Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

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How does solar activity affect the ISS?

Currently the sun is launching some intense solar flares. http://www.guardian.co.uk/science/2011/feb/17/solar-flares-northern-lights-uk Th article I've linked also mentions how a "coronal mass ...
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2k views

Impulse - distance question [closed]

What impulse should be applied to an object of mass m, having a known coefficient of friction u to get to a distance d ? Thanks! Update 14.02.2011: I still wasn't able to find an answer to this. ...
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30 views

Particle slides on incline where incline angle increases with rate $\omega$: why does kinetic energy have a term $(1/2)m(\omega^2 x^2)$?

A particle slides on a smooth inclined plane whose inclination is $\theta$ is increasing at a constant rate $w$. If $\theta = 0$, at time t = 0 at which time the particle start from rest, Find the ...
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38 views

rotational springs

With a normal spring, you compress it using a linear force to store energy and then it decompresses and releases the energy, again in a form of linear force. Is there a mechanical mechanism that ...
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1answer
25 views

Variable tension in rope connected to mass

Problem 3.9 from Kleppner and Kolenkow's text An Introduction to Mechanics involves a uniform rope of length $L$ and mass $m$ that is connected at one end (its "bottom" end) to a block of mass $M$ and ...
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35 views

Reversing time for a closed system of particles

For a closed system of particles, the lagrangian in classical mechanics is $$L=\sum \frac{1}{2}mv_a^2 - U(\mathbf{r_1},\mathbf{r_2}, \cdots)$$ For an arbitrary position function $x(t)$, to see the ...
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34 views

Tension along a curved surface [closed]

I'm curious what the tension in a rope will be when its exposed to a uniform load. Assuming a similar setup to this question what will the tension along the rope/tube be?
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44 views

Classical Mechanics — Sign of work done

It seems that work has two possible ways to decide it's sign: Whether you take the perspective of the system or the surrounding (whether you consider work done on the system as positive, or work done ...
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26 views

Equations of motions uneven see-saw

How do I set up equations of motions for a see-saw where the distance between the masses $m_1,m_2$ to the pivot are given by $\ell_1, \ell_2$, respectively? My idea was to first set one of the masses ...
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2answers
84 views

Definition for potential energy

I came across this definition for potential energy: If we let $T$ be the Kinetic energy, we have that: $$T = \frac{1}{2}mv^2 \implies T = \frac{1}{2}m{x'}^2$$ $$T'= mx'x'' = F(x)x' \implies \\T = ...
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97 views

Galilean relativity & the road to special relativity

Firstly, I just want to make sure that I've understood the notions of relative and absolute quantities correctly. Elementary analysis shows that position and velocity are relative quantities. Indeed, ...
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30 views

Kinetic energy dissipation in braking a vehicle

Let's say a vehicle that weighs 20t is hauling along at 50m/s and we want to brake it down to a full stop. The kinetic energy we need to dissipate into heating up the brakes is ...
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1answer
49 views

Q: Goldstein chapter 1 problem 16: Finding the generalized potential from the force

I have started to work through Herbert Goldstein's, Charles Poole's and John Safko's Classical mechanics, and I am having a bit of trouble with one of the problems (chapter 1 problem 16). The problem ...
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47 views

Potential for particle rolling down slope of arbitrary shape

I've been thinking about how to calculate the potential $V(x)$ of a particle rolling under the force of gravity down some curve, given by $f(x)$ (suppose nonincreasing). My idea was to simply ...
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1answer
39 views

Minimum distance between two bodies attached by a spring

Take two bodies of masses m and M attached by a spring of constant K on a smooth horizontal surface. The system is at rest. A constant force F acts on body M, horizontally. To study the motion of the ...
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1answer
23 views

Motion in oscillating field: expanding in powers of $\xi$ [closed]

I'm reading an excerpt from Landau/Lifschitz's Mechanics book about motion in oscillating fields. Two equations for the motion of a particle with mass $m$ are set out: \begin{equation} m\ddot{x} = ...
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1answer
104 views

simple question on torques on an ellipsoid

I have an ellipsoid, and in the reference frame where the x-, y- and z-axis are aligned with its eigenvectors I compute the torque $\vec\tau$ acting on it. And I'm asking myself how can I quantify ...
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1answer
58 views

Hamilton-Jacobi problem

In analytical mechanics by Fasano and Marmi they consider the Hamilton-Jacobi equation for a conservative autonomous system in one dimension with the following Hamiltonian, \begin{equation} ...
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1answer
25 views

What can I say about a graph depicting orbit a particle has gone through? Acceleration VS friction

I have an orbit in which a particle is told to have gone through. There is a straight part, and a curved part. I am asked to mark the right statements, which are: a. Without any further data, there ...
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1answer
81 views

Holonomic constraints and degrees of freedom?

Can we see that a constraint can decrease the degrees of freedom of a system if and only if it is holonomic. Either way please can you explain why?
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1answer
65 views

Why does the following contradiction arise in Lagrangian Formalism?

If we look at the Lagrange's equation $\frac{d}{dt}(\frac{\partial L}{\partial \dot{q_i}})- \frac{\partial L}{\partial q_i}=0$ It is clear that Lagrangian is invariant under a Transformation $L ...
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1answer
65 views

Does it take more effort to move against earth's rotation?

I know that if we stand still, we are traveling at 0 m/s relative to the Earth. But if we move against the rotation of the Earth we lower our speed, so, wouldn't we have to fight against the ...
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1answer
23 views

How to visualize the holonormic constraint $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0

A holonormic $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0 appears in Goldstein's Classical Mechanics Pg 12. Where $i$, and $j$ are particles, however $c_{ij}$ is not defined. How someone deduce the ...
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1answer
71 views

Lagrange equation and a force derivable from a generalized potential

I was reading the solution of this exercise and I have a doubt: A point particle moves in space under the influence of a force derivable from a generalized potential of the form $$U(r,v) = ...
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1answer
67 views

Showing time-invariance of Lagrangian with time-displacement operator

I am trying to show that the time-invariance of the Lagrangian of a simple one-particle system implies energy conservation for that system. The first step is, well, to show that the Lagrangian is ...
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1answer
63 views

Euler-Lagrange equation with torsion, question on derivatives

Consider a mechanical system, the Lagrangian of which is: $$-L(u,\dot u)=\int\left(\dfrac{\partial^2 u}{\partial x^2}\right)^2\mathrm{d}x$$ This would correspond to a system in torsion, for example. ...
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52 views

Where is the energy stored in destructively-interfering waves?

Let's say we have two waves moving along a string. One of them is represented by the function: $$f_1(t)=\sin(\omega t)$$ The other one is represented by a function: $$f_2(t)=-\sin(\omega (\tau-t))$$ ...
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1answer
96 views

Mathematical pendulum in accelerating frame of reference [closed]

An aquintance of mine, who is a first year physics student was given a simple task as a homework-like task, which is about determining the ratio of periods between two equal-parameter mathematical ...
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2answers
128 views

Taking moments about two different points in a system of forces

If you have a system of forces and you take moments about two different points will the moment be the same?
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1answer
66 views

How to calculate the deceleration of two trains moving with the same velocity? [closed]

Two trains travelling on the same track are approaching each other with equal speeds of 40m/s. The drivers of the train begin to decelerate simultaneously when they are just 2km apart. If the ...
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1answer
226 views

How much force can bolt cutters exert?

What's the mechanical advantage of an ordinary, let's say, 3 feet long bolt cutters? How many pounds can they exert? I'm asking because I have a lock which is apparently immune to over 9 tons of ...
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1answer
292 views

Rolling without slipping and friction

When a ball rolling without slipping along an inclined plane reaches the bottom, it has a linear velocity $v$ and angular velocity $\omega\ =v/r$ at the bottom. Then it continues its motion on the ...
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1answer
72 views

What are the necessary/sufficient conditions for a system to be Hamiltonian/non-Hamiltonian?

