Classical mechanics Definition and 1000 Threads

I chose coordinates where down is positive. So the force going up is $$F_{up} = mg - cv^2$$ $$a = g + \frac{c}{m}v^2$$ $$a = g + \frac{c}{m}v^2$$ $$a = g \left(1 + \frac{v^2}{v_t^2}\right)$$ $$a = \frac{dv}{dt} = v\frac{dv}{dy} = g \left(1 + \frac{v^2}{v_t^2}\right)$$ I used normal separation of...

Hi there, I am an undergrad 1st year student in Physics. I wanted to self study the classical mechanics so that i can get hold of some very important concepts before it begins to rush in our class. Can you suggest me a basic Classical Mechanics book of undergrad level that will help to learn...

There was an old thread comparing the difficulty of classical mechanics and electromagnetism. The consensus was that electromagnetism is more difficult, and substantially so according to some. The thread was no longer open for replies, but it got me suspecting that we're comparing apples to...

I'm a college freshman who might major in physics, but I'm still undecided. This semester, I registered for Classical Mechanics (intermediate, not introductory) but have lately reconsidering this. There are a few reasons for this: 1) I feel a little behind on math. I just started multivariable...

I know we can't use classical mechanics to describe or measure the quantum. That is not what I'm asking. I am asking whether particles still follow the same rules like action/reaction if there is a force involved. If electron A interacts with electron B, is Newton's 3rd law still being applied...

From what I understand, constraint forces do no work because they are perpendicular to the allowed virtual displacements of the system. However, if you consider an unbalanced Atwood machine, in which both masses are accelerating in opposite directions, you'll find that the tension force of the...

Greeting, I wanted some suggestion regarding classic and essential papers to read in Classical Mechanics. The first semester is over, and I want to expand upon what I have learnt. If there is some paper or topic in particular that you found interesting personally early on, it would be helpful. I...

I solved this question until the end of the "c)Find the distance until the boat completely stop" However I can not solve the integral I encounter in the solution of the last part of c). Would you please check for math and maybe my mistakes and tell me what to do? Here:

I believe I solved this. Is this solution true? Can please anyone just check?

Please help please

Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) ##r'##, ##v'## and ##a'## are the position, velocity and acceleration vectors, all relative to...

Lets do it for the left (the right will be similar): ##r_{left}=[(L-a\sin\theta)\sin\phi,(L+a\cos\theta)\cos\phi]## so ##v_{left}=[-a\dot{\theta}\cos\theta\sin\phi+(L-a\sin\theta)\dot{\phi}\cos\phi,-a\dot{\theta}\sin\theta\cos\phi-(L+a\cos\theta)\dot{\phi}\sin\phi]##. Is this right?

Alright my idea is that, in order to show that ##f_i(q_i, p_i)## is a constant of motion, it would suffice to show that the Hamiltonian is equal to a constant. Well, the Hamiltonian will be equal to a constant iff: $$f(q_1, q_2, ..., q_N, p_1, p_2,..., p_N) = \text{constant}$$ Which is what...

When calculating force due to surface tension across a hemispherical drop, we look at only the circumference and multiply it by the value of surface tension. When we know that it is the surface tension which is responsible for the curved surface of the liquid drop, why don't we calculate the...

I'm reading a book on Classical Mechanics (No Nonsense Classical Mechanics) and one particular section has me a bit puzzled. The author is using the Euler-Lagrange equation to calculate the equation of motion for a system which has the Lagrangian shown in figure 1. The process can be seen in...

Some information Newton's second law in a non-inertial frame is given by: Where: 1) ##A## is the translational acceleration, ##\Omega## the angular velocity and ##\dot \Omega## the angular acceleration (all relative to the inertial frame attached to the ground ##F##). 2) r', v' and a' are...

In the given problem, i can understand that after placing the two blocks in equilibrium it oscillates with an amplitude of The answer for (b) is given as To my knowledge, m2 separate from m1 when the acceleration is greater than gsinø and so they should be separating only at max displacement...

