What is Classical mechanics: Definition and 1000 Discussions
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).
The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, made predominantly in the 18th and 19th centuries, extend substantially beyond earlier works, particularly through their use of analytical mechanics. They are, with some modification, also used in all areas of modern physics.
Classical mechanics provides extremely accurate results when studying large objects that are not extremely massive and speeds not approaching the speed of light. When the objects being examined have about the size of an atom diameter, it becomes necessary to introduce the other major sub-field of mechanics: quantum mechanics. To describe velocities that are not small compared to the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. However, a number of modern sources do include relativistic mechanics in classical physics, which in their view represents classical mechanics in its most developed and accurate form.
Homework Statement
I'm working (self-study) through Goldstein et al, Classical Mechanics, 3rd Edition, and I'm currently stuck on Problem 8.11:
A particle is confined to a one-dimensional box. The ends of the box (let these be at \pm l(t)) move slowly towards the middle. By slowly we mean...
Homework Statement
Around vertical axis ##O## a body on picture below (see attachment) is being rotated with constant angular velocity ##\Omega ##. On the circle we have a body with mass ##m##, that can feels no friction. Find position of that body as function of ##\phi ## and time. Calculate...
Ayo everybody, I'm doing a problem about theory of small oscilatons (see pic) and I got the following for potential energy:
V= mg(\frac{l_{2}}{2} +\frac{l_{1}}{2} \theta^{2}_{1} + \frac{l_{2}}{4} \theta^{2}_{2}) (after the aproximation cos \theta ~ 1 - \frac{\theta^{2}}{2}
Knowing that V...
Hi all,
I'm a first year undergrad and I'm currently struggling with Physics. I aced high school physics (A-levels) but for my first class test at uni, I got a 50% and now I'm not sure if I'll be able to make this to 90%+ during the second class test (in exactly a month from now).
We are...
The time has come to schedule for next semester's classes. I will be a senior in physics and choosing some electives. I am trying to decide between taking matrix theory (linear algebra) or graduate level classical mechanics. I really WANT to take the mechanics course but I feel that maybe I...
Homework Statement
A particle of mass m moves under an attractive central force of Kr^4 with an angular momentum L. For what energy will the motion be circular? Find the frequency of the radial oscillations if the particle is given a small radial impulse.
Homework Equations...
Homework Statement
Determine possible trajectories for particle with constant magnitude of velocity |\dot{\vec{r}}| = v0 and constant angular momentum \vec{L} = \vec{L}0
Homework Equations
|\dot{\vec{r}}| = v0
\vec{L} = \vec{L}0The Attempt at a Solution
I know that L dot is zero and...
First-Order Extrema in "Classical Mechanics", Theoretical Minimum
In the 3rd lecture of Classical Mechanics, 2011, by Dr. Susskind in his Theoretical Minimum series, he talks about calculating extrema, saddle points, etc. to "first order".
"if you move a little bit, the potential is zero, to...
I am studying for the mechanics modules of A level mathematics under EdExcel.So far the books seemingly published to support the specifications aren't doing a very good job.The examples in the books don't tell the students how to solve problems in the exercises, which is a sheer let down.I want...
I just took Physics I last semester, but I still feel there is so much more to learn about classical mechanics. I could work on 100 different problems involving binary stars, rockets, or rotating objects - but then a slight twist is thrown in on the problems, then something new to have to...
From (Marion 5th ed. Problem 9-15)
A smooth rope is placed above a hole in a table. One end of the rope falls through the hole at t = 0, pulling steadily on the remainder of the rope. Find the velocity and acceleration of the rope as a function of the distance to the end of the rope x...
I was recommended this by a friend. I'm going to get K&K but I was wondering what you thought of this book if you have read it. Is it good for beginners? Comprehensive? General comments?
Thank you,
Tridian
John Taylor "Classical Mechanics" Chapter 5, Problem 29
Homework Statement
An undamped oscillator has period t(0)=1 second. When weak damping is added, it is found that the amplitude of oscillation drops by 50 percent in one period r1. (the period of the damped oscillations defined as time...
