Mechanics (Greek: μηχανική) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in displacements, or changes of an object's position relative to its environment.
This branch of physics has its origins in Ancient Greece with the writings of Aristotle and Archimedes (see History of classical mechanics and Timeline of classical mechanics). During the early modern period, scientists such as Galileo, Kepler, and Newton laid the foundation for what is now known as classical mechanics.
It is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light.
It can also be defined as a branch of science which deals with the motion of and forces on bodies not in the quantum realm. The field is today less widely understood in terms of quantum theory.
I would like to buy a Fundamentals of Fluid Mechanics for Engineer textbook. I have 2 options, they are:
1. https://www.amazon.com/dp/0133521702/?tag=pfamazon01-20
2. https://www.amazon.com/dp/0132788128/?tag=pfamazon01-20
Can someone please tell me which one of above Fluid Mechanics textbook...
A longer pendulum swings slower. So changing the length l of the pendulum changes the period T, which affects the timekeeping accuracy. But the problem is talking about the body on the spring, not the string. So the second formula cannot be applied here directly and I don't know how to progress...
I can’t find the chapter list online, does anyone know what topics are covered in John Taylor’s classical mechanics? Would it be similar to what’s covered in Newtonian mechanics, but obviously more advanced.
Cheers in advance 👍
I'm interested in learning orbital mechanics but I haven't taken a class in numerical methods yet. Do I really need to take a whole class in numerical methods before learning orbital mechanics, or can I get by if I self-learn a smaller portion of the syllabus of a numerical methods class? If so...
[Mentor Note -- thread moved from the technical forums to the schoolwork forums]
I have a hollow-cylinder wheel model, braked with brake pads located at a distance d of the wheel's center axis. The brake pads have a contact area S. They are also forced towards the wheel with a pressure p. The...
Just earlier today i was practicing solving some ODEs with the power series method and when i did it to the infinite square well i noticed that my final answer for ##\psi(x)## wouldn't give me the quantised energies. My solution was
$$\psi(x) = \sum^{\infty}_{n=0} k^{2n}(\cos(x) + \sin(x))$$...
Very basic question here, about statistical independence in quantum mechanical experiments. The quote from PD below is what prompted the question.
When we talk about "some kind of pre-existing correlation" are talking about a simple correlation in the sense of the correlation of sunglasses and...
These are all the chapters for introductory mechanics in my textbook. What I have been doing is reading the chapter then following it up with watching a tonne of lectures and worked examples on that topic and attempting to do the problems.
I’m on Applying Newton’s laws and I’ve been studying it...
Hello all,
I have some issues understanding the inertial-frame (or global-frame, G-frame) versus the body-frame (B-frame) when it comes to simulating the motion of a rigid body in 2 dimensions (planar body mechanics) in a system of ODEs. I have been self-learning from textbooks on simulating...
I have tried solving this by splitting the load into two parallel coplaner loads as the Hint below the question suggests but while i was computing the values i realized that, i'll have 4 variables with only 3 equations.
two forces and the two distances to forces from their respective axes.
i've...
So I was looking at this example problem in my textbook and I don’t understand how they got -168.1 degrees. The part I’m confused with is the first part of the 2nd picture, there’s a coma in the inverse tan, I don’t know what that means.
The best I could do was draw a forces diagram. I know that friction would be working up when the block is on the point of slipping down the plane and friction will be acting down the slope against the direction of motion when the block is on the point of slipping up the slope. (not even sure if...
I want to share my recent results on the foundation of classical mechanics. Te abstract readWe construct an operational formulation of classical mechanics without presupposing previous results from analytical mechanics. In doing so, several concepts from analytical mechanics will be rediscovered...
I have read about several approcahes to bypass some classical restrictions to quantum facts such as the electron being in a torus-like shape to avoid ,the greater than speed of light, rotation paradox . Could you recommend websites , sources or books that give good classical analogy to quantum...
A very simple (I thought!) question:
I'm just looking at the first part, finding the reaction at the hinge A.
Here is my annotated diagram, with the reaction and A resolved into it's X and Y components, the force at E labelled as Fe and the length of ED labelled as L.
Considering the body...
To solve a particle on a sphere problem in quantum mechanics we get the below equation :##\left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right)-\frac{m^{2}}{\sin ^{2} \theta}\right] \Theta(\theta)=-A \Theta(\theta) ##
To solve this differential equation, we...
Good afternoon,
I am struggling to find the solution at Q2 and Q3. For Q2 the absolute pressure at point 1 is at the bottom of the tank, so do i need to use the formula P=Patm+qgh ? If using this formula I've got a bigger number than 100Pa.
Same issue for Q3, isn't the pressure at point 2...
Moderator's note: Spin-off from previous thread due to topic change.
Because it doesn't work. Bohmian time evolution doesn't involve the coarse graining steps that are used in his calculation. A delta distribution remains a delta distribution at all times and does not decay into ##|\Psi|^2##.
Let ##|l,m\rangle## be a simultaneous eigenstate of operators ##L^2## and ##L_z## and we want to calculate ##\langle l,m|cos(\theta)|l,m'\rangle## where ##\theta## is the angle ##[0,\pi]##. It is true that in general ##\langle l,m|cos(\theta)|l,m'\rangle=0## ##(1)## for the same ##l## even if...
