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 there a trajectory which is not a solution of the equation of motion but satisfies all conservation laws?

I'm wondering whether conservation laws are sufficient to imply equations of motions. Specifically: 1) In classical mechanics of point particles, are conservation of energy, conservation of momentum ...
3
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3answers
855 views

Classical/Quantum Coin Toss

I am having a brainfreeze moment and have confused myself, help appreciated! Classical Coin: Heads OR tails. Quantum Coin: Superposition Heads AND Tails. Classical Mechanics: Deterministic (in ...
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0answers
49 views

Calculate the acceleration of the trailing muon bunch

Two separate suitably short but intense bunches of muons, "A" and "B", are both supposed to be constantly accelerating (in an otherwise sufficiently flat region) with constant proper acceleration ...
22
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3answers
692 views

How many points are required to make a black box

I have a black box with an arbitrary mass distribution inside it. I want to replace that object with n point masses without changing any mechanical properties of the box (center of mass, total mass, ...
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3answers
3k views

How much torque does it take to turn a doorknob? [closed]

How much torque does it take to turn a doorknob? I'm not looking for an exact answer, just a ballpark for someone who doesn't have a sense of everyday amounts of torque. Here's a very ordinary ...
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0answers
70 views

Hamiltonian system: match transformations and constants of motion

I have a problem about the interpretation of an exercise. Given the following Hamiltonian $$H=\frac{\mathbf{p_0}^2}{2m}+\frac{\mathbf{p_1}^2}{2m}+\frac{\mathbf{p_2}^2}{2m}-2V(\mathbf{r_1}- \mathbf{...
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0answers
94 views

A quicker way to verify that a function is a constant of motion?

I have three particles that we can indicate with $\alpha$ ($\alpha$=0,1,2), they are identified by the $r^i_\alpha$ coordinates and $p^\beta_j$ conjugata momenta ($\beta=0,1,2$ and $i,j=1,2,3$). I ...
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2answers
491 views

How to calculate pressure exerted on the wheels of a robotic car?

I need some help in designing my robotic car. So its going to have 4 wheels, each driven by a 12-volt motor. It occurs to me that the weight of the chassis itself will exert some pressure on the ...
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0answers
374 views

Dose the gravitational force produces precession in the spinning top?

I'm new at classical mechanics but the text book says there is the torque in the spinning top which generated only by gravitation. It is hard to explain the situation, I've add the link. http://...
0
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2answers
143 views

Hamiltonian equations: can I divide a solution of motion for a constant?

I'm solving an exercise about Hamiltonian equations. I have followed the proceeding below. The results given by the book are different to mine because its first result is the half of mine (and the ...
1
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1answer
352 views

Solving equation of motion of two massive particle exerting the gravitational force each other

I'm trying to analyze the motion of the particles which exert the gravitational force each other. Let $M_1$, $M_2$ be the masses of the particles, and the equation of motion of particle $M_1$ $$ F=G\...
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2answers
5k views

Which is more efficient: a larger wheel or a smaller wheel?

I'm designing a 2-wheeled cart that I plan to rig to a donkey for hauling work around a farm. I'm wondering if there are mechanical advantages to using smaller wheels (like 40 cm diameter) vs. using ...
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10answers
4k views

What is the Earth truly rotating about/revolving around?

Earth rotates on its axis and revolves around the sun, the sun revolves around the galaxy, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all ...
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6answers
15k views

Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result. The riddle goes as follows: "imagine you are shrunk to the size of a coin (i....
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1answer
358 views

What are the physics behind the Coriolis effect? [closed]

What causes the Coriolis effect?
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3answers
953 views

Addes mass forces: can a force depend on acceleration?

My friend and I had a little discussion about added mass forces. I always interpreted $F=ma$ as a cause-effect relationship, so I find rather uneasy to accept that the cause can instantaneously ...
0
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1answer
67 views

Doubt about coordinates and point of equilibrium

I'm solving an exercise about small oscillations and I have a doubt about coordinates that I have to use. This is the text of the exercise: "A bar has mass M and lenght l. Its extremity A is hooked ...
3
votes
1answer
357 views

A different proof for 6 degrees of freedom

I want a different proof of 6 degrees of freedom of a solid object made of $N$ particles. I am thinking along these lines: The definition of rigid body is $$\left\lvert \vec{r_i}-\vec{r_j} \right\...
2
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2answers
696 views

Rotating spring system: Is my intuition correct?

