Classical mechanics Definition and 1000 Threads

I composed a problem and propose it here. I know the solution so it just for fun of the participants. There is a cylindrical bobbin of radius ##r##; the bobbin rotates about its central axis with angular velocity ##\omega=const>0##. An inextensible weightless string is coiled around the...

Hi All, What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum...

Is there any deep reason behind this? per example the principle of least action or something else?

How can I derive that the work of a force perpendicular to velocity is always zero from the theorem of Noether? I have heard that there is a relation between these two but in Google I found nothing. Thank you very much

Classical mechanics: a minimal standard course by Sergei Winitzki. It is not probably going to help you if you already did not know the subject but is a great refresher nonetheless. He also includes a differential equations refresher that I found invaluable. Looks like he has a ton of other...

Homework Statement hi i was doing a practice physics junior olympiad paper when i got stuck in question 11 in this link [/B] https://www.scribd.com/document/244111815/SJPO-2013-Special-Round-pdf Edit by moderator: Inserted relevant extract of the PDF so that helpers do not have to...

I have a question regarding the ontology of the many-worlds interpretation which by my assumption shows some deficiencies in this way of thinking. When many worlders describe branching and effects giving rise to multiple worlds they typically invoke Schrodinger cat-type experiments where from a...

Based on my current understanding of the problem I do not see this following derivation as valid, although this is what was given in my course notes. Although this particular example is from an undergraduate physics course this is not a homework problem: I'm confused about the underlying...

I would like one that is not very mathematically intense, and not to advanced, thanks for any replies.

I would be very grateful for help with deriving the following equation... "A smooth fixed plane is inclined at 30 degrees to the horizontal. A wedge of mass M and angle 30 degrees is held on the surface so that its upper face is horizontal, and a particle of mass m rests on this face. The...

Homework Statement Hello! I apologize for my poor setup, first post. I am given a system of two rods, hope you can see my image.http://file:///C:/Users/Mikkel/Downloads/Mek2_exam_Jan2016_final.pdf One along the x-axis with mass = 2m and length = 2l Another perpendicular with the other with...

Homework Statement A rope of length L is falling off an incline. Part of the rope is still on top of the horizontal surface. There is no friction between the incline and the rope. The incline is at an angle theta above the horizontal. a) What is the magnitude of the acceleration of the rope...

Namasté, I'm an avid tennis player trying to deepen my understanding of tennis and its equipment. I hope to learn more about this subject. Thank you. :) Cheers, Yesudeep.

Hello! I try to think about the Foucault pendulum with the concept of parallel transport(if we think of Earth as being a perfect sphere) but I can't quite figure out what the vector that gets parallel transported represents(for example, is it the normal to the plane of oscillation vector?). In...

Homework Statement A uniform spool of mass M and diameter d rests on end on a frictionless table. A massless string wrapped around the spool is attached to a weight m which hangs over the edge of the table. If the spool is released from rest when its center of mass is a distance l from the edge...

Homework Statement A classical particle with total energy E moves under the influence of a potential V(x,y) = 3x3+2x2y+2xy2+y3. What is the average potential energy, calculated over a long time? Homework EquationsThe Attempt at a Solution I think that this can be solved using Virial Theorem...

Homework Statement Verify the Work-Energy Theorem W=ΔK for a bead of masd m constrained to lie on a frictionless stick rotating with angular velocity ω in a plane. Homework Equations W =∫ F⋅dr, K =m/2 v^2 [/B] The Attempt at a Solution Adopting polar coordinates the velocity is v = r' +r*Θ'...

Homework Statement Hello, I solved others but not 6.9: Find the equation of the path joining the origin O to point P(1,1) in the xy plane that makes the integral ∫(y'2 +yy' + y2) dx stationary. ∫ from O to P. y' = dy/dx Homework Equations I need use ∂f/∂y = d/dx (∂f/∂y') (euler-lagrange...

Hi i am trying to understand Borh's scattering but i need article that will teach me step by step. Do you know any?

I am a high school student looking for some amazing lectures online to study classical mechanics for a regional qualifying camp for ipho.