I know four different forms in which an SHM can be represented after solving the differential and taking the superposition acos(wt+Ø) asin(wt+Ø) acos(wt-Ø) asin(wt-Ø) where a- amplitude In the above image they took B as negative in order to arrive at acos(wt+e). If i already knew i wanted...

Exercise statement: Given the action (note ##G_{ab}## is a symmetric matrix, i.e. ##G_{ba} = G_{ab}##): $$S = \int dt \Big( \sum_{ab} G_{ab} \dot q^a\dot q^b-V(q)\Big)$$ Show (using Euler Lagrange's equation) that the following equation holds: $$\ddot q^d +...

So the Bernoulli's Equation.. My question : Are the terms on the left hand side equal to the total mechanical energy? So can I rewrite this equation as ?

I'm stuck from the beginning. I though I understood the difference between ## \delta## and ##d##, but apparently I was wrong, because I don't know how to exploit it here... Any hint would be greatly appreciated Thank Ric

For the first part, I considered the Force acting on it by all charges as given by $$\vec {F} = \Sigma_{j} \frac{m_{i} m_{j}}{\left(r_j - r_i \right)^{1.5}} \vec{r_j} - \vec {r_i} = \Sigma_j m_i \vec {g_j} $$ Where ##\vec{g_{j}}## represents gravitational acceleration of ##m_i## due to jth mass...

What types of math should a student be comfortable with going into a classical mechanics class at the level of Landau and Lifshitz? And are there any additional types of math that aren’t required, per se, but would be beneficial to know (for said course)?

Hi! So this is my first homework ever of Hamiltonian dynamics and I am struggling with the understanding of the most basic concepts. My lecturer is following Saletan's and Deriglazov's and from what I have read and from my lectures, this is what I think I know. Please let me know if this is...

I thought it would be a good idea to pretend that the walls are stationary and that each time the particle hits a wall, it gets a velocity addition of the velocity of the wall it’s hitting. Using this I ended up at the formula V = initial velocity of particle + n(velocity of left wall) +...

Hello, First time poster. I have taught High School Physics courses for 5 years now. I am interested in teaching it out of the typical order of Kinematics then Dynamics. This will be for next year if I go through with any changes. I am interested teaching the beginning more like this...

Why is the gravitational potential energy of the chain's center of mass equal to the total kinetic energy of the disc after it was fully wrapped? My first thought was to write ##E_{0}=(M/2+M)g∗2πR=E_{f}= Ep## (from the chain) ##+Ec## (from the disc). Instead he wrote ## mg \frac{l}{2} ## = ##...

Source = John R. Taylor, Classical Mechanics, page 651 + page 677 Trying to solve, A mass m is thrown from the origin at t=0 with initial three momentum p_0 in the y direction. If it is subject to a constant force F_0 in the x direction, find its velocity \mathbf{v} as a function of t, and by...

In page 49, chap 8 of the book "classical mechanics point particles and relativity" of Greiner, there is the following sentence: "In order to become independent of the coordinate frame, a set of orthogonal unit vectors is put at the point of the trajectory of the mass point given by ##s##."...

I've taken intro to classical mechanics, but am really not sure about how this example calculates the friction force and the normal force...I usually break down the force vector into components, and I understand that this is probably a much more simple way to calculate the perpendicular and...

Hello, I am confused between the two books. I am looking for a text that would provide sufficient theoretical insight into the topics and provide a good set of problems that would help me understand the topic well enough. What would be your suggestion? PS- Taking a cursory look at both the...

Let's say we are in outer space.Suppose I have 2 metallic balls A and B with initial velocity 0 and same mass M and a baseball bat.Let's say I hit the ball A with force F and ball B with F' in such a way that F>F'.Ball A attain final velocity V in time T and ball B attain final velocity V' in...

I have tried using Conservation of Energy but I'm getting incorrect answer.

The final answer should have a negative b^2⋅r(dot)^2⋅r term but I have no idea how that term would become negative. Also I know for a fact that my Lagrangian is correct.

