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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Equivalent spring-constant for infinite square grid of springs

Consider an infinite square grid, where each side of a square is a spring following Hooke's law, with spring constant $k$. What is the relation between the force and displacement between two points? ...
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4answers
890 views

Oscillate a swing without touching the ground

Is is possible to set a swing into oscillations without touching the ground? This occurred to me while watching the second pirates movie. There is a scene where the ship's crew is suspended in a cage ...
2
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1answer
340 views

Cheetah prosthesis efficiency

I want to compare the much-talked about Cheeta running prosthesis to a the normal running process in terms of force and energy, but I don't know where to start. How would you start the comparison? A ...
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3answers
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Why does the cart move? [duplicate]

A while ago someone proposed the following thought experiment to me: A horse attached to a cart is resting on a horizontal road. If the horse attempts to move by pulling the cart, according to the ...
6
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2answers
512 views

What are the normal modes of a vertical rope?

Closely related to this question on traveling waves on a hanging rope, I would also like to know what the normal modes are on a rope that hangs vertically, fixed at both ends. Tension in the rope ...
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2answers
367 views

Will a wave packet undergo dispersion when traveling down a hanging rope?

Suppose I tie one end of a rope to my ceiling and the other end to a spot on my floor directly underneath it. Because the rope has some mass, the tension varies along the rope, from highest at the ...
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5answers
345 views

Driving on snowy roads

'tis the season as they say! It seems to me obvious that it's better to drive in high gear on snowy roads to reduce the torque. However, there are completely opposite advices being given on ...
3
votes
4answers
529 views

Rolling stone on a frictional surface

Consider a spherical rigid stone rotating with angular velocity $\omega$ being dropped vertically onto a horizontal rigid surface with the coefficient of friction $\mu$. Can the stone roll on the ...
3
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3answers
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If a vehicle is rolling down a hill, will its speed depend on the size of the wheel?

If I am sitting on a skateboard and travel downhill, will the velocity depend at all on the size of the wheel? The skateboard is only powered by gravity. There are a lot of variables to consider. ...
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2answers
704 views

Does the cube stay on the loop-de-loop?

Suppose a cube of mass $m$ enters a loop-de-loop of radius $r$, travelling halfway around and reaching the top. At the top, it has velocity $v$, and the second half of the loop is frictionless. How ...
2
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2answers
507 views

Physics of a fixed wheel moving on a flat surface held at distance from a center point

Ok, so my boss is trying to make a car turntable. In essence, he has a two boards that sit atop a rotating ring. He wants to put two wheels at the end of each board (8 wheels total). He thinks that ...
3
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1answer
412 views

Soliton mechanics

How much of classical mechanics can be modelled with solitons? What I am aware of is that single solitons behave in a way like free particles: they move along as stable entities with constant ...
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10answers
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Mechanics around a rail tank wagon

Some time ago I came across a problem which might be of interest to the physics.se, I think. The problem sounds like a homework problem, but I think it is not trivial (i am still thinking about it): ...
2
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1answer
126 views

How long does it take a object captured by a star falling to the center?

If the captured object do not have tangential velocity, it's just the free-fall time. But when it has, it may take longer time to fall in, right ? The function should be $\ddot{r} = -GM/r^2 + ...
27
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8answers
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Classical mechanics without coordinates book

I am a graduate student in mathematics who would like to learn some classical mechanics. However, there is one caveat: I am not interested in the standard coordinate approach. I can't help but think ...
2
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1answer
857 views

Relation of angular speed of a rigid body to Euler's Angles

My Question was like this and i have realised few things and still have some doubts I have a book in which a paragraph goes like this Now, $\dot\phi$, $\dot \theta$, $\dot\psi$ are respectively ...
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4answers
1k views

How far does a trampoline vertically deform based on the mass of the object?