Homework Statement An object of mass m = 300g is attached to a spring with a constant k = 3.0Nm-1 and is at rest on a smooth horizontal floor in a fluid where the resistive force is assumed to be linearly proportional to the velocity v. the object is then displaced 10mm to the right of the...

First off, I'd like to note that I am by no means a physics expert. I am merely a high school student and a physics/maths enthusiast, nothing more, so if my thoughts are completely dysfunctional and downright incorrect, which is more than a distinct possibility, please tell me. I recently took...

Hi, when do we use hamiltonian vs. Newtonian mechanics or even lagrangian formulations? pros and cons? I am thinking molecular dynamics codes

Hello, I will take Classical Mechanics I (upper division) course fall of 2017. I have not seen Mechanics material since fall of 2014 and would like suggestions on how to review the concepts prior to taking the class. I was pretty good in that class and do not need to "re-learn" anything per...

I am reading Chapter 9 of Classical Mech by Goldstein.The symplectic condition for a transformation to be canonical is given as MJM' = J, where M' is transpose of M. I understood the derivation given in the book. But my question is : isn't this condition true for any matrix M? That is it doesn't...

Hello everyone. So I wanted to get some opinions on what some of you thought was a better choice, as far taking PDE's or classical mechanics 2 goes. First let me start off by giving a little info; I've already taken calc 1-3 and ordinary differential equations, physics 1 & 2...

Homework Statement The Observer (me) is at Inertial Frame of Reference: 1) I am sitting at a car moving east v=30 km/h relative to earth A bird flying east v = 10 km/h relative to earth What is the speed of bird for me? 2) I am sitting at a car moving east v=30 km/h relative to earth A bird...

Homework Statement A spherical satellite of radius r is moving with velocity v through a uniform tenuous atmosphere of density ρ. Find the retarding force on the satellite if each particle which strikes it (a) adheres to the surface and (b) bounces off it elastically. I know the answer should...

Here's what my prof says: "Define F_{mean} to be the mean force, F_close to be the force on the side of the Earth closer to the moon, and F_far to be the force on the side of the Earth furthest away from the moon. On the closer side the net force is F_close - F_mean > 0 On the further side the...

Homework Statement I'm doing a question from a past paper, preparing for an upcoming exam. There is no solutions so I was wondering if my answer is correct for all parts. Take a star to be a uniform sphere with mass M_{i}=3.0 \times 10^{30} Kg and radius R_{i} = 7.0 \times 10^{8}m that...

Homework Statement Find the angle Theta so that the system is in equilibrium Mass of each block: 2 Kg Mass of ring: 4π Kg Homework Equations Static equilibrium: Rotational equilibrium The Attempt at a Solution Static equilibrium: 2g + 2g + 4πg = Normal N = 4g + 4πg Taking...

I could've peeked at the solution manual and end with it at that. However, I'm trying to change this nasty habit and solve this problem myself. I might be too ambitious. Here goes. Homework Statement Consider the infinite Atwood's machine shown. A string passes over each pulley, with one end...

Homework Statement (2) Suppose a particle of mass m is subjected to a repulsive force F = +kx. (a) What is the general solution for the motion of the system? (b) If the particle begins with a position x(0) = x0 and with velocity v(0) = v0 at t = 0 what are the values of the constants appearing...

This is not a homework question, I'm just curious. Suppose you had a sailboat sailing on calm water. Let's say the sailboat is capable of sailing at 10 knots under the current wind conditions using only its sails. Now say the sailboat had a small propeller motor that was capable of propelling...

Homework Statement Question :- A block of mass ##5 kg## is attached to a spring. The spring is stretched by ##10 cm## under the load of the block. A impulse is provided to the block such that it moves up with a velocity of ##2 m/s##. Find the height it will rise. Homework Equations ##F_s =...

Homework Statement Planet X of mass mx = 2.1 × 1024 kg orbits S in uniform circular motion at a distance rx and with a period Px = 2.1 years (=66225600 s). The mass of the star S is MS = 2 × 1031 kg and its radius is RS = 3.2 × 108m. Homework Equations T=2pi * sqrt(r3/(GM) The Attempt at a...

