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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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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8 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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23 views

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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35 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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1answer
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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6answers
97 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
30 views

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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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
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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8answers
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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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1answer
51 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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0answers
35 views

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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0answers
52 views

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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0answers
29 views

Find the angle of the projectile [on hold]

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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0answers
30 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
64 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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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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0answers
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
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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1answer
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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3answers
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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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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 ...
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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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2answers
78 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
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
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 ...
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0answers
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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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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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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1answer
81 views

How much force would it take for you stop the Moon from crashing into the earth once it has started to fall?

In my previous question, I asked how much force it would take to destabilize the Moon's orbit enough for the moon to start falling into the Earth and collide. Assume this has already happened. Now, ...
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1answer
28 views

How to calculate the pressure inside hose subjected to weight? (Example)

Example: Suppose we have a garden hose laid on a concrete floor. This garden hose is made out of rubber and is sealed on both sides. It is completely filled with water with no air bubbles whatsoever. ...
3
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3answers
45 views

If a bullet penetrates a bag, how come the repulsive force is constant?

I was doing a question on energy and forces, and it goes as follows:(Doesn't require knowledge of calculus): If a bullet with velocity $v$ penetrates a bag upto a distance $x$, then find the ...
1
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1answer
34 views

An impulse is given to a sphere out of the center?

I'm wondering what will happen if there is an impulse $J$ given to a sphere mass $M$ out of its center? I'm sure that it will rotate about the center, but what is its translational motion? It will ...
0
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1answer
35 views

Wind resistance [closed]

You have a metal plate/sign (max weight $5\, \text{kg}$) $1200\, \text{mm}$ long and $400\, \text{mm}$ high pivot/hinge at its base. A windspeed of $90 - 100\, \text{km/h}$ is applied to one face of ...
1
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0answers
26 views

How to calculate the torque of this example? [closed]

I was thinking a long time to solve this question .. I want to calculate the rope tension .. I want to use the torque to solve it .. What I managed to do is the following : $torque = ? - mg *cos(20) ...
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0answers
38 views

Higher order versions of momentum? Can conservation principles be established and used? [closed]

Question Can higher order derivatives of momentum be useful in creating theories of dynamics if they have conservation principles? Even if they aren't needed, could it be done in theory? For ...
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2answers
43 views

Intuition behind Airy waves dispersion relation

Using Airy wave theory, one can derive the dispersion relation of water waves (under some physical assumptions): $$ \omega^2 = gk\tanh{kh} $$ where $k$ is the wave number, $h$ the distance from the ...
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2answers
42 views

Motion of an object in a moving car and collison

I came across an interesting question today at work. 'Imagine traveling in a car. The passenger has a glass bottle in their hand. In which direction relative to the moving car should the passenger ...
2
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0answers
41 views

Kinetics of gas molecule [closed]

In the explanation of the nature of gases we use the kinetic formula $PV=1/3(mnc)$ where $p$ is pressure, $v$ volume, $m$ mass, $n$ number of molecules and $c$ means root mean square velocity. But in ...
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0answers
61 views

Clarification on conservation of energy for (or internal potential energy of) $N$ particle system

In Goldstein's Classical Mechanics, it says: Consider now the right-hand side of Eq. (1.29). In the special case that the external forces are derivable in terms of the gradient of a potential, the ...
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1answer
38 views

Complex Coordinate change

I have a simple question where I must change the coordinates of a system however I am unsure whether I am correct. I am changing from Cartisian to complex coordinates. Let's say I only have $x$ and ...
0
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0answers
22 views

Conservation of angular momentum in a system under torque

Let's say we have a particle $A$ like this which is located in the disk $c$. Consider that the particle itself is not moving, but in general it is constrained to the semicircle $d$, in that if it ...
3
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2answers
67 views

How can I use a magnet to lift a paperclip?

This question has been asked already, but no satisfying answer came up. All the answers seem to push the problem further, but do not explain clearly what is going on. I will reformulate it for a ...
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0answers
20 views

Will Energy and Work equal to each other between two closed systems linked by one shareable object?

Two closed systems are linked to each other. Both use same object. In one of this closed systems was spent energy to change physical property of shareable object. After this object transformation, ...
1
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3answers
211 views

Time derivative of a function in Phase Space

Consider a function $\mathcal{H}(q_i,p_i;t)$ such that it obeys the equation: $$ \frac{d\mathcal{H}}{dt}=\frac{\partial\mathcal{H}}{\partial t}$$ What does this equation imply (read: mean), ...
3
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2answers
100 views

What is the minimum force required to move this block

Please don't report. It's not a homework question. Yesterday on my physics test there was this question. there is a block of mass $m$ connected to a spring as shown in the figure. the spring constant ...