[tag:classical-mechanics] entails the study of the trajectory of bodies under the influence of forces. More specific subtopics are: [tag:newtonian-mechanics], [tag:lagrangian-mechanics], [tag:hamiltonian-mechanics] for point particles and [tag:fluid-dynamics], [tag:statistical-mechanics] and ...
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0answers
14 views
stable equilibrium in the system
I'm trying to understand the solution of the following problem.
A solid cube of uniform density and sides of b is in equilibrium on top of a cylinder of radius R. The planes of four sides of the ...
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1answer
24 views
Wave function interpretation $y(x,t) = (0.35m)\sin(10\pi t-3\pi x + \frac\pi{4})$
Wave function interpretation $y(x,t) = (0.35m)\sin(10\pi t-3\pi x + \frac\pi{4})$
I used to deal with function with one variable
And now theres are two, how can I interpret them?
Is $10\pi$ still ...
3
votes
2answers
49 views
Why are some jenga pieces easier to remove than others?
Jenga is a game place with wooden blocks stacked on top of one another in an alternating pattern. Players take turns removing blocks from any layer and placing them on top.
As the game progresses ...
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1answer
38 views
Another Inclined plane question
I did the FBD, and I found too many variables which are not eliminating...Moreover, I believe this question is based on kinetic and static friction. But, $\mu$ here is ambiguously defined...How Do I ...
-4
votes
1answer
43 views
Center of mass of three particles of masses 1kg, 2kg, 3kg lies at the point (1,2,3) [closed]
Center of mass of three particles of masses 1kg, 2kg, 3kg lies at the point (1,2,3) and center of mass of another system of particles 3kg and 2kg lies at the point (-1,3,-2).
Where should we put a ...
4
votes
1answer
59 views
Peculiar Hamiltonian Phase space
I was solving an exercise of classical mechanics :
Consider the following hamiltonian
$H(p,q,t) = \frac{p^2}{2m} + \lambda pq + \frac{1}{2}m\lambda^2\frac{q^6}{q^4+\alpha^4}$
Where ...
1
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0answers
42 views
Why is the angle of impact complementary to the angle of launch in the simple equations for the range of a projectile?
I'm using the standard equation for the range of a projectile:
\begin{align}
d &= \frac{v\ \text{cos}\theta}{g} \left( v\ \text{sin}\theta + \sqrt{v^2\ \text{sin}^2\theta + 2gy_0}\right)
...
3
votes
3answers
116 views
Physical interpretation of Poisson bracket properties
In classical Hamiltonian mechanics evolution of any observable (scalar function on a manifold in hand) is given as
$$\frac{dA}{dt} = [A,H]+\frac{\partial A}{\partial t}$$
So Poisson bracket is a ...
2
votes
1answer
62 views
Physics of a cold and hot top
Imagine two tops made up of exactly one thousand atoms. One is kept at 4 degrees Kelvin, the other at room temperature.
1. Would they weigh the same given an arbitrarily precise scale in the Earth's ...
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2answers
55 views
Constant of gravity in earth fixed coordinate system
I have this problem:
If the constant of gravity is measured to be $g_0$ in an earth fixed
coordinate system, what is the difference $g-g_0$ where $g$ is the
real constant of gravity as ...
1
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0answers
38 views
impulse problem [closed]
The figure above shows a plot of the time-dependent force $F_x(t)$ acting on a particle in motion along the x-axis. What is the total impulse delivered to the particle?
...
2
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1answer
37 views
Is there a typo in this modified Lennard-Jones potential?
The standard 12-6 Lennard Jones potential is given by
$$U(r_ij) = 4\epsilon\left[ \left(\frac{\sigma_{ij}}{r_{ij}}\right)^{12} - \left(\frac{\sigma_{ij}}{r_{ij}}\right)^{6} \right]$$
where ...
0
votes
1answer
42 views
Calculating the moment inertia for a circle with a point mass on its perimeter
I want to calculate the tensor of the moment of inertia. Consider this situation:
The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm ...
1
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0answers
16 views
Acceleration by spherical particles (micron-scale) by an external force
I am looking for an expression for the velocity of a micron sized (1 - 10 micron diameter) sized particles under accelerating forces.
