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; ...

learn more… | top users | synonyms (1)

1
vote
1answer
116 views

Forces and angles

"The little ball with the mass of 100g has gotten stuck in a chute as depicted in the picture. What forces, and how large are they, that are acting on the ball?" This is how I solve it: I find ...
4
votes
1answer
669 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
-2
votes
1answer
705 views

Confusions about rotational dynamics and centripetal force

I am a high school student. I am having confusions about the centripetal force and rotational motion . I have known that a body will be in rest or in uniform velocity if any force is not applied. But ...
0
votes
3answers
335 views

How to create frame of reference?

Is this possible to create a inertial frame of reference in the earth? How it is possible?
1
vote
2answers
1k views

A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
1
vote
0answers
524 views

Torque, lever and mass

The Force used in a catapult is exerted near its axis. If we double the length of the arm of the catapult, but still use the same Force at the same point as before near the same axis, does the ...
2
votes
2answers
676 views

How do centripetal forces and gravity work for objects in a rotating cylinder?

The following is a question from a past exam paper that I'm working on, as I have an exam coming soon. I would appreciate any help. A fairground ride takes the form of a hollow, cylinder of radius $...
2
votes
3answers
1k views

Why does a rod rotate?

I'm a physics tutor tutoring High School students. A question confused me a lot. Question is: Suppose a mass less rod length $l$ has a particle of mass $m$ attached at its end and the rod is ...
5
votes
3answers
1k views

Does more rain strike a vehicle while moving or while stopped (or neither)? [duplicate]

Assume there is a rainstorm, and the rain falling over the entire subject area is perfectly, uniformly distributed. Now assume there are two identical cars in this area. One is standing still, and ...
4
votes
3answers
657 views

$\hbar \rightarrow 0$ in quantum mechanics

We often see a limit $\hbar \rightarrow 0$ in quantum mechanics and sometimes it's related with symmetry breaking. Can someone briefly write the story behind this limit?
10
votes
0answers
341 views

Extended Born relativity, Nambu 3-form and ternary (n-ary) symmetry

Background: Classical Mechanics is based on the Poincare-Cartan two-form $$\omega_2=dx\wedge dp$$ where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. By the other hand, ...
2
votes
0answers
132 views

Closed-form equation for orientation and angular velocity over time

If a rigid body, rotating freely in 3d, experiences no friction or other external forces and has an initially diagonal inertia matrix $\mathbf{I}_0$ (with $I_{11}>I_{22}>I_{33}>0$) and ...
4
votes
4answers
476 views

Would a phone move upon vibration in a completely uniform situation?

I was sitting down yesterday and saw my phone vibrate on a side, and it moved about a centimetre per vibration. I wondered why it moves, and thought perhaps that the side it was on had a slight slope,...
-1
votes
1answer
3k views

Standing Waves: finding the number of antinodes [closed]

A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is ...
0
votes
2answers
6k views

Calculating phase difference of sound waves

An observer stands 3 m from speaker A and 5 m from speaker B. Both speakers, oscillating in phase, produce waves with a frequency of 250 Hz. The speed of sound in air is 340 m/s. What is the phase ...
4
votes
1answer
124 views

Scaling arguments for the Contact mechanics between two elastic spheres

I am studying a bit granular dynamics and I have seen that two spheres of radius $R$ in contact with a contact area of radius $a$ would need an applied force $F$ on this two spheres that is nonlinear ...
6
votes
2answers
1k views

Invariance, covariance and symmetry

Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from quantum field theory? Thanks!...
-2
votes
2answers
88 views

Force applied in a body moving at high speed [closed]

Consider a rod of length $l$ and uniform density is moving at high speed. I want to deflect the rod where should I need to apply the minimum force, so that the rod is deflected..?
3
votes
1answer
1k views

Statics of Rigid Bodies — Can there be two possible solutions?

I've been working on a question and there seem to be two possible solutions. My own solution does not match the one given in the book. However, after resolving forces and taking moments with both ...
2
votes
0answers
59 views

When can a center of mechanical momentum frame be found for an electromagnetic system?

In classical mechanics, a center of mechanical momentum frame can always be found for a system of particles interacting with one another locally. For an electromagnetic system where the charges ...
2
votes
2answers
859 views

Geometrical interpretation of complex eigenvectors in a system of differential equations

Let's consider a system of differential equations in the form $$\dot{X} = M X$$ in two dimensions ($X = (x(t), y(t))$). In the case that $M$ has real values, it is easy to give a geometric ...
0
votes
1answer
6k views

Goldstein's Classical Mechanics exercises solutions [duplicate]

Does anyone know where I can find some (good) solution of Goldstein's book Classical Mechanics?
3
votes
2answers
173 views

Friction on roads

I have a question with which I am having trouble. A 71m radius curve is banked for a design speed of 91km/h. Given a coefficient of static friction of 0.32, what is the range of speeds in which a car ...
1
vote
1answer
705 views

what's the center of mass for triatomic-molecule system

My text use the following example to explain the center of mass. There are three balls (mass $m$) sitting in the origin, at $x=l$ and $x=2l$, each two mass are connected with a spring of constant $k$. ...
1
vote
3answers
115 views

is frictional force right or wrong

an experiment to disprove the statement--"frictional force is irrespective of the surface area in contact." take a x rs note. fold it in a half and put it in the pocket of a shirt. then invert the ...
3
votes
1answer
159 views

When is classical mechanics valid for describing motion of atoms?