If a baseball is dropped on a trampoline, the point under the object will move a certain distance downward before starting to travel upward again. If a bowling ball is dropped, it will deform further ...
7
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6answers
1k views

Is rotational motion relative to space?

Let's assume that there is nothing in the universe except Earth. If the Earth rotates on its axis as it does, then would we experience the effects of rotational motion like centrifugal force and ...
13
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2answers
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Is kinetic energy a relative quantity? Will it make inconsistent equations when applying it to the conservation of energy equations?

If the velocity is a relative quantity, will it make inconsistent equations when applying it to the conservation of energy equations? For example: In the train moving at $V$ relative to ground, ...
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5answers
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What sustains the rotation of earth's core (faster than surface)?

I recently read that the earth's core rotates faster than the surface. Well, firstly, it's easier to digest the concept of planetary bodies, stars, galaxies in rotation and/or orbital motion. But, ...
9
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4answers
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Which is easier, pushing or pulling?

It is generally assumed, from a person's perspective, that pushing a cart is more easier than pulling one. But why? Is there any difference in terms of force required to achieve the same amount of ...
0
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2answers
615 views

Transmission of energy in medium and wave nature (periodicity)? [closed]

Is there any example of a transmission of energy in a medium that does not show wave nature?
11
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2answers
634 views

A problem inspired by the ice hockey game

Question shortly: How far would a hockey puck slide in two different cases: The puck is sliding (translation) on ice and spinning on its flat surface. The puck is sliding on ice without spinning. ...
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3answers
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Why is it hopeless to view differential geometry as the limit of a discrete geometry?

This is a follow-up question to Introductions to discrete space-time: Why is this line of thought hopeless? Classical mechanics can be understood as the limit of relativistic mechanics $RM_c$ ...
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2answers
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The Impossibility ( or Possibility) of Solving $N$-Body Problem

One can obtain the solution to a $2$-Body problem analytically. However, I understand that obtaining a general solution to a $N$-body problem is impossible. Is there a proof somewhere that shows this ...
9
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1answer
643 views

Coriolis force and Newton's third law

I would like to ask a stupid question here. If a body 'b' moving downward with a velocity v in a rotating frame of reference with angular velocity w, and w and v not being parallel and anti parallel. ...
11
votes
3answers
696 views

Which direction will Coriolis forces deflect a bubble?

If I throw a ball straight up, it deflects slightly to the west due to Coriolis forces. If instead I watch a bubble float up in water, is the bubble deflected west, east, or neither? I think the ...
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2answers
216 views

Gravity and Collision of two continuous mass distributions [closed]

How could one explain the collision of two continuous mass distributions in view of gravitation (Newtonanian and General relativity) ?
3
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1answer
313 views

Distinguishing mechanical systems from general dynamical systems

[Remark: I admit that my first attempt on What makes a space a real space? was rather ill-posed and led to some confusion. Sorry for that, but please give me a second try. Part of the confusion arose ...
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1answer
263 views

What makes a space a real space?

By "real space" I mean a space in which physical particles move. Consider a color sphere and let a bunch of objects "move" on its surface. "Move" means "change colors". Let there be some rules ...
12
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4answers
1k views

How to sail downwind faster than the wind?

Recently a group set a record for sailing a wind-powered land vehicle directly down wind, and a speed faster than wind speed. Wikipedia has a page talking about it, but it doesn't explain exactly how ...
11
votes
3answers
912 views

Imagine a long bar floating in space. What force does it exert on itself in the middle due to gravity?

Problem If you had a long bar floating in space, what would be the compressive force at the centre of the bar, due to the self-weight of both ends? Diagram - what is the force at point X in the ...
1
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1answer
2k views

What is the direction of the friction force on a rolling ball?

Suppose you have a solid ball on a horizontal table. What is the direction of friction force when the ball I pushed horizontally and starts rolling? Why is the direction of friction as it is? Which ...
57
votes
9answers
5k views

Is Angular Momentum truly fundamental?