I searched for a definition of Hamiltonian system on Huang and Tuckerman text but have not found anything precise. So intuitively I suppose: Hamiltonian system= a system which admits a complete ...
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1answer
165 views

Find angular velocity of motor

I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong. Basically ...
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1answer
45 views

What am i doing wrong here(dynamics)?they should give the same answer [closed]

So a body $m$ is on a uniform circular motion ($\omega = d\theta/dt = \text{constant}$), it is suspended by an inextensible rope with negligeable mass: First picture so: $$ -mg + T \cos \alpha = ...
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1answer
144 views

Analytical Mechanics [closed]

I see that $W_a(1) = \dot U_a(1)=\ddot{X_a}(1) = 0.3 $ Since $U_{O'}=0 $ then O' is Instant centre of rotation. Then $U_b = 2U_a = 0.6$ I tried a lot, about a week, i find the speed, but there ...
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1answer
205 views

Torque and Car parked on slope [closed]

I have a homework question in which a car of mass $M\ kg$ is parked on a hill inclined at $25^o$ The car is facing up the hill and I am told that the wheels are $3\ m$ apart and the centre of mass is ...
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2answers
349 views

Why is angular velocity of any point about any other point of a rigid body always the same?

I have the following question regarding an ideal rigid body. Firstly, is it always true without any exceptions that the angular velocity of any point about any other point on a rigid body is always ...
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1answer
91 views

determining phase constants in SHM [closed]

A particle moves along the x axis. It is initially at the position $x$ of $0.300 m$, moving with velocity $v$ of $0.070 m/s$ and acceleration $a$ of $-0.330 m/s^2$. Suppose it moves with constant ...
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1answer
51 views

Questions about basic jump physics

This is a problem a friend and I are working on for an undergrad reading course. Our goal at the end is to make an accurate two-dimensional model of the human jump using Processing by the end of next ...
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1answer
89 views

Gravitational work

As far as I know gravitational work is independent from the path of the object, and I have an object that goes up on a inclined plane to a certain height, and than, after the object reaches the edge ...
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1answer
157 views

Power dissipation in High Voltage Cables

I was doing the following physics problem in physics class: You have two dimensionally identical pieces of metal, one made from aluminium the other made from iron. It is given to us that ...
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1answer
149 views

Latent heat of solidification

What is the heat release mechanism involved in solidification from liquid phase? Is the energy transferred to nucleation centres?
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1answer
97 views

Landau Mechanics equation 16.9

I am having trouble deriving the equation 16.9 from Landau's Classical Mechanics book. This equation is the maximum kinetic energy of a particle if a massive particle with mass $M$ disintegrates into ...
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1answer
234 views

Equation for Terminal Velocity on an inclined plane and the time it takes to reach it

Now I'm doing a research on the matter similar to this thread : Terminal Velocity of identical shape/size objects which is very self explanatory and very helpful. However in my case, the objects will ...
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1answer
178 views

Pressure inside a plastic bottle filled with water and squeezed by X weight?

I'd like to know how it'd be possible to calculate the pressure inside a plastic bottle filled with water and squeezed by say 20 kg sitting on the bottle, which is lying on its side (so that ...
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1answer
61 views

Torque in a 2-segment robot leg

I have a (hypothetical) robot with two legs, each with 2 segments, with a joint at the body of the robot and in the 'knee' of each leg, as in this (poorly-drawn) diagram: (Sorry about the quality and ...
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1answer
89 views

Is a motor HP torque directly proportional to the increasing HP among identical motors?

Say you have three motors: Motor 1 = .10 HP with x torque, performing task A Motor 2 = 1 HP with y torque, performing task A Motor 3 = 10 HP with z torque, performing task A If the motors are the ...
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1answer
71 views

If you dig a deep tunnel, will the rock sublimate?

If a tunnel is dug deep inside the crust (but before reaching places where the rock is liquid), how will the enormous downwards pressure manifest itself? Will the difference in pressure ...