...

I think i could deal with this problem interpreting this force like a central force, what seems pretty nice to me, since in a circular orbit the force will always pass through the center, if it is perpendicular to the velocity. I thought, since the force is central and in this case, spherically...

I thought in this equations f is the man's pull\ f + dm*g = T < 600 Where dm is equal to the mass of the string that pull the up part (15-x) after descending x meters. dm/(15-x) = m/15 And, to the man: W - f = Mx'' I can solve this, and i got ~8m/s Is this right?

Solution on the link: https://www.slader.com/textbook/9780321675460-university-physics-13th-edition/269/exercises/12/

So I understand that time is now part of the four vector, and so dividing delta X by delta t (time according to me), would produce just c as the first dimension of the vector, which gives us no intuition as to how fast time is moving for the observer, so is not useful. I understand why we...

A Problem is posed for a flight from Melbourne to Cairns. Using the formula for rotational speed at latitude - 1) The latitude of Melbourne is approx 38 degrees south with a rotation velocity of 820 miles/hr 2) The latitude of Cairns is approx 17 degrees south with a rotation velocity of 994...

Hello : as i read during quarantine introduction to elementary particles by griffth i encounter the following paragraph "When we speak of the "velocity" of a particle (with respect to the labo- ratory), we mean, of course, the distance it travels (measured in the lab frame) divided by the...

I was studying how to derive the cross-section formula in the CoM frame from Mandl & Shaw QFT's book, and they state the following formula for the relative velocity (I'm going to use Vanhees71's notation though) $$\omega_1 \omega_2 v_{rel} = [(p_1 p_2)^2 - m_1^2 m_2^2]^{1/2} \ \ \ \ (2)$$ Then...

If you derive the equation for orbital velocity you get \begin{equation} v_{orbit} = \sqrt{\frac{GM}{R}} \end{equation} and for escape velocity you get \begin{equation} v_{escape} = \sqrt{\frac{2GM}{R}}=\sqrt{2}\,v_{orbit} \end{equation} I'm wondering if there is a logical/geometrical...

I first calculated initial velocity: √7.09^2+1.07^2=7.17028 acceleration=√7.22^2+2.47^2= 7.63 then i substituted all values into this equation: final velocity=initial velocity + acceleration x time so, final velocity=82.0285 so the magnitude= final velocity-initial velocity= 74.858271 is...

I first calculated the velocity v: √2.8^2+6.3^2= 6.8942 then i used it as the final velocity, so final velocity=6.8942 and the initial velocity=0 acceleration=9.8 Then i substituted them into this equation: final velocity=initial velocity + accelerationxtime then time=0.703489843 hence i...

I do not understand part b. I know that x180/pi changes the value into a degree, but i do not understand what's going on inside the bracket. And how did the equation calculated the direction?

This is the graph I was given and the answer options. Since the graph is a straight line moving towards the positive direction I thought that meant it was traveling at a constant speed moving in the positive direction. That ended up being the wrong answer. Can anyone offer insight, I missed each...

My answers: a) At points d the instantaneous velocity should be greatest since slope of c-d is greatest I think b) At point e and g instantaneous velocity is 0 c) at points b, c, and f instantaneous velocity is negative. Could you please verify my answers?

Hello, I wrote a program that adds force to a car like so: Engine Force = Power / Velocity Drag Force = -Velocity² Net Force = Engine Force - Drag Force = Power / Velocity - Velocity² I'd like to determine power based on how fast I want a car of a given mass to reach a given speed, for...

This isn't right, is it? -\dfrac{GM}{R}+\dfrac12 v^2=-\dfrac{GM}{R+h} v=\sqrt{\dfrac{GM}{R}}\left( 1-\sqrt{\dfrac{R}{R+h}}\right) He's doing energy conservation. The mechanical energy at the Earth's surface is equal to the energy when the speed is 0.

For: a) Avdol did the work because he is the force that is causing the displacement, right? b) Is there another formula we would have to use? I am confused at how this would work out and what the answer would be.

We have 2 different formulas for escape velocity. and . If we look at the first formula we see that escape velocity is inversely proportional to the square root of Radius of Earth. While in the second formula, escape velocity is directly proportional to the square root of Radius of Earth. We...

θ=90°= π /2 so the instantaneous angular velocity dθ/dt= lim∆ t -> 0 (θ(t + ∆ t)-θ(t))/(∆ t) When I calculate it out it is π /2 radians per second. Is this correct?

Below is the work I've attempted. I used 2 PE b'c there were 2 point charges, and only one KE b'c only the proton is moving. The final equation in case it's hard to see is V(esc) = sqrt (4kQq / mr). I'm not sure if I did it right. Did I set up this equation right? and I am also not sure what...

Hello everyone, I have a problem where I have to find the final displacement and final velocity which I have found however, I want to post few variations for that same problem which I am curious. It is more for my own knowledge > I would appreciate any help Please follow graph below with...

To simulate the trayectories of solar systems around a black hole (i.e. a galaxy) I have 3 classes in C++: cSystem, cBlackHole and cGalaxy. cSystem assigns initial values of position, velocity, etc to a solar system. cBlackHole does the same but just for the black hole. And cGalaxy mixes...

The Wikipedia article on Lorentz transformations is a bit confusing by its using speed and velocity almost interchangeably: of course γ (Gamma) stays the same, but (letting c=1) t'=γ(t-vx) , then if this is v⋅x, and x stays the same, then there would be a difference if something were going away...

I know that taking the scalar product of the harmonic (Laplacian) friction term with ##\underline u## is $$\underline u \cdot [\nabla \cdot(A\nabla \underline u)] = \nabla \cdot (\underline u A \nabla \underline u) - A (\nabla \underline u )^2 $$ where ##\underline u = (u,v)## and ##A## is a...

Hi all, I can't find a single thing online that translates a cartesian velocity vector directly to spherical vector coordinate system. If I am given a cartesian point in space with a cartesian vector velocity and I want to convert it straight to spherical coordinates without the extra steps of...