Tagged Questions

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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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) ...
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3answers
1k 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 ...
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1answer
81 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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1answer
105 views

Calculating how a polygon bounces off a plane

I'd like to calculate how polygons bounce off a plane. In this picture, the square doesn't bounce straight up, but instead it bounces somewhat to the right and starts spinning. But I have no idea ...
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2answers
328 views

Row of pivoted magnets and energy scale

This question is about a system involving a horizontal row of length L of equally spaced pivotable magnets, each with a pole at either end. These magnets will often be referred to as units. So each ...
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2answers
113 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 ...
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1answer
102 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? ...
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1answer
130 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 ...
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1answer
553 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 ...
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6answers
718 views

Is there a momentum for charge?

Since mass and charge behave similarly, so, just like center of mass, I define a point center of charge, that is defined by $$\vec r_{qm} = \frac {\sum{q_i \vec r_i}} {\sum{q_i}}$$ where $\vec r_i$ ...
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0answers
42 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 ...
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2answers
189 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 $v$.
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2answers
303 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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1answer
144 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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1answer
50 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 ...
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1answer
100 views

What lifting mechanism is likely to have the best energy recovery ratio? [closed]

Suppose I was designing an apparatus which needed to lift 250kg 5cm high, hold it there for a few seconds, and then lower the object back to the original height. Such a process would need to be ...
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2answers
501 views

Hamiltonian of Harmonic Oscillator with Spin Term

We have the usual Hamiltonian for the 1D Harmonic Oscillator: $\hat{H_{0}}=\frac{\hat{P^2}}{2m} + \frac{1}{2}m \omega \hat{X^2}$ Now a new term has been added to the Hamiltonian, $\hat{H} = ...
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2answers
4k 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 ...
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2answers
1k 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 ...
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1answer
975 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 ...
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1answer
2k views

Floating Objects and Weight

The Situation: A ball is placed in a beaker filled with water and floats. It is also attached to the bottom of the beaker via a string. The Question: The ball is attached to the beaker, thus ...
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1answer
78 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 ...
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1answer
440 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 ...
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1answer
80 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 ...
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1answer
394 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 $n$ ...
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1answer
433 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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3answers
180 views

How to create frame of reference?

Is this possible to create a inertial frame of reference in the earth? How it is possible?
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2answers
403 views

A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
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0answers
268 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 ...
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2answers
327 views

How do centripetal forces and gravity work for objects in a rotating cylinder?

The following is a question from a past exam paper that I'm working on, as I have an exam coming soon. I would appreciate any help. A fairground ride takes the form of a hollow, cylinder of radius ...
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3answers
695 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
3answers
454 views

Does more rain strike a vehicle while moving or while stopped (or neither)? [duplicate]

Assume there is a rainstorm, and the rain falling over the entire subject area is perfectly, uniformly distributed. Now assume there are two identical cars in this area. One is standing still, and ...
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0answers
270 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, ...
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0answers
114 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 ...
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4answers
210 views

Would a phone move upon vibration in a completely uniform situation?

I was sitting down yesterday and saw my phone vibrate on a side, and it moved about a centimetre per vibration. I wondered why it moves, and thought perhaps that the side it was on had a slight ...
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0answers
93 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 ...
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0answers
195 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
481 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
74 views

Force applied in a body moving at high speed [closed]

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..?
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1answer
619 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
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0answers
56 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 ...
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2answers
411 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 ...
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1answer
3k views

Goldstein's Classical Mechanics exercises solutions [duplicate]

Does anyone know where I can find some (good) solution of Goldstein's book Classical Mechanics?
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2answers
156 views

Friction on roads

I have a question with which I am having trouble. A 71m radius curve is banked for a design speed of 91km/h. Given a coefficient of static friction of 0.32, what is the range of speeds in which a car ...
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1answer
251 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 $k$. ...
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3answers
110 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 ...
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1answer
130 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 ...
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2answers
397 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 ...
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3answers
455 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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2answers
1k views

Whats the anti-torque mechanism in horizontal take-off aircraft?

In most helicopters there is the anti-torque tail rotor to prevent the body from spinning in the opposite direction to the main rotor. What's the equivalent mechanism in horizontal takeoff single ...