I have aerosols in mind.
This is what I have in mind
The ...
0
votes
1answer
56 views
Why does Lagrangian of free particle depend on the square of the velocity ?
Why does Lagrangian of free particle depend on the square of the velocity ?
For example, $L(v^4)$ also doesn't depend on direction of $v$.
2
votes
1answer
52 views
Pendulum Wave Period
Recently I've seen various videos showing the pendulum wave effect. All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$.
I am trying to work out the relationship ...
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votes
1answer
53 views
Why is there no such thing as a body in a state of acceleration?
It appears that velocity is a quantity of motion meaning that all objects can have assigned to them a particular velocity. Through the application of forces (ex: gravity, E&m) we measure changes ...
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votes
1answer
39 views
Is this a correct interpretation of pressure?
So I am told that pressure = Force per Area --> F/A..
When considering the units of Force I find that force = kg * m/s^2
When considering the units of Area I find that area = m^2
Thus the units of ...
1
vote
2answers
56 views
How to determine a reaction force?
An object sits on an inclined plane. The weight of the object will have a normal and parallel component. I always thought that the reaction of the plane was simply the negative of the normal component ...
0
votes
1answer
51 views
Stopping distance of two objects with equal Kinetic Energy
I'm working on a problem regarding two objects with the same kinetic energy.
Two objects with masses of $m_1$ and $m_2$ have the same kinetic energy are both moving to the right. The same constant ...
10
votes
1answer
231 views
In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?
The Lennard-Jones potential has the form:
$$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$
The (attractive) $r^{-6}$ term describes the ...
-5
votes
0answers
48 views
Would there be any possibility for anyone to survive when a Boeing 747 crashes to pacific ocean with its normal cruising speed? [closed]
I know no case of anyone surviving when an aircraft of the size of Boeing 747 crashes to ocean with its normal cruising speed, but in physics sense, would there be any possibility of anyone surviving ...
1
vote
1answer
37 views
Finding the coffecient of restitution
A ball moving with velocity $1 \hat i \ ms^{-1}$ and collides with a friction less wall, afetr collision the velocity of ball becomes $1/2 \hat j \ ms^{-1}$. Find the coefficient of restitution ...
1
vote
1answer
73 views
Double Compound Pendulum: why use inertia about the center of mass for bottom pendulum?
I'm trying to wrap my head around the kinetic energy of a double compound pendulum, like the one shown in the Wikipedia article on double pendulums.
I know for computing the kinetic energy of the ...
0
votes
1answer
26 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 ...
2
votes
1answer
105 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 $n$ ...
-1
votes
1answer
90 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 ...
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4answers
118 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
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0answers
70 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 ...
0
votes
3answers
128 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 ...
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0answers
61 views
Small oscillations [closed]
I am asked to consider a fixed homogeneous rod of length $2L$ and mass density $\rho$ It is centered around $O$. A particle with mass M is moving in the same plane. The attractive force between the ...
4
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0answers
191 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, ...
1
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0answers
44 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
0answers
52 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 ...
1
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0answers
27 views
Doubling the energy of an oscillating mass on a spring [closed]
From this question:
Question 1.
What do we need to change in order to double the total energy of a mass oscillating at the end of a spring?
(a) increase the angular frequency by $\sqrt{2}$.
...
2
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1answer
62 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? ...
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2answers
47 views
Force applied in a body moving at high speed
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..?
2
votes
1answer
83 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
40 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 ...
0
votes
2answers
106 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
265 views
Goldstein's Classical Mechanics exercises solutions [duplicate]
Does anyone know where I can find some (good) solution of Goldstein's book Classical Mechanics?
1
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1answer
41 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
4answers
64 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 ...
2
votes
0answers
31 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 ...
3
votes
2answers
135 views
what's the physical significance of the off-diagonal element in the matrix of moment of inertia
In classical mechanics about rotation of rigid object, the general problem is to study the rotation on a given axis so we need to figure out the moment of inertia around some axes. In 3-dimensional ...
12
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1answer
230 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 ...
2
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3answers
138 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 ...
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1answer
55 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 ...
15
votes
5answers
273 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., ...
3
votes
2answers
76 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?