This may seem like a slightly trite question, but it is one that has long intrigued me. Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...
6
votes
3answers
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Constraint force on a rod

I really hope someone will take a quick look at the following, I would just love to better understand it... This exercise is from Arnold's "Mathematical Methods of Classical Mechanics", p. 97 in the ...
4
votes
2answers
810 views

Question about moment of inertia and velocity

First off, I swear this is not homework. I'm doing some practice problems because I got an exam coming up. I'm stuck on this one: I figured I would use energy conservation for this problem. So since ...
24
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12answers
3k views

Will a ball slide down a lumpy hill over the same path it rolls down the hill?

Suppose I have a lumpy hill. In a first experiment, the hill is frictionless and I let a ball slide down, starting from rest. I watch the path it takes (the time-independent trail it follows). ...
2
votes
3answers
162 views

What condition is fulfilled by the path of a mass sliding down a lumpy hill?

Suppose I have a hill that goes up and down unevenly. It's frictionless, and I want to slide a point mass down the hill. I am interested in the path it takes. (By "path" I mean the trail it leaves ...
4
votes
4answers
677 views

Are the physical laws scale-dependent?

If you read the article "More Is Different", by P.W. Anderson (Science, 4 August 1972), you will find a deep question: are the physical laws dependent of the size of the system under study? As an ...
4
votes
3answers
389 views

How do molecules vibrate after collision?

The difference between kinematics and dynamics that Grisha pointed to in his answer comes up in a similar but slightly more complicated case: Consider (in 1D) two point-like particles connected by a ...
30
votes
17answers
3k views

Why does one experience a short pull in the wrong direction when a vehicle stops?

When you're in a train and it slows down, you experience the push forward from the deceleration which is no surprise since the force one experiences results from good old $F=m a$. However, the moment ...
1
vote
3answers
350 views

Where do atoms go after collision?

[I edited the question according to Mark's and Grisha's answers.] Consider two point-like particles of equal mass colliding centrally in 2D. The final directions of the momenta of the two particles ...
5
votes
1answer
711 views

Equilibrium and movement of a cylinder with asymmetric mass centre on an inclined plane

A cylinder whose cross section is represented below is placed on an inclined plane. I would like to determine the maximum slope of the inclined plane so that the cylinder does not roll. The mass ...
3
votes
1answer
570 views

Does the friction force change directions with a change in reference frame?

In a basic friction problem with Block A sliding on top of Block B, the direction of the friction force is usually explained as being simply the opposite of the direction of motion. So if Block A is ...
6
votes
6answers
1k views

Simple three-body-problem?

Consider the problem of three bodies two of which having mass M, one of them having mass m. Body m is in the middle between the other two, coupled to them by two equal linear springs in rest. Now fix ...
0
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4answers
1k views

4th equation of motion

Ive been given the 4 equations of motions The fourth being: $$s=ut+\frac{1}{2}at^2$$ If rearranged it forms the quadratic equation $$at^2+2ut-2s=0$$ But that means that t has 2 values. Will ...
1
vote
5answers
565 views

Why do we automatically assume that the velocity vector $\vec{v}$ and location vector $\vec{r}$ are independent?

I'm not sure if it's relevant, but I'm talking about a situation where a particle is moving in an electro-magnetic field. As I understand, if we see the term $\nabla \cdot \vec{v}$ or $\nabla \times ...
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votes
2answers
5k views

Period of Precession [closed]

I'm trying to find the period of precession for a gyroscope. Now I was able to find the angular precession rate, which was 1.132 rad/s, but I have no idea how to convert this to a 'period', and google ...
0
votes
2answers
316 views

Angular Momentum and Force [closed]

I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not ...
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2answers
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Angular Momentum and Average Torque

Refer to number 6. This is the one I'm stuck on. So angular momentum is conserved right, so initial angular momentum is equal to final angular momentum. Initial is 7.87 so final must be 7.87, right? ...