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 $$...
15
votes
2answers
490 views

Classical results proved using quantum mechanics

Are there any results in classical mechanics that are easier to show by deriving a corresponding result in quantum mechanics and then taking the limit as $\hbar\rightarrow0$? (Are there classical ...
3
votes
3answers
967 views

Lagrangian mechanics and time derivative on general coordinates

I am reading a book on analytical mechanics on Lagrangian. I get a bit idea on the method: we can use any coordinates and write down the kinetic energy $T$ and potential $V$ in terms of the general ...
2
votes
2answers
2k views

Whats the anti-torque mechanism in horizontal take-off aircraft?

In most helicopters there is the anti-torque tail rotor to prevent the body from spinning in the opposite direction to the main rotor. What's the equivalent mechanism in horizontal takeoff single ...
0
votes
1answer
144 views

Hollow stone columns provide more support?

In history class in elementary school I remember learning that the Greeks would build their stone columns hollow because they thought this provided more support. Is it true that a hollow column is ...
16
votes
5answers
444 views

Does the mass point move?

There is a question regarding basic physical understanding. Assume you have a mass point (or just a ball if you like) that is constrained on a line. You know that at $t=0$ its position is $0$, i.e., $...
4
votes
3answers
337 views

Runge-Lenz vector and Keplerian Orbits

Is the loss of closed Keplerian orbits in relativistic mechanics directly tied to the absence of the Runge-Lenz vector?
0
votes
1answer
7k views

Finding the acceleration at an angle

"What's the maximum acceleration you can achieve in a a water-slide at a 34 degree angle (If you can't use your arms and legs)"? This is the free-body-diagram that I drew, assuming $g = 10m/s^2$: ...
4
votes
2answers
413 views

Higher order covariant Lagrangian

I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at Klein-...
1
vote
2answers
304 views

Resolution of vectors

What is the fundamental basis of resolution of vector. Suppose we have a vector $\vec{mg}$, now we resolve it into two components, horizontal and vertical. My question is what is the basis for telling ...
5
votes
2answers
277 views

Hooke's Law, Phase Space and Classical Geometry

Hooke's Law tells us that $m\ddot{x} = -kx$. We can apply the chain rule to rewrite $\ddot{x}$ as follows: $$\frac{\operatorname{d}\!^2x}{\operatorname{d}\!t^2} = \frac{\operatorname{d}\!v}{\...
3
votes
2answers
2k views

Is a heavier skier faster? [duplicate]

Is it true that a heavier skier goes faster? If it is, why is that? My intuition would be that the speed gained by a skier should be independent from its mass, since both its acceleration and the ...
4
votes
1answer
222 views

(Re-)use of a space elevator (basic mechanics and potential energy source)

It's said that if a space elevator were made then it would be much more efficient to put objects in orbit. I've always wondered about the durability of a space elevator though. I don't mean the ...
34
votes
4answers
7k views

What's the real fundamental definition of energy?

Some physical quantities like position, velocity, momentum and force, have precise definition even on basic textbooks, however energy is a little confusing for me. My point here is: using our ...
0
votes
2answers
823 views

FWHM in resonance amplitude square derivation

Consider a linear harmonic oscillator subject to a periodic force: $$ \ddot x + 2 \beta \dot x + \omega _0 ^2x = f_0\cos \omega t$$ The solution tends to: $$A \cos (\omega t - \delta)$$ where: $$...
5
votes
1answer
318 views

Mechanical shock resistance as a function of shape

I have a system where I'm dropping glass tubes filled with some sample from a certain height, along a track. I can apply a back-pressure of air to push them down faster, and in general the faster they ...
4
votes
2answers
483 views

Conservation of Linear Momentum at the point of collision

This is a pretty basic conceptual question about the conservation of linear momentum. Consider an isolated system of 2 fixed-mass particles of masses $m_1$ and $m_2$ moving toward each other with ...
1
vote
2answers
417 views

effect of vertical collision on kinetic friction and subsequent change in horizontal velocity

Suppose somehow a block of mass $m$ is moving on ground, and the coefficient of kinetic friction between the block and the block is $\mu_k$. If I drop a tennis ball(of same mass) on it from a height, ...
0
votes
4answers
2k views

How do you tell what forces do no work?

The total mass of the children and the toboggan is 66 kg. The force the parent exerts is 58 N (18 degrees above the horizontal). What 3 forces/ components do no work on the toboggan? I said the ...
2
votes
1answer
208 views

Is there a geometrical way to obtain a relationship between these vectors?

Suppose we have a setup like this. Here $a_1,a_2,b_1,b_2$ are acceleration magnitudes($b_1,b_2$ being relative) and $P,Q,R,S$ are not pulley/blocks but are points on the rope. If I use a geometrical ...
5
votes
1answer
874 views

Intuition behind classical virial theorem

I am continuing to brush up my statistical physics. I just want to gain a better understanding. I have gone through the derivation of the classical virial theorem once more. I have thought about it, ...
3
votes
1answer
479 views

Intuition behind Work

I have a doubt in understanding the intuition behind the concept of work. First of all, I think this isn't duplicate, I've searched on the site, and the closest thing I've found was this post which is ...
12
votes
1answer
524 views

Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
8
votes
6answers
16k views

Why does higher acceleration minimize a car's fuel consumption?

I generally try to optimize my car's fuel consumption when driving, using my car's real-time MPG gauge and average-trip MPG indicator. Until recently, I believed the slower the acceleration, the ...
1
vote
1answer
95 views

kinetic energy of the stone

Suppose we have a man traveling in an open car (roof open) with speed $v$ towards right (man faces right). He throws a stone (mass $m$) towards right, in his frame-forward with speed $V$. In the ...