Homework Statement
A massless wire hoop of radius R is rotating in a horizontal plane about its central point with constant velocity ω. There is a tube of negligible mass pinned across the hoop on a line passing through the central point. Inside this tube is a spring of negligible mass with...
Wheres the limit between quantum mechanics and classical mechanics.
I mean,when can I expect quantum behavior on a system, is it depends on the system size?Tempature? Something else...and if so what are the numbera for those limits.
As we know in nature everything is continuous, so, the...
Homework Statement
a particle of mass m moves on the orbit r= a cos(θ), a>0.
Find the force acting on the particleThe Attempt at a Solution
I had this formula in my notebook:U(r)= E-(L^2/2mr^2)(1+(1/r^2)(dr/dθ)^2)
Using it I got U(r)=E-L^2a^2/2mr^4
and F(r)=-dU/dr= (-5L^2a^2/2mr^5)...
John Taylor "Classical Mechanics" Chapter 3, Problem 7
1. Homework Statement [/b]
The first couple of minutes of the launch of a space shuttle can be described very roughly as follows: The initial mass is 2x10^6kg, the final mass (after 2 min) is about 1x10^6 kg, the average exhaust speed is...
Why is it that in the damped simple harmonic equation, the force constant can take on all values, but the force constant corresponding to the classical harmonic oscillator potential in the Schrodinger equation can only take on discrete eigenvalues?
Hey all,
suppose there's a particle with Potential Energy : U(x) = A*[ x^(-2) - x^(-1) ] , where A is a constant.
I'm supposed to find the energy required to make the particle go from periodic movement to unlimited movement.
First thing I did was U '(x) = 0 to find the balance points, now...
Homework Statement
If anyone could help me with this classical mechanics exercise I would be very grateful! The exercise is as follows:
The muon (μ) is a particle with mass mμ=207me, with me being the electron mass. The pion (∏) has a mass of m∏=273me. The pion can decay into a muon...
Am I "ready" for Classical Mechanics?
Hello again, PF. I have a question about the Classical Mechanics course I'm taking this coming fall.
Thanks to having a few cruddy enrollment times in the past year, I've been taking my courses a bit out of order, but without any problems or conflicts...
Homework Statement
Problem 27 Experiment needed first: The hallmark of inertial ref. frames is that any object subject to 0 net force travels in straight line at a constant speed. Consider the following experiment: I am standing on the ground (which we shall take to be an inertial frame)...
Homework Statement
The two vectors a and b lie in the xy plane and make angles (alpha and beta) with the x axis. a. by evaluating a dot b in two ways prove the well known trig identity cos(alpha-beta)=cosalphacosbeta +sinalphasinbeta
Homework Equations
adotb=abcostheta=axbx+ayby
The...
John Taylor "Classical Mechanics" Chapter 3, Problem 1
Homework Statement
Consider a gun of mass M (when unloaded) that fires a shell of mass m with muzzle speed v. (shell's speed relative to gun is v). Assuming gun is completely free to recoil (no ext. forces on gun or shell), use...
Homework Statement
Consider the classical system of a mass of one kg attacked to the ceiling with a spring constant k=50N/m.
The mass is held at rest such that the spring hangs vertically but is not extended. The mass is then released and falls under gravity. Neglect air resistance.
1...
My requirements are :
- Text should be at an undergrad level (I will be starting my 2nd year soon).
- Should contain a large number of solved examples, but not many questions (I would like the questions to be of good quality though, so that I don't have to choose which questions to...
There is an article I am reading,
http://authors.library.caltech.edu/38643/1/PhysRevLett.110.174301.pdf
I don't quite understand a lot of where this guy is coming from. I do not have much background in Lagrangian and Hamiltonian formulations, but it is vital that I can formulate some sort...
I was just wondering, what book would you suggest for me as a undergrad student going into 1st year at university. I will be completing an honours in math and physics, and I just want some material to self-learn over the summer and to keep myself occupied. My prior physics knowledge includes...
