# Tagged Questions

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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### Static plane in an inertial frame of reference

Suppose we are given a mechanical frame consisting of two points. How can we prove that assuming any initial conditions there is an inertial frame of reference in which these points will be in a ...
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### Is there symmetry in 2d stress tensor in linear elastic fracture mechanics?

Assumptions: Cross terms in strain tensor are defined as equal $\varepsilon_{xy} = \varepsilon_{yx}$. pure mode I crack. Far from crack tip, material is purely elastic and we are way below yield ...
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### How do I show that there exists variational/action principle for a given classical system?

We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
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### Calculation of the maximum load to the bar

Looking for a way of calculating the maximum weight (W) to the rod with the given length (L) where the rod did not break and that only bend for (b) mm. Need only approximative solution (read: ...
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### Is there a valid Lagrangian formulation for all classical systems?

Can one use the Lagrangian formalism for all classical systems, i.e. systems with a set of trajectories $\vec{x}_i(t)$ describing paths? On the wikipedia page of Lagrangian mechanics, there is an ...
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### Why do control moment gyroscopes exhibit “torque amplification”?

There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
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### About constructing potential energy functions

There are many classical systems with different potential functions. My problem is that I do not understand how one can construct a certain potential function for a certain system. Are there any ...
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### What is the inertial frame that explains the Foucault Pendulum?

I know that the Foucault pendulum rotation in relation to Earth is a proof that the object is inertial in relation to the distant stars. But what makes them more important than the Earth? Are they an ...
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### Am I talking about the correct units here? [closed]

Paolo made a move I knew from dozens of townie soccer games played under lights on the fenced-in macadam pitch next to the elementary school in Badalucco, packed tight between Via Cristoforo Colombo ...
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### Rope wrapped around a cylinder

If a rope is wrapped aound a cylinder what is the relationship between the amount of wrap and the ability to resist slipping off of the cylinder? An example would be if I had a 180 degree wrap and ...
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### Origins of the principle of least time in classical mechanics

Is it possible to derive the principle of least time from the principle of least action in lagrangian or hamiltonian mechanics? Or is Fermat's principle more fundamental than the principle of least ...
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### How does Newton's 2nd law correspond to GR in the weak field limit?

I can only perform the demonstration from the much simpler $E = mc^2$. Take as given the Einstein field equation: $G_{\mu\nu} = 8 \pi \, T_{\mu\nu}$ ... can it be proved that Newton's formulation ...
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### how to represent the effect of linking rigid-bodies together?

I have 2 rigid-bodies (b1,b2) if i linked one to the other (as if they are conjoined together) , how to represent b1 effect on b2 and b2 effect on b1 Is there any LAW that affect the ...
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### The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available

If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
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### Problem based on Rotational Motion [closed]

A spool of mass $\mathsf m$ and inner radius $\mathsf r$ and outer radius $\mathsf{2r}$, having moment of inertia $\Large\mathsf{\frac{mr^2}{2}}$ is made to roll without sliding on a rough ...
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### Does mass affects accelleration of an object in a sloapy movement? [duplicate]

Possible Duplicate: Would a light or a heavy ball roll fastest down a slope? Is there a change of the accelleration of an object moving on a sloapy plane if the mass is changed?
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### How fast will the projectile go the second time?

Say I have a linear motor [aka rail-gun] and use a x amount of electrical power. I fire the gun and the object exits at velocity v. I then reuse the same object as my projectile and fire the ...
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### Do all closed systems, only considering kinematic/mechanical principles, exhibit time reversal symmetry?

It makes a lot of sense to me to imagine a cannonball flying through space as not so much experiencing a macroscopic non-conservative drag force, but as pushing a bunch of air molecules and giving ...
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### Why doesn't phase space contain acceleration/forces?

I'm watching some Physics lectures on the internet by Leonard Susskind: http://www.youtube.com/watch?v=pyX8kQ-JzHI&feature=BFa&list=PL189C0DCE90CB6D81&lf=plpp_video In this lecture, and ...
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### Distance a curveball travels?

I've seen some discussions regarding the movement of a spinning object, say a curveball. However, all have been largely qualitative. I was wondering if anyone has seen or worked through a ...
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### Violation of conservation of energy and potential energy between objects

I would like to clarify my question. I have numbered them to be independent questions For any conservative fields, $\vec{F} = -\nabla U$. Which means the restoring force is opposite to the ...
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### Rolling resistance and static friction

I am a bit confused about the relation between rolling resistance and static friction. I have often heard that it is the static friction that lets the wheel roll. Consider the following two cases: ...
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### Tolerance of Natural Frequency & Resonance?

I'm writing a report at the moment about natural frequency, driving frequency and resonance - and I was wondering, is there a typical % tolerance inside which the driving frequency will cause ...
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### Gears and efficiency/speed

For Christmas me and my brother got an AR Drone, the propellers are on a large gear, which is rotated by a small gear that is connected to the motor. This means the small gear (and therefore the ...
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### Does the potential energy of fluid rising on a string change?

Lets say I have a glass of water at rest. Then I go and hang a string above the water (vertically), such as the end of the string is immersed in the water. Over time some of the water is going to ...
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### Is it possible to break bulletproof glass with your voice?

In The Adventures of Tintin, an opera singer (the Milanese Nightingale) broke a bulletproof glass case using her voice. Is that scientifically possible? From the Wikipedia page, a typical bulletproof ...
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### Conjugate Variables and Fourier Transforms in Classical Physics

Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be ...
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### Determine the tensor of contraint and deformation of a cube under compression

We have a cube under compression with dimension l1*l2*l3, is put between 2 rigid plates in the axis 1 (two plates block the deformation of the cube in thí axis), the cube is also put on a rigid plate, ...
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### Question Based On Galileo's Law Of Falling Bodies

Galileo discovered that the distance fallen is proportional to the square of the time it has been falling.Why is it proportional to the square of the time and not just time? i.e $d \propto t^2$ why ...
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### How much effect does the mass of a bicycle tire have on acceleration?

There are claims often made that, eg, "An ounce of weight at the rims is like adding 7 ounces of frame weight." This is "common knowledge", but a few of us are skeptical, and our crude attempts at ...
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### Spin angular momentum of a system of particles : Is there any energy associated with it?

Consider a system of point particles , where the mass of particle $i$ is $μ_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the ...
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### Converting angular velocity to linear velocity through friction

A very basic question here; it's related to this one, but not quite the same. If a rotating rigid body (a sphere for the sake of discussion) with mass $m$, radius $r$ and inertial tensor $I$ has ...
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### Some questions about the logics of the principles of independence of motion and composition of motion

In high-school level textbooks* one encounters often the principles of independence of motion and that of composition (or superpositions) of motions. In this context this is used as "independence of ...
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### Calculating stress without strain

I am working on an algorithm for a real-time simulation. I would like to calculate to extremely permissive tolerances approximate values for the stress within a 2D geometry. It will not be difficult ...
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### Why do balls in a spinning ellipsoid move to the minor axis plane?

There is a question concerning the Physics of a small child's tall that has been bothering me for some time now. I have investigated this to a small degree, but I have not been able to find a ...