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; ...

learn more… | top users | synonyms (1)

2
votes
0answers
115 views

Surface normal on the earth to the sun at a given point in time

How complicated is it to calculate a surface normal on the spherical approximation of the earths surface pointing towards the sun at a given point in time? What I try do is to highlight a small area ...
7
votes
1answer
1k views

How did Feynman derive the physics of medallion vs. plate wobble rate?

I am referring to this: Within a week I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red ...
3
votes
2answers
398 views

Why does $\frac{\partial \mathbf{v}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$?

Why is the following equation true? $$\frac{\partial \mathbf{v}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$$ where $\mathbf{v}_i$ is velocity, $\mathbf{r}_i$ is the ...
2
votes
2answers
5k views

Normal force: up or down?

The normal force obviously always has direction perpendicular to the surface of contact, but I'm a bit confused about its sense: is it going 'up' or 'down'? I've seen articles on the web that describe ...
3
votes
1answer
600 views

Energy of a rotating disc around different moments of inertia

Lets take a disc that is rolling without slipping which has moment of inertia $I=kmR^2$. It will have total kinetic energy $E=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2=\frac{1}{2}mv^2(1+k)$. Lets now use ...
3
votes
2answers
2k views

How do you calculate potential energy given a force that is dependent on time?

The restoring force of a spring is F(x) = -k(x-x0)exp(-t/T) where k and T are constants, x is the position of a mass on the spring, and x0 is the position of equilibrium of the spring. How do you ...
1
vote
1answer
315 views

Modellng mechanical behavior of heat shrink film

Consider a heat shrink film (as used in shrink sleeves that decorate plastic or glass bottles). These materials are produced by blow extrusion. When the film is heated (hot steam, hot air or ...
3
votes
2answers
416 views

How did L.H. Thomas derive his 1927 expressions for an electron with an axis?

I'm looking at the 1927 paper of Thomas, The Kinematics of an Electron with an Axis, where he shows that the instantaneous co-moving frame of an accelerating electron rotates and moves with some ...
6
votes
1answer
543 views

Circular motion when F=ma'

I apologize in advance if this question is deemed too general or too similar to this and this question. How would mechanics be different if $F=mx'''$ instead of $F=ma$? I feel like I have ...
10
votes
2answers
863 views

If the Earth didn't rotate, how would a Foucault pendulum work?

How does the Foucault pendulum work exactly, and would it work at all, if the Earth didn't rotate?
9
votes
5answers
5k views

Why Do Hurricane Balls Spin So Fast?

I was wondering if anyone could offer an explanation as to why the balls described in this video spin so fast. Here's the setup: Two metal balls are wielded together. When spun with air, they ...
2
votes
1answer
148 views

Confusion with the torque

Consider an imaginary vertical plane. Now say, a body is falling freely (under earth's attraction). If you consider any axis that is perpendicular to that plane. We get a non-zero value for torque. ...
2
votes
1answer
915 views

Lean angle of a turning bicycle

I'm asked to derive a relationship for the leaning angle of a bicycle with the following specs: Center of gravity for bike and rider is a distance $L$ above the ground when vertical, and the total ...
0
votes
2answers
259 views

Stress and strain

Let us consider a rod having a young's modulus $Y$. Let it be of length $l$, and suppose it is suspended from a point P. Let us pull the rod with a force $F$ at a point Q which is at a distance $2/3l$ ...
1
vote
2answers
812 views

kinetic energy and conservative force field

The kinetic energy of a particle is a periodic function in time. Does it imply that the particle is in a conservative force field and there are no dissipative forces acting on it at any instance of ...
3
votes
2answers
1k views

Integrals of Motion

Landau & Lifshitz write on the first page of chapter 2 of their Mechanics book (p.13) The number of independent integrals of motion for a closed mechanical system with $s$ degrees of freedom ...
2
votes
2answers
334 views

pressure exerted by fluid

If I had a flexible tube sealed at both ends and I submerged it in water (held vertical) Would the bottom half of the tube compress and the top half expand? What would the pressure in the tube be? Say ...
2
votes
2answers
955 views

Does the phase space (configuration and momentum space) of particles have a Euclidean norm? Does it have a useful meaning of “distance”?

Often in engineering physics, different vector spaces are used to visualize the trajectories (evolution) of systems. An example being the 6n dimensional phase space of n particles. It is not very ...
3
votes
2answers
943 views

Complete vs General Integral of first order PDE

The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics: ... we should recall the fact that every first-order partial differential equation has a solution depending ...
3
votes
4answers
2k views

“Regular” 20-sided die, vs “life counter” 20-sided die. Same probabilities?

Regular dice are made such that opposite sides of the die add to 1+the number of sides. For example, a 20-sided die has 14 and 7 opposite of each other, adding to 21. For certain types of games, ...
6
votes
2answers
922 views

What is the highest energy position for a double pendulum? And for which energy positions is it chaotic?

Math/physics teachers love to break out the double pendulum as an example of chaotic motion that is very sensitive to initial conditions. I have some questions about specific properties: For a ...
11
votes
1answer
212 views

Theorems on instability of classical systems of charged particles?

Classically, a hydrogen atom should not be stable, since it should radiate away all its energy. I remember hearing from my favorite freshman physics prof ca. 1983 about a general theorem to the effect ...
6
votes
3answers
827 views

Point particle moving on a frictionless semicircular hill

Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary ...
17
votes
1answer
1k views

Mechanics + Thermodynamics: Bouncing Ball

In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated: A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 ...
5
votes
2answers
347 views

Tracking photon color in Bell experiments

In parametric down-conversion, it is said that a driving photon is converted into two entangled photons whose frequencies add up to the driving frequency. Yet in discussions about entanglement ...
6
votes
2answers
321 views

Physical Interpretation of a Scalar Quantity Related to Currents/Conservation Laws

Let $Q_{ab} = (\psi_{;a})(\psi_{;b}) - (1/2)g_{ab}|\nabla \psi|^2$ be the energy-momentum tensor of the wave equation in some space time. I will use semicolons to refer to covariant differentiation ...
9
votes
3answers
628 views

How do we explain accelerated motion in Newtonian physics and in modern physics?

Maybe my question will seem stupid, but I am not a physicist so I have some problems understanding a classic Newtonian experiment: in the bucket experiment, why does he have to introduce the absolute ...
1
vote
1answer
3k views

How to calculate the exit velocity of a coil gun projectile?

First off, what quantities need to be factored in? Voltage and current through the coils, the magnetism of the projectile, the magnetic fields, etc.? Next, how would you calculate the speed of the ...
4
votes
1answer
180 views

Name of the guy that Feynman mentioned during a lecture: the diagram is of a chain hanging over a triangle

In a Feynman book, he talks about a man (I believe he lived 400-500 years ago) that discovered something about the dimensions of triangles (I think)by hanging a chain around the triangle. I've ...
1
vote
2answers
482 views

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface?

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface? The question I am working on is: A projectile is launched vertically from ...
6
votes
4answers
333 views

Maximal Gravity

I found this interesting problem in Introduction to Classical Mechanics with Problems and Solutions by David Morin: Given a point $P$ in space, and given a piece of malleable material of ...
5
votes
2answers
1k views

How is angular momentum conserved when a spinning top finally stops spinning?

Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
11
votes
2answers
578 views

Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
31
votes
4answers
8k views

Why can't we feel the Earth turning?

The Earth turns with a very high velocity, around its own axis and around the Sun. So why can't we feel that it's turning, but we can still feel earthquake.
2
votes
1answer
232 views

Lagrange's equations: What is $\dot{q}_j$?

I'm looking at the solutions to a problem about a uniform thin disk. For the sake of this question, I start with $$L=\frac{1}{2}m\left( r\omega \right)^2$$ Then we plug it into Lagrange's equations: ...
3
votes
3answers
430 views

D'Alembert's Principle: Where does $-Q_j$ come from?

This is a follow-up question to D'Alembert's Principle and the term containing the reversed effective force. From the second term of Eq. (1.45) $$\begin{align*} \sum_i{\dot{\mathbf{p}}_i \cdot ...
0
votes
1answer
787 views

D'Alembert's Principle and the term containing the reversed effective force

For our Classical Mechanics class, I'm reading Chapter 1 of Goldstein, et al. Now I come across Eq. (1.50). To put it in context: $$\begin{align*} \sum_i{\dot{\mathbf{p}_i} \cdot ...
3
votes
1answer
270 views

Coincidence detectors in Bell tests: How close is close enough?

When is a coincidence a coincidence? We know that to identify entangled photons, the electronics is set to look for simultaneous clicks at opposite detectors. The size of the window is to some degree ...
1
vote
2answers
263 views

Why isn't pressure used for flight?

Why isn't pressure used as flight? I've heard that 2L bottles can hold a pressure of up to 90 PSI safely. Since $F = PA$, if the nozzle of a pressure rocket is about 4 inches squared in area, that ...
2
votes
2answers
553 views

Non-Linear Density Shell Problem

I'm trying to understand Newton's Shell Theorem (Third) http://en.wikipedia.org/wiki/Shell_theorem However this applies to a sphere of constant density. How is this formulated for sphere of varying ...
1
vote
1answer
197 views

Is it theoretically possible for the orientation angle of a projectile to remain exactly equal to the orientation of velocity?

This question is sparked by my answer to this question: Is this simulation following real physics? After examining the math, I don't see how it is theoretically possible for the situation simulated ...
14
votes
4answers
6k views

When is the Hamiltonian of a system not equal to its total energy?

I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
5
votes
1answer
2k views

Invariance of Lagrange on addition of total time derivative of a function of coordiantes and time

My question is in reference to Landau's Vol. 1 Classical Mechanics. On Page 6, the starting paragraph of Article no. 4, these lines are given: If an inertial frame $К$ is moving with an ...
0
votes
2answers
203 views

How could pinion in automatic quartz watch be rotated at 100K RPM?

Wikipedia article on automatic quartz watch describes the watch mechanism as follows: a rotating pendulum is attached to a pinion and when the wearer moves his hand the pinion is rotated at up to 100 ...
1
vote
3answers
3k views

A spinning bullet

I know the rifling in a gun or rifle puts a spin on the bullet along the axis of trajectory. Now I don’t understand exactly what does it make the trajectory more stable and the travel grater?
4
votes
1answer
461 views

Invariance and forms of the Lagrangian

I have been doing Landau and due to its concise style been facing a few problems. I hope you can help me out here somehow. 1)Does the "homogeneity of space and time" essentially talk about the ...
3
votes
1answer
2k views

what is uniform velocity?

i have a very basic question from school days. what does it mean to say an object is moving with uniform speed? it seems to me now that it should be an unit dependent concept. for example if speed is ...
2
votes
2answers
82 views

In a gas of particles, how is the displacement vector related to the number density?

Suppose I have a gas of particles that is initially uniformly distributed so that the number density is $n_0$ (number of particles per unit volume), and then I displace the particles by the vector ...
2
votes
2answers
2k views

Stress vs Strain for mild steel

After Yield point on stress strain diagram the under curve occurs what does it mean what will happen for the mild steel at that particular time and again why the curve goes to up and reaches ...
4
votes
1answer
623 views

Collision between a rod and a bullet

There lies a homogeneous rigid rod of mass $M$ and of length $H$ on a frictionless table at rest. A small bullet of mass $m$ moves toward the rod with velocity $v_0$, perpendicular to the rod and ...