Classical mechanics Definition and 1000 Threads

how is md^2r/dt^2 . dr/dt = d/dt (1/2 m (dr/dt)^2 ) Thank You

Homework Statement Now these two blocks are pulled separately by x1 and x2 distance. Find the frequency of shm Homework Equations a = -w^2 x The Attempt at a Solution Now after m1 being pulled, it moves with acceleration a1=Force of spring/m1. acceleration of block 2 = a2=/force of...

Homework Statement I'm having some issues understanding a number of concepts in this section here. I attached the corresponding figure at the end of the post for reference. Issue 1) 1st of all, I understand that a Hamiltonian can be written as such $$H = T_2 - T_0 + U$$ whereby ##T_2##...

Homework Statement [/B] A mass ##m## travels in a straight line with velocity ##v_0## perpendicular to a uniform stick of mass ##m## and length ##l##, which is initially at rest.. The distance from the center of mass of the stick to the path of the traveling mass is ##h##. Now the traveling...

Homework Statement The skier is skiing without friction down the mountain, being all the time in a specified plane. The skier's altitude y(x) is described as a certain defined function of parameter x, which stands for the horizontal distance of the skier from the initial position. The skier is...

Homework Statement A spring with spring constant k is attached to a box of mass M in which is placed a small body of mass m. The system is displaced a distance A from equilibrium and released from rest. Find the normal force between the box and the small mass as a function of time. For what...

Homework Statement Homework EquationsThe Attempt at a Solution I have done part a, I have no idea on part b, here is my attempt,

Homework Statement The problem is to take a small ball of mass m on a uniform rod of mass m which is hung on a hinge vertically downward, they're asking to find the velocity to be imparted for it undergo a complete rotation. I have the kinetic energy bit worked out but I'm getting the wrong...

I have no prior experience in physics, but I am a math undergrad so I know calculus, differential equations, linear algebra and stuff like that. So I'm ready to move from the conceptual "bedtime story physics" to stuff with real mathematical rigor. So, what is classical mechanics all about...

I'm looking for a source of harder mechanics problems, preferably with solutions. I'm supposed to use the Young and Freedman book, but I find it rather teadious and superficial; most problems don't match the difficulty and depth of the ones on the exam. I had my mid-term tests recently, and got...

I came to know that time evolution in classical mechanics is highly non linear. Is there any case that it become linear?

Why is it easier to balance a bicycle that is moving fast, rather than one that is moving slow?

Homework Statement A bowling ball sits on the smooth floor of a subway car. If the car has a horizontal acceleration a, what is the acceleration of the ball? Assume that the ball rolls without slipping. Homework Equations torque = R x F = Iα aball= Rα Isphere = (2/5) MR2 The Attempt at a...

Homework Statement A bead is placed on a rod with coefficient of friction m, it's accelerated from rest with angular velocity a, find the time it takes to start moving. Neglect gravity Homework Equations Force of friction =Nm The Attempt at a Solution They said there's no gravity, so i don't...

In the following diagram, a frictionless disc is supported by a massless string. This problem was given by the author of a book, and a solution was given to some questions that were asked about this diagram. One thing the author said in one of the solutions, was that the tension in the string...

I'm sophomore in physics looking for best free books for classical mechanics and for vibrations and waves. Anyone with references pleaseThank you

I have been studying classical mechanics for a while from Goldstein book and can't go ahead of the following derivation. I understand the method of Lagrange's multipliers for getting extrima of a function subjected to equality constraints but can't understand it's relevance here because in that...

Homework Statement A bead of mass m slides in a frictionless hollow open-ended tube of length L which is held at an angle of β to the vertical and rotated by a motor at an angular velocity ω. The apparatus is in a vertical gravitational field. a) Find the bead's equations of motion b) Find...

In the Classical Mechanics volume of The Theoretical Minimum, he writes a shorthand equation for a small change in a function. Please could someone explain exactly what it means and where it comes from?

Why object in the space will continue moving foever if the object is in dynamic equilibrium?

Hello PF, I am taking classical mechanics this fall and I am horrified. I am just not sure if I have the mathematics background for the class. I am still finishing differential equations (about half way done) and I am almost done with calculus 3. The pre-requisite for the class is DE...

I've been working on a crude N-body simulator which allows N bodies of equal masses to interact gravitationally in 2 dimensions. My goal is to model the formation of Solar System. Each body is modeled as a circle with a radius as a function of its mass, in such a way that all bodies have the...

Homework Statement The following structure,A force F is applied to the right hinge.If the mass of the rods are equal ,and the length of the rod is equal,the intial angle is also equal to 90 degrees (a square),What is the intial acceleration of leftmost hinge ? Homework Equations Coordinate...

When discussing about generalized coordinates, Goldstein says the following: "All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ...

Hello all. This is my first post. I am very passionate with physics even if i did not study them at university. I studied administation and another degree in economics and politics. However, i love physics so much and i decided to learn more about this subject. So, i searched MIT's undegraduate...

Hi everyone. So I'm going through Landau/Lifshitz book on Mechanics and I read through a topic on inertial frames. So, because we are in an inertial frame, the Lagrangian ends up only being a function of the magnitude of the velocity only (v2) Now my question to you is, how does one prove that...

Here's a question that I've been trying to solve for a while but keep on running into dead ends, and I can't seem to find any info on the internet to help me. Anyways I was wondering what the integral of torque is? For my specific example I have a rod that is not equally balanced on a fulcrum...