Are there any unanswered questions in classical mechanics?
By unanswered I mean unanswered and attempted. I could easily think of a question which has never been asked.
Edit: Sorry about the misspelled thread title.
Homework Statement
A student kicks a frictionless puck with initial speed ## v_0 ## so that it slides straight up a plane that is inclined at an angle ## \theta ## above the horizontal.
Write down Newton's second law for the puck and solve it to give it's position as a function of time
How...
what are the differences? Every example I find usually has a derivative or integral or some kind of calculus defined concept that seems to make it easier or more understandable
I'm reading Classical Mechanics (Taylor), and the 6th chapter is a basic introduction to calculus of variations. I'm super confused :confused:
I've tried to go to other sources for an explanation, but they just make it even worse!
So, let me see if I can get some help here...
Hello folks. I am taking some courses next semester over at Wayne, one of which is a 500 level, graduate level difficulty mechanics course. It's the course typically taken at the 300 level. I was wondering if anybody knew of a great book for this course at this level. I have both Taylor and...
In Taylor's advanced text on classical mechanics, he gives an example of a non-holonomic system, I find this part very strange.
He gives the example of a hard rubber ball being rolled in a triangle on a flat surface, the point is that if you take the ball out through the triangle and back to...
Hello. In Molecular Dynamics simulations, the Newton's equation of motion is used to calculate the time evolution of system. Once, I read in an introductory text that when the thermal de Broglie wavelength $$\Lambda=\frac{h}{\sqrt{2\pi mkT}}$$ is much smaller than the interparticle distance...
Hi
Question 1
i was wondering if there is any method to find the point from which the angular momentum is a conserved quantity. let me e.g. choose the case of a planet moving in an orbit around the sun. In this case, the angular momentum measured from the center of mass as the point of reference...
Energy "formulation" of classical mechanics?
When discussing the different formulations of classical mechanics, those that are always mentioned are Newtonian, Lagrangian and Hamiltonian mechanics. However, it is my understanding that when dealing with conservative forces in Newtonian...
Hello, so i just received a copy of introduction to classical mechanics by kleppner and kolenkow in the mail today. I was so excited unwrapping it but when i saw it i was very disspointed. it turns out the person sent me the "special indian edition". i was pretty upset and I'm thinking of...
Homework Statement
This is question 3.7 from Gregory's Classical Mechanics textbook.
A symmetric sphere of radius a and mass M has its center a distance b from an infinite plane containing a uniform distribution of mass ## \sigma ## per unit area. Find the gravitational force exerted on the...
Ok, so I know that law of conservation of linear momentum holds in a system in a particular direction, provided no net external force is acting in that direction. So, if we drop a ball on the Earth surface from a height much less than Earth's radius and then to analyze its momentum, we take...
Homework Statement
"The shortest path between two point on a curved surface, such as the surface of a sphere is called a geodesic. To find a geodesic, one has to first set up an integral that gives the length of a path on the surface in question. This will always be similar to the integral...
A 1kg wooden block is being pressed against a wooden wall by 12N. If the block is initially at rest will it move upward, downward or remain at rest?
Picture of problem is in link below along with my working out. co-effecient of static friction of wood on wood is 0.50. I have also made...
Author: John Taylor
Title: Classical Mechanics
Amazon Link: https://www.amazon.com/dp/189138922X/?tag=pfamazon01-20
Prerequisities: A Lower-Division mechanics course
Contents: Upper-Division of undergrad
Having gone through Hailliday-Resnich mechanics, I'm looking for something a step above this.
I'm taking second year mechanics next year, but I'd like to get a head start on it (considering that I move faster on my own, anyway).
I'm looking at either Kleppner, or Taylor right now, but I'm...
Author: Herbert Goldstein (Author), Charles P. Poole Jr. (Author), John L. Safko (Author)
Title: Classical Mechanics
Amazon Link: https://www.amazon.com/dp/0201657023/?tag=pfamazon01-20
Prerequisities:
Contents: