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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Is it reasonable for a heavy door to “open by itself” (ie from differences in air pressure) if it had already been slightly ajar?

If you consider a basically uniform massive door (say, 300 N) where there is some coefficient $\mu_{s,k}$ of static and kinetic friction between the thing on the inside of the door, and where the ...
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37k views

Formula for a ball rolling down an Inclined Plane

Suppose we set up an experiment where we have an inclined ramp, and a spherical basketball. If we were to assume the ball to be perfectly round, and rolls down in a vertical manner and the situation ...
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231 views

Violation of conservation of energy and potential energy between objects

I would like to clarify my question. I have numbered them to be independent questions For any conservative fields, $\vec{F} = -\nabla U$. Which means the restoring force is opposite to the ...
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794 views

Most elegant/fundamental formulations of the laws of classical mechanics? [closed]

Newton tried to do it with three laws/statements. While the first can be derived from the second, the three form a pretty nice framework. Later on, I've encountered Lagrangian Mechanics, which ...
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303 views

Under what conditions do the Galilean transformatons become more accurate?

For S and S' in standard configuration, the Galilean transformations are: x' = x - vt, y' = y, z' = z, t' = t From the Lorentz transformations for v << c: x' = x - vt, y' = y, z' = z, t' = t ...
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32 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
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52 views

How is it possible to exert a force on a static object?

Assuming mass doesn't change, force is defined as mass * acceleration. Acceleration is the change in velocity as time changes. How is it possible then to exert a force on an object that doesn't move? ...
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64 views

Projectile motion of a grenade [closed]

A small hand grenade is thrown with an initial speed V0 forming an angle ɵ with the horizontal ground. Assume that at its highest point the grenade explodes and is split into two identical ...
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45 views

Position, velocity and acceleration vs time graphs

I'd like to draw graphs of a vehicle and I have a position vs time table. I can set the points but how am I supposed to join them, straight or hyperbole ? If the object is accelerating which is yes ...
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146 views

“Principle of least action” and “Principle of conservation of energy”: Which one is fundamental and which one is derived? [closed]

Suppose I throw a ball upwards. First it will rise under gravity and then fall under gravity. During the rising part the kinetic energy gradually decreases and the potential energy increases until ...
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139 views

What is the difference between vortexing and centrifuging?

I understand that vortexing will result in mixing / re-suspension of particles, and that centrifugation will result in the separation of particles. However, what is the difference in the physics that ...
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61 views

Harmonic oscillator and cyclic coordinates

I am reading goldstein there is some comment I don't understand. Consider the following hamiltonian $$H = \frac{p^2}{2m} + \frac{kq^2}{2}$$, which can be rewritten as follows $$H = \frac{1}{2m}(p^2 ...
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59 views

Is this an error?

The teacher wrote the following: There is a dot missing where the green arrow is, right? After applying Euler's theorem, the term in brackets becomes $x_j$, but we need it to be $\dot{x_j}$, don't ...
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232 views

Why does the work-energy theorem need to include internal forces?

Can anyone kindly explain me why work energy theorem must also include internal forces? The proof of work energy theorem is derived from Newton's laws of motion, but Newton's laws of motion don't ...
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278 views

Friction of a rolling cylinder

I was wondering why friction vectors are drawn differently regarding a cylinder rolling on a surface and a cylinder rolling down an inclined surface. Since friction is responsible for the rotational ...
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86 views

Mechanical equivalent to electric circuits

Could one build a mechanical equivalent to electric circuits ? I'm considering mechanical waves (like shock waves) travelling through a medium here. I'm aware that due to the high loss and practical ...
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1answer
86 views

Allowed Virtual Displacements

I am having trouble understanding the kinds of virtual displacements which are permitted for a given constrained system. I have a specific example in mind: A block of wood resting on a table parallel ...
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146 views

Why is centre of mass taken as integral of x.dm and not m.dx?

Forgive me if I'm being naive, but, I don't understand why the X-coordinate of the Centre of mass is taken as an integral of x.dm and not m.dx. I understand the summation part, but how do we convert ...
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59 views

What are the proper unit types for the calculation of the frequency of a tuning fork? [closed]

Wikipedia Article on the subject The formula states that the calculation of the frequency with cylindrical tines should be $$1.875^2/(2\pi L^2)\times(Er^2 /(4P))^{1/2}$$ where the variables are ...
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106 views

how is this kind of rolling motion possible?

I was solving this problem : Suppose you put a sphere in a rough ground with velocity of center of mass $v_{cm}= v_o$ in the positive $x$ axis and with anticlockwise angular momentum $\omega_o$ so ...
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333 views

How to work out the gravitational potential energy of rotating rod

I know that the kinetic energy of a rotating rod is $$ KE_{rot}=\frac12I\omega^2 $$ where $I$ is the moment of inertia. But is there some way to calculate gravitational potential energy using just ...
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54 views

Generalised velocities enough to be deterministic in Lagrangian mechanics?

In classical determinism we need to know $2n$ quantities of our system and the equation of motion to predict it's future. In Lagrangian mechanics this is equivalent to knowing $q$ and $\dot q$, the ...
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234 views

Having trouble understanding spectral lines

In my notes I wrote that Rutherford's model of the atom could not explain spectral lines, because that is what my textbook says. I'm not really sure about the details of spectral lines though. I know ...
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222 views

How does the masless pulley gets the force from rope?

I have seen whenever we solve for forces on pulley by rope we take the force on pulley exactly as the tensions in the rope around it. But , why do we do this ? Exactly how does the rope exerts forces ...
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85 views

Can someone explain what's the difference between all these terms in “Simple Words” with their “applications”? [closed]

I'm very confused between all these terms. Can someone explain what's the difference between Classical Mechanics, Relativistic Mechanics, Quantum Mechanics, Quantum Field Theory, ...
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96 views

Calculate small small oscillations of a pendulum

The system is setup as follows: A point $O_1$ moves along the $x$ axis with it's $x$ coordinate being $a\sin(\omega t)$ and $\omega\ne\sqrt{\frac{g}{l}}$. There's a pendulum attached to $O_1$ of ...
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Energy conservation $\iff \frac{dE}{dt} = 0\ $?

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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1answer
68 views

Can individual forces be regarded as momentum flows? [closed]

Net force on an object can be defined in two ways equivalently (from a classical point of view): $$\vec{F} = m\frac{d\vec{v}}{dt}=\frac{d\vec{p}}{dt}$$ Looking at the last expression (definition in ...
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226 views

Momentum and Kinetic Energy Conservation in Inelastic Collision

Let a ball fall freely to the ground, hit and bounce back. Assume mass of the ball does not change during this. Since momentum is conserved in all collisions, $p_i = p_f$ In this example, the system ...
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55 views

How do I prove that frequencies that are irrationally related lead to quasi-periodic motion?

Consider the equation: \begin{equation} \dot{x} = Mx, \end{equation} where \begin{equation} M = \begin{pmatrix} i\omega_1 & 0 & \cdots & 0 \\ 0 & i\omega_2 & \cdots & 0 \\ ...
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57 views

If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also?

If $(q,p)$ to $(Q,P)$ is a canonical transformation, then does this imply $(Q,P)$ to $(q,p)$ is also, assuming Hamilton's equations hold for the coordinates $(q,p)$? This seems like it should be true ...
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691 views

Net work done for rubber bands

I know that work is done on a rubber band to extend it, and then the rubber band does work to contract. However, then what is the net work done? If it returns to its original length, is the area ...
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119 views

If a body is floating in a static fluid, then the volume of the displaced fluid equal to the volume of the inmerse part of the object (proof)

Suppose an arbitrary body is floating in a static fluid, either totally or partially immersed in it, then the volume of the displaced fluid equal to the volume of the immersed fraction of the object. ...
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78 views

Simplifying Friedmann's Equation

So we have one of Friedmann's equation: $$\rho_c = \frac{3H^2}{8\pi G}$$ Using This website, resources where gathered for specific times in the universe. The resources being the Hubble constant at ...
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91 views

Confusion about units of angular momentum

According to multiple sources the SI units for angular momentum are kg * m$^2$ / sec I am confused about the derivation for this. Here is what I have done: $$L = I \cdot \omega \\ = m \cdot r^2 ...
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194 views

Is it possible to deduce the Archimedes' law of the lever using only the laws of conservation of the physics?

Is it possible to deduce the Archimedes' law of the lever using only the laws of conservation of the classical mechanics? I never saw (which is strange), but I think that it's possible.
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766 views

Equilibrium of Force Systems including Torque

please help me to solve this problem.. this is only the #3 on my homework and the only thing i didn't know here is how to calculate the tension T. please teach me how to solve the tension here ...
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606 views

Equations of motion for bob-on-a-string — am I missing some terms?

The dynamics of a type of physical system I am currently working on are modeled in most of the literature by replacing the moving parts of that system with an equivalent set of pendulums. Parameters ...
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202 views

Magnitude of force to keep stick in equilibrium [closed]

Problem statement A straight and homogenous stick with mass m is pressed against a wall with the force F. The stick is horizontal perpendicular against the wall. Given that the friction between the ...
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2answers
485 views

6 Story Building Swaying, Normal? [closed]

Preface: I'm currently sitting at my desk on a 5th floor in a South Florida office building, as I was earlier this morning when I felt the building sway slightly. It wasn't continuous and the ...
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1answer
63 views

Something about collision [closed]

A sphere P of mass m, travelling with speed $u$, makes a head-on collision with a stationary sphere Q also of mass m. After the collision, the velocities of P and Q are $v_1$ and $v_2$ ...
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1answer
386 views

How is the equation of motion for a real scalar field derived from the Lagrangian?

The Lagrangian for a real scalar field is: $$\mathcal{L}=\frac{1}{2}\eta^{\mu \nu}\partial_{\mu}\phi\partial_{\nu}\phi-\frac{1}{2}m^2\phi^2 $$ How can I derive the dynamics of this field from this ...
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1answer
167 views

Say we're driving a bike and suddenly hold the brakes?

It's easy for me to imagine that if we brake the front wheel then there is a chance that I'll flip. On the other hand if I brake the back wheel, there is no way it'll happen no matter how fast I ...
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1answer
652 views

Why is the optimum wheel size of a bicycle about the same as that of a car?

The optimum wheel diameter of cars and bikes appear to be roughly the same, certainly well within an order of magnitude. This is despite very different average speeds and propulsion mechanisms. Can ...
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1answer
78 views

How must you spin the ball to make it alternate between 2 positions? [closed]

Assume any parameters you may need. Thanks in advance.
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398 views

Terminal velocity for falling in a shaft

One falls slower in a mine shaft than in free air. This is due to collisions with the walls. How should one model the terminal velocity in the presence of such collisions?
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335 views

Angular Momentum and Force [closed]

I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not ...
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71 views

Average acceleration: why I am getting different results?

Let's consider a simple school problem. A car starts moving during 3 seconds with a constant acceleration of 1 m/s^2. Then it stops accelerating and moves 3 seconds more with a constant speed. Find ...
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1answer
33 views

Viscous fluid boundary condition

Consider an incompressible viscous fluid of kinematic viscosity $ν$ , dynamic viscosity $µ$ and density $ρ$ . A viscous boundary layer is located over a solid surface at $y = 0$ and $x > 0$. The flow ...
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38 views

“Sweet Spot” of Rod-Pendulum - Problem Clarification

I came across this problem in a book (shortened for brevity): Consider a rod of mass $m$ pivoted about one end, with the other end to rotate. Let the center of mass be a distance $a$ from the ...