Classical mechanics Definition and 1000 Threads

I tried finding the potential due to a small element dM of the ring let's say dV, the summation of dV for all the dM's of the ring will give the potential at the point P, but since every element dM of the ring is at a different distance from the point P I am unable to come up with a differential...

the gravitational potential energy of a body at any point is defined to be negative of the work done by the conservative force(gravity in this case) from bringing it to that point from a given reference point. if the reference point is taken to be at infinity and the potential energy at this...

the point on the string at a distance r from the pivot is rotating in a circle of radius r and hence a centrifugal force of magnitude mw^2r can be said to act on it where m = (M/L)r . hence the T = centrifugal force T = (M/L)(wr)^2 but my book says otherwise. also can the string with mass be...

On page 41 for the spontaneous disintegration of a particle into two, Landau states the total momentum in the C system is zero. On page 43 for the disintegration of many particles into two, Landau states: In the C system... every resulting particle (of a given kind) has the same energy... I...

I know that I need to find the equation of the line of motion of the two particles, the dot product of which with one of the options will give 0. I began with founding the coordinates of center of mass: R = (m1r1+m2r2)/(m1+m2) = (2a/3, 0, a/3) and velocity of the center of mass: V =...

I am a layman with very little experience in math and physics and recently I became curious about how to analyze dampened oscillations occurring in fluid mediums, such as those following a disturbance in a pool of water. What sort of math and physics is required to understand this phenomenon and...

Suppose I have a perfectly circular pool which is four meters in radius, two meters in depth, and filled with water. Say I drop a steel ball with a radius of five centimeters into the middle of the pool from a height of five meters above the water's surface. After three seconds, what will be the...

The first part is easy, we have 2T= Mg T= 0.5 Mg Now for the second part where I'm having trouble understanding Morin's solution: I take the normal force on a small circle arc to be N, we know that the y component of the normal force must be balance with Mg for the whole disk, therefore Ny =...

Are there any lecture notes that closely follow Classical Mechanics by Goldstein? I am asking this since I am seeing some comments in this forum that it contains some conceptual errors, e.g. nonholonomic constraints. If there is a book that "closely" follows Goldstein, it will be good too.

This problem is hard. It found it listed among problems discussed in a classical mechanics course for physicists at the university of Pisa and don't have a full solution. It's not 100% guaranteed that there's a nice close-form solution, but probably yes; and if not, there should be some trick to...

Please critique this text. It came from a research article* I found but I'm only interested if the sentence is 100% accurate or not and not in the specifics of the article itself. Are they suggesting Hilbert space is always infinite? Thanks. Quantum mechanics is infinitely more complicated than...

I'm studying Ergodic Theory and I think I "got" the concept, but I need an example to verify it... Let's take the simplest possible 2D classical harmonic oscillator whose kinetic energy is $$T=\frac{\dot x^2}{2}+\frac{\dot y^2}{2}$$ and potential energy is $$U=\frac{ x^2}{2}+\frac{y^2}{2}$$...

Hi- So I have been studying physics for a long time, and I love most parts of it, but I have a love-hate relationship with classical mechanics. Every time I read my textbook I can work my way through it and it makes sense to me, but one or two days later I forget all the formulas I have...

We have a rod ##AB## of mass ##m##, a force (perpendicular to AB) is applied at ##A##. I want to know how much force will ##B## going to feel? When ##F_1## is applied at ##A## rod will rotate about its COM (which lies at the Center) and hence the point ##B## will also move (a little downwards...

Hi, I am confused by a point which should be relatively simple. When we consider classical motion of a particle in a central field U(r), we write the total energy E = T + U, where T is the kinetic energy. The kinetic energy contains initially r, r' and φ' (where ' denotes the time derivative)...

Summary:: Is there somebody can help me？ The book about Mechanics analysis or classical mechanics,if you have read some good books, please recommend them to me, I will be very grateful.

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.