Homework Statement A friend and I are going through Vladimir Arnold's Mathematical Methods of Classical Mechanics, but I think my lack of a background in pure math / proofs is seriously hampering my ability to do any of the problems in the first chapter. For example: PROBLEM. Show that if a...

Homework Statement A particle of mass m is subject to a force F (x) = -kx. The initial position is zero, and the initial speed is v0. Find x(t). Homework Equations F = m*v*dv/dx = -kx v = dx/dt The Attempt at a Solution I'm new to differential equations, so please excuse me if I make any...

I just finished my junior year in high school. In college, I hope to major in physics and was interested in the honors versions of freshman introductory physics. These all have the prerequisite of a calculus-based mechanics course and use Kleppner as their mechanics textbook. I have so far only...

I came across this article about the near absence of continuum mechanics in university-level physics education: http://www.troian.caltech.edu/papers/Gollub_PhysToday_Dec03.pdf I have wondered this issue myself: why is continuum mechanics mainly studied by engineers rather than physicists, even...

An isolated mechanical system can be represented by a point in a high-dimensional configuration space. This point evolves along a line. The variational principle of Jacobi says that, among many imagined trajectories between two points, only the SHORTEST is real and is associated with situations...

I've been thinking about centripetal force and its effects on motion in uniform circular motion. I've actually found it difficult to accept that velocity magnitude can ever be maintained constant. Here is why: if this is our velocity vector, v, at the top of the circle: → Then the centripetal...

I am currently studying collisions in high school and my teacher told us that, in order to calculate the direction of each object after a 2-body collision, we could change the values in the relative velocity terms of the equation of the coefficient of restitution to the components in x and y. Is...

Hey guys! I'm currently on my junior year and I will be taking advanced classical mechanics next semester. My lectures will consist mainly on Lagrangian and Hamiltonian mechanics and I am currently in need of a good book in classical mechanics. I have used Kleppner and Kolenkow's An Introduction...

Hi people. Here the situation. Balloon filled with air I throw in the air. Balloon starts to move upstairs. It slows down and then is starts to fall down to the Earth. I'm interesting only in the movement of upstairs. Here the picture. In the first case (left) I choose the direction of...

I made the problem up myself, so there might very well not be a rational answer that I like! Homework Statement A point-particle is released at height h0 is released into a parabola. The position of the particle is given by (x, y) and the acceleration due to gravity is g. All forms of friction...

Homework Statement The situation is that of Goldstein's problem 1.21 (or 1.19 in some editions): "Two mass points of mass m1 and m2 are connected by a string passing through a hole in a smooth table so that m1 rests on the table and m2 hangs suspended. Assume m2 moves only in a vertical line."...

Hi all, I am looking for a good introduction to classical mechanics. I have looked at some book recommendations online but I am having trouble choosing the right book for me. Right now, I know no physics, so I need to start from the very beginning which I think is classical mechanics. I am self...

I need a book written just on the style of Classical Mechanics by Goldstein. I don't remember the book name and author but it is just the copy of the book Classical Mechanics by Goldstein. Please guide.

Homework Statement To calculate moment of inertia of a solid sphere of uniform density[/B]Homework Equations $$ I = \int r^2 dm$$ The attempt at a solution I consider an elemental disk of small thickness ##d\theta## ##dm = \frac{M}{4/3 \pi R^3}*\pi R^2\cos^2\theta* Rd\theta##...

Homework Statement A simple harmonic oscillator has a potential energy V=1/2 kx^2. An additional potential term V = ax is added then, a) It is SHM with decreased frequency around a shifted equilibrium b) Motion is no longer SHM c)It is SHM with decreased frequency around a shifted equilibrium...

Very dumb classic mechanics question here: The other day I caught sight of a trivial objects arrangement: a basketball placed on top of a 6-sided cardboard box on the floor, and I wondered how the weight of the hollowed sphere could cause bending on the supported, flat top surface of the box...

here is the link to walter lewin video lecture please jump to 13:13 8.01x - Lect 2 - 1D Kinematics - Speed, Velocity, Acceleration i thought that all meter ruler/ meter stick use ± 0.1 cm as uncertainty .how did he get ± 0.5 cm?

In 3rd edition of Goldstein's "Classical Mechanics" book, page 335, section 8.1, it is mentioned that : In Hamiltonian formulation, there can be no constraint equations among the co-ordinates. Why is this necessary ? Any simple example which will elaborate this fact ? But in Lagrangian...

Consider a sphere constrained to roll on a rough FLAT HORIZONTAL surface. A book on classical mechanics says it requires 5 generalized co-ordinates to specify sphere's configuration: 2 for its centre of mass and 3 for its orientation. I did not understand why 3 for orientation. I guess only 2...

I'm interested in understanding the key physical differences between classical and quantum dynamics. I understand that spin (intrinsic angular momentum) is one major physical difference.* So I wonder whether all else flows from this? Or are there other major (unrelated) physical differences...

How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction? from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ; (where er and eθ are unit vectors in the radial direction and the direction of increase of the...

Homework Statement Let's say that I have a potential ##U(x) = \beta (x^2-\alpha ^2)^2## with minima at ##x=\pm \alpha##. I need to find the normal modes and vibrational frequencies. How do I do this? Homework Equations ##U(x) = \beta (x^2-\alpha ^2)^2## ##F=-kx=-m\omega ^2 x## ##\omega =...

Hello, Homework Statement I'm given the following exercise: "A rod with neglected thickness exists. What is the relation between the α,β angles to Euler angles of orientation? α is defined as the angle between the rod and its projection on the XY plane. β is defined as the angle between the...