I start out by substituting rcos(Θ) and rsin(Θ) for x and y respectively. This gives me z=(b/2)r^2. The Lagrangian of this system is (1/2)m(rdot^2+r^2⋅Θdot^2+zdot^2)-mgz. (rdot and such is the time derivative of said variable). I then find the time derivative of z, giving me zdot=br⋅rdot and...

The first force components: Fx = ax + by², Fy = az + 2bxy, Fz = ay + bz² I calculated the integral V=-∫Fdr, using dr=(dx,dy,dz) The result I found was -(1/2(ax²)+2azy+2bxy²+1/3bz³) The answer in the book (Kibble's Classical Mechanics): -(1/2(ax²)+azy+bxy²+1/3bz³)The second force: Fr = 2ar sin θ...

Hi. There is a worked example in this book on P168-169 titled "Chain on a scale". Two different ways of obtaining the solution are shown. I am confused about the 2 different methods. Method 1 equates the rate of change of momentum of the chain to the net force on the chain giving F. Method 2...

Probability density function plays fundamental role in qunatum mechanics. I wanted to ask if there is any analogous density function in classical mechanics. Obviously if we solve Hamilton equations we get fully deterministic trajectory. But it should be possible to find function which shows...

Hi, I hope I am in the right section of the forum. I was trying to understand the following algorithm: https://benchmarksgame-team.pages.debian.net/benchmarksgame/program/nbody-python3-1.html and particulary this part: def advance(dt, n, bodies=SYSTEM, pairs=PAIRS): for i in range(n)...

There is a cornering maneuver in rallying called the "Scandinavian flick" or the "pendulum turn". It involves steering away from the corner before actually steering into the corner. This creates a pendulum effect which makes the car turn more sharply into the corner. Sorry for the poor video...

Hey, I solved a problem about a double pendulum and got 2 euler-lagrange equations: 1) x''+y''+g/r*x=0 2) x''+y'' +g/r*y=0 (where x is actually a tetha and y=phi) the '' stand for the 2nd derivation after t, so you can see the basic harmonic oscillator equation with a term x'' or y'' that...

In the Classical Dynamics of Particles and Systems book, 5th Edition, by Stephen T. Thornton and Jerry B. Marion, page 220, the author derived Equation (6.67) from Equation (6.66) which is the following: Equation (6.67): $$\left(\frac{\partial f}{\partial y} − \ \frac{d}{dx}\frac{\partial...

What exactly is this equation telling me? How can I use it to work out the Equations of Motion given an equation of potential energy? Won't I have to solve a PDE? I'm extremely sorry if this question comes off ignorant.

1st page of Chapter 7, p.276, very last line, p=p'. I get that in Newtonian mechanics, the forces, times and masses are the same in two different inertial reference frames, but shouldn't the momenta measured be different?

Lets neglect conservation of momentum and assume that all frames of reference are inertial. Now imagine three objects: the sun, the Earth and an asteroid. In the inertial frame of the sun, Earth and asteroid are flying towards each other ( velocitys v and -v). Now imagine you are standing at...

I just finished the intro physics sequence at my college, and I wanted to work through the Feyman lecture Vol.1, with the workbook, over the summer. Does anyone know of any sample curriculum used for this book? Or perhaps, knows a good way to work through the book?

I first found ##v_{B}## by ##E_{p,A,B} = mgh_{1} = E_{c, B} = \frac{1}{2}mv_{B}^2 \therefore v_{B} = \sqrt{2gh_{1}} ## After this I made several failed attempts basically trying to find its final velocity so I could use conservation of energy. Spliting the velocity into its components never...

Why is Kinetic energy a scalar quantity? I read in an article, it said, when the velocity is squared, it is not a vector quantity anymore. Can someone fill in the gaps for me? I can't quite get what that article said. And I would be pleased if you provide some other examples other than kinetic...

Homework Statement A drop of water fall towards the ground with initial mass [m][/0] and radius [r][/0] (assume the initial shape of that water drop is sphere). the air resistance is F=½.ρ.A.[v][/2].C (C is the drag coefficent, A is the area that the air contact with the water drop and ρ is the...