Consider a solid spherical object of uniform density that is rotating on an axis A1. Perpendicular to that axis one can draw another line that passes through the sphere. On this axis, on both sides of ...
3
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4answers
3k views

Can Newton's laws be explained by Quantum Physics? [duplicate]

I have only basic knowledge of physics. Could you please explain to me if a "Quantum" laws can theoretically (perhaps in the future?) be used to explain everything in macro levels? I'm having ...
0
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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 $v_2$ respectively. ...
3
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2answers
1k views

Equal mass on either end of a spring

I'm taking physics this term and this is the first time taking physics in 3 years. Here is my homework question (of course those variables all have values but we'll use variables for now): Consider ...
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3answers
2k views

What happens when a ball stops bouncing?

If I were to drop a bouncy ball onto a surface, each successive bounce will be lower in height as energy is dissipated. Eventually, however, the ball will cease to bounce and will remain in contact ...
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2answers
52k views

Conceptually, what is negative work?

I'm having some trouble understanding the concept of negative work. For example, my book says that if I lower a box to the ground, the box does positive work on my hands and my hands do negative work ...
3
votes
2answers
633 views

Deriving $T = F\ r = I\alpha$ for a rigid body

For a single point mass : $\tau=F_{t}r=ma_tr=(m r^2)\alpha = I\alpha$ For multiple point masses bound together : $\sum \tau_i = (m_ir_i^2)\alpha = I\alpha$ But how do we go from that to $I\alpha = ...
3
votes
1answer
788 views

Intuitive explanation for why same force applied farther from a hinge causes larger angular acceleration than if applied closer?

A standard example of a problem involving torque is opening a door - the same force F applied far from the hinge causes a larger angular acceleration than if applied close to the hinge. I always had ...
2
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2answers
2k views

Getting started with Landau Physics course [closed]

I want to learn Physics in my own time. I am an electrical engineer, working in the same field and am tremendously interested in Physics. I have heard a lot about the 10 book series of Landau ...
1
vote
1answer
515 views

Inclined plane question [closed]

An object, mass $m$ is placed on an incline, angle $\theta$. System is at equilibrium. coefficients of static and kinetic frictions are $\mu_s$ and $\mu_k$ respectively. Then: 1) What is the Total ...
2
votes
1answer
175 views

What is the distance traveled

the red dots represent a side view of path traveled, F is downward force and the tool used here is a pen placing parallel to the coin I have newly started to study mechanical physics. based on study, ...
0
votes
2answers
452 views

Wave function interpretation $y(x,t) = (0.35m)\sin(10\pi t-3\pi x + \frac\pi{4})$

Wave function interpretation $y(x,t) = (0.35m)\sin(10\pi t-3\pi x + \frac\pi{4})$ I used to deal with function with one variable And now theres are two, how can I interpret them? Is $10\pi$ still ...
4
votes
2answers
876 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 ...
0
votes
1answer
911 views

if a simple pendulum is dropped in a elevator with a acceleration greater than acceleration due to gravity then what will be its frequency

if a simple pendulum is dropped in a elevator with a acceleration greater than acceleration due to gravity then what will be its frequency ? We know time period depends on frequency.
0
votes
1answer
197 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 ...
2
votes
6answers
848 views

Centripetal Force Acceleration

In uniform circular motion, acceleration is $\frac{v^2}{r}$ and time which it acts $\rightarrow 0$. So $\Delta v = 0$, but then why/how does direction change, when the acceleration should be ...
1
vote
1answer
94 views

How large of a solar sail would be needed to travel to mars in under a year?

I'm attempting to approach this using the identity $$F/A = I/c$$ I can solve for Area easily enough $$A = F(c/I)$$ and I know the distance $d$ is $$d=1/2(at^2)$$ But I'm having difficulty trying to ...
4
votes
1answer
250 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 $\lambda,m,\...
1
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0answers
880 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) \end{...
6
votes
3answers
2k 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 ...
3
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0answers
149 views

Physics of a cold and hot top

Imagine two tops made up of exactly one thousand atoms. One is kept at 4 kelvin, the other at room temperature. Would they weigh the same given an arbitrarily precise scale in the Earth's ...
6
votes
2answers
142 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 what ...
5
votes
2answers
358 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 ...
0
votes
2answers
188 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 ...
2
votes
1answer
257 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 $\epsilon$...
0
votes
1answer
1k 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 ...
15
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6answers
1k 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 $\vec r_i$ ...
0
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2answers
335 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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1answer
223 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
54 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 ...
-1
votes
1answer
192 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 ...
2
votes
2answers
861 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} = \hat{...