[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 ...
2
votes
1answer
133 views
What is actually a resonating vibration and resonance?
What is actually a resonating vibration and resonance?
I have searched many books and made Google search too but couldn't understand it clearly.
3
votes
2answers
44 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 ...
3
votes
3answers
795 views
Could life survive a pole shift caused by an asteroid collision?
Could life on earth survive a large pole shift caused by an asteroid collision?
I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational ...
2
votes
1answer
61 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 ...
0
votes
1answer
36 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 ...
0
votes
2answers
104 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 ...
-4
votes
1answer
42 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
2answers
795 views
Rigid body dynamics joints
I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
4
votes
1answer
437 views
What are examples of classical physical systems having polynomial observables of degree greater than 2?
Specifically: What are empirically well-understood examples of (integrable) Hamiltonian systems whose Hamiltonians include polynomial expressions, in the canonical coordinates $\{q^i,p_i\mid ...
4
votes
1answer
58 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 ...
0
votes
3answers
2k views
Difference b/w Kinetics & Kinematics w/concrete example
(I know whether I understand this or not doesn't matter much to my work & study but am just curious.)
I still can't differentiate in my head kinetics and kinematics (similar thread is found but ...
1
vote
0answers
40 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
113 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 ...
0
votes
2answers
51 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 ...
20
votes
4answers
746 views
Is there a Lagrangian formulation of statistical mechanics?
In statistical mechanics, we usually think in terms of the Hamiltonian formalism. At a particular time $t$, the system is in a particular state, where "state" means the generalised coordinates and ...
1
vote
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?
...
0
votes
3answers
3k views
Yield Strength versus Ultimate Strength
What is the qualitative difference between these two:
As seen on the table Typical yield and ultimate strengths.
I am trying to resolve the meaning of the phrase "contact yield stress" from C. ...
2
votes
1answer
35 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
40 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
vote
0answers
15 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
75 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 ...
2
votes
1answer
102 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 $n$ ...
4
votes
1answer
92 views
Liouville's theorem and gravitationally deflected lightpaths
It is customary in gravitational lensing problems, to project both the background source and the deflecting mass (e.g. a background quasar, and a foreground galaxy acting as a lens) in a plane.
Then, ...
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 ...
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 $v$.
10
votes
1answer
220 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 ...
-2
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 ...
0
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 ...
6
votes
2answers
585 views
Can a force in an explicitly time dependent classical system be conservative?
If I consider equations of motion derived from the pinciple of least action for an explicilty time dependend Lagrangian
$$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$
under what ...
0
votes
1answer
103 views
Do all black holes spin in the same direction?
My question is as stated above, do all black holes spin the same direction?
To my knowledge, the spin in the direction of the spin of the matter that created them. Another similar question was asked ...
1
vote
2answers
52 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
48 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 ...
-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
66 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 ...
1
vote
5answers
221 views
Are Uncertainties in Measurements Important?
In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is ...
0
votes
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
votes
1answer
87 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 ...
1
vote
1answer
845 views
Dimensional Analysis: Buckingham Pi Theorem
I am studying for a fluids quiz and I am having a few problems relating to dimensional analysis but for the time being fundamentally I have a problem selecting the repeating variables. Like does ...
1
vote
0answers
68 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 ...
3
votes
1answer
173 views
Can I find a potential function in the usual way if the central field contains $t$ in its magnitude?
I'm working on a classical mechanics problem in which the problem states that a particle of mass $m$ moves in a central field of attractive force of magnitude:
$$F(r, t) = \frac{k}{r^2}e^{-at}$$
...
4
votes
0answers
51 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 ...
0
votes
3answers
125 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 ...
4
votes
0answers
190 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
vote
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 ...
0
votes
0answers
60 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 ...
2
votes
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? ...
1
vote
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 $\sqrt{2}$.
...
0
votes
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..?