At the time of release, the equation of motion of blocks A and B T-m_ag = m_aa and T=m_b\omega^2R respectively, where T is the tension in the string. Solving for the acceleration a then gives a=\frac{m_b\omega^2R - m_ag}{m_a}. Not sure what I did wrong or what incorrect assumptions I made...
Since we are dealing with an ideal rope, we have that ##T_1=T_2=T_3=F and T_2+T_3=2F=(m+m_p)g\Leftrightarrow F=\frac{m+m_p}{2}g.##
##T_4=3F+(m+m_p+M_p)g=\frac{3}{2}(m+m_p)g+(m+m_p+M_p)g=(\frac{5}{2}m+\frac{5}{2}m_p+M_p)g## and ##T_5=mg-2F.##
Is this correct? If not, I woould appreciate a brief...
Summary:: Torsional stress on freely spinning shaft?
Hey guys,
I’m having some confusion with a certain section of the “Torsion” chapter in my mechanics of materials book: “power transmission”.
Please see the problem below. This is very easy to SOLVE (basically plug and chug with the...
I have a question understanding the reasoning in the book.
The book says in one dimension F=-dU/dr(p.185). From this, the system is stable at distance a when U'(a)=0 and U''(a)>0 where U is differentiated with respect to r.(p.217)
My question arises from the instance of a pendulum where a...
Hello!
I am new to mechanics of materials and I am very confused about the problem below. So the shear formula is:
tau = VQ/It
From the book (Hibbeler) I understand that Q is "y'A', where A' is the cross-sectional area of the segment that is connected to the beam at the juncture where the...
We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...
Hi I'm reading classical mechanics by Taylor and there is a section about Kepler orbits that i find very interesting so i'd like to see more of classical mechanics with space applications. I appreciate rigouros mathematical books, thanks
Hi, was wondering if anyone is familiar with Symon Mechanics 2nd and 3rd edition. Is there a significant difference between these editions? Ie., content, quality of printing, major corrections?
In non relativistic quantum mechanics, the expectation value of an operator ##\hat{O}## in state ##\psi## is defined as $$<\psi |\hat{O}|\psi>=\int\psi^* \hat{O} \psi dx$$.
Since the scalar product in relativistic quantum has been altered into $$|\psi|^2=i\int\left(\psi^*\frac{\partial...
1) Considering the forces on one of the moons, I have: ##\frac{GMm}{(10R)^2}+\frac{Gm^2}{(20R)^2}=m\frac{v^2}{10R}\Leftrightarrow v=\sqrt{\frac{G}{10R}(M+\frac{m}{4})}.##
2) Considering the initial situation in which the satellite is at rest on the surface of the planet...
1) Since the rod is uniform, with mass m and length l, it has a linear mass density of ##\lambda=\frac{m}{l}##, so ##I_{rod_O}=\int_{x=r}^{x=r+l}x^2 \lambda dx=\frac{\lambda}{3}[(r+l)^3-r^3]=\frac{\lambda r^3}{3}[(1+\frac{l}{r})^3-1]=\frac{1}{3}mr^2[3+\frac{3l}{r}+\frac{l^2}{r^2}].##...
I heard something today about the "informational interpretation" of quantum mechanics and a phrase used was "it from bit." Is there actually such a thing? What does it mean, and how is it distinguished from other interpretations like MWI or Copenhagen?
* The general formula for the magnetic moment of a charge configuration is defined as ##\vec{\mu} = \frac{1}{2} \int \vec{r} \times \vec{J} \,d^3r##* For an electron it's said that the correct equation relating it's spin and magnetic moment is is
##\vec{\mu} =g\frac{q}{2m}\vec{S}##
* It's...
When I read about the launch location, it is explained that the French Guiana launch site was chosen because it is close to the equator, which means it started with a larger tangential speed than if it were launched from a US location. However, doing the numbers, I find that an initial...
Lagrangian mechanics is built upon calculus of variation. This means that we want to find out function which is a stationary point of particular function (functional) which in Lagrangian mechanics is called the action.
To know what this function is, action needs to be defined first. Action is...
In his solution, Morin solves the problem as the hint suggests: cutting the chain into small pieces, taking the component of the external forces along the curve (which is just the component of gravity here) and summing up an in integral, obtaining 0. He then claims that because the "total...
Lets take the original position of the man to be our origin
The plank is uniform so we can assume its mass to be concentrated at its center i.e. 4m from the origin
Xcom= m1x1+m2x2/m1+m2
=50(0) +150(4) /50+150
=3m
There is no external force on the system so the centre of mass does not move...
Hi Fellas! My first post after a long hiatus from forums. Feeling nostalgia (this is the place where it all began, my fuel for quantum fascination so to speak).
I am revisiting the mathematical formulation of quantum mechanics with the dimensional (MLT) perspective. I want to understand what...
Suppose we've an isolated box having ##N## classical distinguishable particles in it, the box being hypothetically divided into two parts, left and right with both parts identical.
Its said that the probability of having the configuration of ##n## particles in the left side is given as...
The hypothesis is that the force of a real spring can be described as $$F = -kx + \alpha x^2$$ with x being the spring deformation and k its constant. The \alpha x^2 would be the force lost by the spring as x becomes too big. To test that, a system was build with block of mass m suspended by a...
Summary:: I am in the highest level Quantum class at my university- technically considered a grad class. I am an undergrad and need advice on just how to learn it. What study tips? Good Youtubers? Physical simulations? Anything that helped you in quantum mechanics.
Hello! I am an undergrad...