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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Connected Rods Mechanics

Consider three homogeneous rods, each of mass $m$, length $2l$ and moment of inertia $I$, connected by friction free joints at $B$ and $C$. The rods and joints are all moving without friction on a ...
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Why is it possible to drive a nail into a piece of wood with a hammer, but it is not possible to push a nail in by hand?

It is possible to drive a nail into a piece of wood with a hammer, but it is not possible to push a nail in by hand. Why is this so?
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Origin of spin and direction in the magnus effect

If you solve the Bernoulli equation: $$p=p_0-\rho_0{v^2 \over 2}$$ using a complex flow potential for a flow around a cylinder: $$W(z)=v_0 z + {v_0 R^2 \over z} - {\Gamma \over 2 \pi } \ln(z)$$ you ...
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3answers
44 views

Harmonic oscillator with squared damping term

Does a solution exist for a harmonic oscillator with a squared damping term? $$m\ddot{u}+c\dot{u}^2+ku=0$$
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2answers
3k views

Finding angular acceleration from torque

We have to analyze this video Givens: An applied net torque due to the wind on the windmill is equal to 1500 N*m. Each (of the 3) propeller props weighs approximately 45 Kg and has a Moment of ...
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Projectile Motion with Air Resistance and Wind

I am wondering how the general kinematics equations would change in the following situation. If an object were fired out of a cannon, or some sort of launcher, so that it had both an initial velocity ...
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1answer
15 views

Phase Portraits Given Hamiltonian

Given a Hamiltonian say $$ H = 5p^2 $$ What is the correct procedure for producing a phase portrait. My initial thoughts were to solve the system of equations $\frac{dq}{dt} = 0$ and $\frac{dp}{dt} ...
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225 views

A column falls, how will it break?

I'm not expecting a definitive answer. But I would like someone to explain which are the main forces that interact in this situation: An ideal cylindrical column that is at first vertical is pushed ...
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9 views

Impulse response of coupled oscillators

The behaviour of a LTI system can be described entirely by it's impulse response. Imagine the following coupled pendulums have no friction losses. They will have 2 resonant frequencies, one for when ...
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125 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and ...
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Classical Quantum or Relativistic?

An ensemble contains free electrons at 10^3 electrons per m^3 at 10^7 K. What can this ensemble be treated as: a Classical Quantum or Relativistic gas or in some overlapping domain?
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25 views

Energy method to solving equations of motion? Why does this method work and what is it called?

Given the stated system in the photo we are suppose to prove simple harmonic motion when given an initial displacement $x$ I first considered the total energy of the system which we will call $H$ ...
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2answers
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Equivalent spring constant of setup

A mass $M$ is suspended using two springs having spring constant $k_{1}$ & $k_{2}$ with distance from mass as $a$ & $b$ respectively. Find equivalent spring constant of system. So I ...
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6answers
98 views

When we write that $F = -\nabla V$ , what would happen if we ommit the (-) minus sign

I have had this question for a long time. In classical mechanics, if we choose $\mathbf F = -\mathbf \nabla \, V,$ with the minus sign, we can proof the work - kinetic energy theorem. What are the ...
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2answers
593 views

Isolated and non-isolated systems: Momentum?

I'm having a difficult time understanding why two billiard balls colliding is an isolated system, yet a car crashing into a wall is a non-isolated system. Does it really only have to deal with the ...
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1answer
21 views

Diagonal of a thin rectangular foil, inertial principal axis?

I'd like to know if the diagonal of a thin foil is an inertial principal axis. I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a ...
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1answer
31 views

Can point mass have vibrational motion?

Can a point mass have vibrational motion. I have read that reason for point mass is to ensure that we can idealize translational motion and don't have to worry about rotational and vibrational motion. ...
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1answer
511 views

Classical limit of the path integral formulation of quantum mechanics

It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the ...
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1answer
52 views

1kg mass impacting at half light speed - effects?

Such a mass would have kinetic energy approximating a 1 mega-tonne thermonuclear weapon. So, what would such an object do if it hit the Earth? We know how destructive such an energy release can be, ...
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Elastic collision / relative velocity problem [on hold]

I'm having some trouble with a homework exercise and I'd really appreciate some help! I've done the first part correctly (according to the solution sheet), but I can't seem to get the second part ...
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Undergraduate Physics Senior Research Topic (Theory/Mathematical Physics Based) [on hold]

This is most likely a question for those who have experience/knowledge of theoretical/mathematical physics at the graduate level and can provide recommendations following my criteria. Here is some ...
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4answers
86 views

Intuitive explanation of $1/2(at^2)$ motion equation?