Homework Statement [/B] Question :- Find the acceleration of block of mass ##M##. The coefficient of friction between blocks is ##\mu_1## and between block and ground is ##\mu_2##. free body diagram at the end. Variables :- ##f_1## - friction between blocks. ##f_2## - friction between block...

Homework Statement how from this question using Energy principles I can find how frequency depends on g? Homework EquationsThe Attempt at a Solution I know that frequency is sqrt(k/m) this is a formula you use in introductory physics. but I am lost on how to do it from energy route or...

Question :- A car has to move on a path, that is a arc of a circle of radius (##R##). The length of the path is (##L##). Suppose it starts on the highest point of the path, find the highest uniform speed for which, it does not lose contact with the path on any point ? My attempt :- I made a...

In my rough understanding Molecular Dynamics using Classical Newtonian mechanics is a 6N dimensional non linear system. 6N dimension because you have 3 position vectors and 3 momentum vectors for each N particles. Nonlinearity because of the terms in force fields. In principle this system can...

I attempt to solve the brachistochrone problem numerically. I am using a direct method which considers the curve ##y(x)## as a Lagrange polynomial evaluated at fixed nodes ##x_i##, and the time functional as a multivariate function of the ##y_i##. The classical statement of the problem requires...

Homework Statement A solid sphere of density ##ρ## and radius ##R## is centered at the origin. It has a spherical cavity in it that is of radius ##R/4## and which is centered at ##(R/2, 0, 0)##, i.e. a small sphere of material has been removed from the large sphere. What is the the center of...

Homework Statement Find the equation of motion of the object by setting the derivative of the total energy equal to zero. Homework Equations r(theta)=(Rcos(theta), Rsin(theta), q*theta) v(theta)=dr/dt=(-Rsin(theta)dtheta/dt, Rcos(theta)dtheta/dt, q*dtheta/dt) derivative of Total Energy =...

Homework Statement Find the Lagrangian for the double pendulum system given below, where the length of the massless, frictionless and non-extendable wire attaching m_1 is l. m_2 is attached to m_1 through a massless spring of constant k and length r. The spring may only stretch in the m_1-m_2...

Homework Statement A particle of mass m is subject to force F(x)=kx with K>0. The initial starting position is x0 and the initial speed is zero. Find x(t). Homework Equations F(x)=kx F=ma The Attempt at a Solution Honestly, I am totally lost on this. I've written acceleration as v(dv/dx)...

How can I start Classical Mechanics, I mean by the help of which book...

A particle's position is given by $$r_i=r_i(q_1,q_2,...,q_n,t)$$ So velocity: $$v_i=\frac{dr_i}{dt} = \sum_k \frac{\partial r_i}{\partial q_k}\dot q_k + \frac{\partial r_i}{\partial t} $$ In my book it's given $$\frac{\partial v_i}{\partial \dot q_k} = \frac{\partial r_i}{\partial q_k}$$...

Homework Statement Minimize the functional: ∫01 dx y'2⋅ ∫01 dx(y(x)+1) with y(0)=0, y(1)=aHomework Equations (1) δI=∫ dx [∂f/∂y δy +∂f/∂y' δy'] (2) δy'=d/dx(δy) (3) ∫ dx ∂f/∂y' δy' = δy ∂f/∂y' |01 - ∫ dx d/dx(∂f/∂y') δy where the first term goes to zero since there is no variation at the...

Homework Statement A uniform cylindrical drum of mass M and radius a is free to rotate about its axis, which i is horizontal. An elastic cable of negligible mass and length l is wrapped around the drum and carries on its free end a mass m. The cable has elastic potential energy \tfrac12...

Homework Statement I have a block of mass m on a horizontal surface, which is covered in oil. The tell me the viscous resistance force is a function of the velocity, F(v)=-cv1/2, where I am assuming c is a constant of some kind. I need to find the time that it will take for the block to stop...