The full equation $$ Xf = X_o + V_o t + \frac{at^2}{2} $$ is integrated from the velocity function (which was integrated from constant acceleration function), right? The problem is, I can't seem to ...
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43 views

How does the gradient operator pick up a minus sign when the reference frame is switched from one particle to another? [closed]

A potential between two particles, $i$ and $j$, is given as a function only of the separation distance, $$V_{ij} = V_{ij}(|r_i − r_j|)$$ It should follow that the force by $j$ on $i$ is equal and ...
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0answers
29 views

Find the angle of the projectile [closed]

Given: Hmax = 2 * Range Find the angle of the projectile. After using the formula for both Hmax and Range, I got an angle of 74.69 if I am not mistaken. On the math exam teacher said the answer ...
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3answers
723 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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187 views

Problem in Euler-Lagrange imply Newton

I'm self-studying Mechanics and I have a little problem: We can see that in Landau's book or in Wikipedia that when we inject the lagrangian in Euler Lagrange equation the term $\frac{\partial ...
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31 views

Showing the relationship between focal ratio and brightness [closed]

I have an optics question that I have been stuck on for a few days now and I really need some guidance. Any help is appreciated! Question: The f-number (focal ratio) of a lens is the ratio of a focal ...
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1answer
234 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
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2answers
254 views

Does a simple double pendulum have transients?

Suppose, we have the most simple double pendulum: Both masses are equal. Both limbs are equal. No friction. No driver. Arbitrary initial conditions (no restriction to low energies) Does this ...
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2answers
41 views

What is the difference between vortexing and centrifuging?

I understand that vortexing will result in mixing / re-suspension of particles, and that centrifugation will result in the separation of particles. However, what is the difference in the physics that ...
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1answer
65 views

How does the Moon influence atmospheric pressure?

I have just read in the Telegraph an article entitled Moon overhead makes rainfall lighter, scientists conclude. In that article there is the following statement: When the moon is overhead, its ...
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3answers
3k views

Why do we travel in a circle along the Earth?

I know that in order to travel in a circle I have to have a net centripetal force $F=mv^2/r$. I also know that my normal force and gravitational force cancel. How, then, am I traveling in a circle ...
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22 views

Why a wave, travelling in a lighter medium, inverts upon reflection from an interface of a denser medium? [duplicate]

As exactly the title says: Why a wave, traveling in a lighter medium, inverts upon reflection from an interface of a denser medium ? What are the things that go on at the interface ?
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44 views

Motion of Particle due to Lorentz Force

So my professor gave us the following question: A particle with electric charge $Q$ and mass $M$ is initially traveling with velocity $v_0$ in the $x$ direction at time $t= 0$. There is a constant ...
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3answers
43 views

Direction of velocity and acceleration for a pendulum [duplicate]

The image below shows the direction between acceleration and velocity change with time. But it seems to me that the direction is not opposite. Can you please see and tell if this is correct?
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2answers
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How to model/simulate pressures and flows in a network of pipes

I'm having a hard time finding information on how to model/simulate this. I attached a couple files, both of which show an example tank & pump network. It's just nonsense that I made up for this ...
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4answers
153 views

Regarding the usage of 'classical potentials' in quantum mechanics

I am familiar with basic quantum mechanics and I know that there is no concept of 'force' in quantum mechanics, unlike in classical mechanics. Problems in quantum mechanics are solved by writing down ...
3
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2answers
79 views

Again, why is kinetic energy and velocity independent of position coordinates in Cartesian coordinates [duplicate]

This might be a very simple question. I read one previous post Can the kinetic energy be a function of the position vector? I know that in Cartesian coordinates, the kinetic energy ...
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1answer
12 views

Angular velocity when a rod inclined to a wall slips and its subsequent motion observed from the axis of rotation

When a rod inclined to a wall slips, rate of change of which angle does the angular velocity represent? Is it the rate of change of angle with which the rod is inclined to the horizontal ? I'm not ...
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1answer
43 views

Equivalent spring constant of an nth order system [closed]

I am looking for the spring constant of this below diagram I think the solution will look something like this But I am looking for more like a generalized formula. Any help is appreciated. Also ...
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1answer
43 views

Why does quantum mechanics produce different predictions for Bell test experiments than classical mechanics?

I understand that experimental results from Bell test experiments have shown that measured correlation is a cosine function of the angle between the detectors. What I am struggling to grasp is why ...
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3answers
454 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
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3answers
32 views

Effect of internal force on the weight of an object

A man is holding a closed cage on the palm of his hand with a bird in it. When the bird flies with an upward acceleration inside the cage, it feels heavier. But the force due to the bird in the cage ...
3
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3answers
104 views

What is the point of complex fields in classical field theory?

I see a lot of books/lectures about classical field theory making use of complex scalar fields. However why complex fields are used in the first place is often not really motivated. Sometimes one can ...
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3answers
898 views

Boundary layer theory in fluids learning resources

I'm trying to understand boundary layer theory in fluids. All I've found are dimensional arguments, order of magnitude arguments, etc... What I'm looking for is more mathematically sound arguments. ...
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1answer
126 views

Consistent method for finding direction of static friction

I am having trouble coming up with a consistent method of determining the direction of static friction. So far the best I have come up with is: it should oppose the relative acceleration the contact ...
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2answers
27 views

Balancing Utensils: Center of Mass

If you have a cork piece on top of a nail, it is extremely hard to keep it stable, and the slightest action will make the cork fall off. However, when you balance it on top of a nail but put forks ...
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1answer
40 views

Why does the energy of the mechanical wave depend on frequency but the EM wave does not?

Why does the energy of the mechanical wave depend on frequency but the EM wave does not? Are there any implications?
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1answer
209 views

Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...
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2answers
301 views

Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...