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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Lagrangian vs Hamiltonian and symmetry of a theory

It is said that since the path-integral formulation of quantum mechanics/or quantum field theory uses the Lagrangian rather than the Hamiltonian, as the fundamental quantity, it preserves all the ...
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Law of conservation of momentum , elastic collision [closed]

In Law of Conservation of momentum , elastic collision occurs only in an isolated system. A case defined as,when Object A comes with initial velocity and collides with object B which is in rest V= ...
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0G(No motion) scenario detection using Accelerometer and Gyroscope [closed]

I have a gyroscope and accelerometer which I am placing on the wheel of a bicycle to detect the 0G or standstill (when the bicycle exactly reaches to rest) of the wheel. I put the sensor at a R/2 ...
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why will two bodies rotate about their centre of mass if they do so for their mutual attraction

If two bodies rotated because of their mutual attraction. They will do so about their centre of mass. Why is that ? I understand that if there is no external force then the centre of mass must not be ...
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Shape of an inverse cube orbit?

If I have a particle orbiting a central force $$F=-k/r^3$$ what is the shape of the orbit (the radius as a function of the angle)?
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97 views

Elastic collision between two circles [duplicate]

I am trying to calculate the final velocities of two equal mass 2-dimensional circles after an elastic collision. I have tried to figure it out using formulas I know from high school physics, but ...
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71 views

What is the origin of the Maxwell's wheel? [closed]

Tried to find it online, but nothing. Every refers to it and that it's named after the famous James Clerk Maxwell (of the maxwell electromagnetic laws and some other things) but it's like the ...
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A drop falling in the condensed air

A drop is falling in humid air with air resistance equal $F_r = - \alpha v^2$. In $t = 0$ the drop is ideally spherical, $h$ above the ground, has mass $m_0$ and velocity $v_0 = 0$. What mass and ...
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49 views

Tension at different points of a string during vertical circular motion

For a vertical circular motion, its standard to solve for tension at the 4 common points on the circle (North, South, East, West) My question is: Is it possible to solve for tension at other ...
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26 views

Application of centroid of body in real life

What is the practical application of centroid of the body whose centeroid lies out of it. I know that we can balance a body at its centroid but what if lies out of that body?
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42 views

Generating function as a prove of a canonical transformation [closed]

Does the existence of a generating function $ F $ prove that a given transformations is canonical? How? The thing is: Show that the transformation is canonical $$ Q=p+iaq $$ and $$ ...
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77 views

How to prove that “all unaccelerated frames behave likely for all isolated bodies”? [closed]

Say in an unaccelerated frame "S" a "isolated body A" moves with constancy of velocity , can we predict mathematically that any other such body B will move with same velocity in that frame.... My ...
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Time Symmetry in two body problem

I was solving Two-body problem in two dimension numerically using second order Taylor expansion. In order to check the time-symmetry of the energy, I considered the following equations. \begin{align} ...
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Consider a particle of reduced mass $\mu$ orbiting in a central force with $U=kr^n$ where $kn>0$ [closed]

Consider a particle of reduced mass $\mu$ orbiting in a central force with $U=kr^n$ where $kn>0$. (a) Explain what the condition $kn>0$ tells us about the force. Sketch the effective ...
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62 views

Work Done On Circular Motion

I am trying to find the total work done on a ball, $m=0.8kg$, tied to a rope of r=1.6m length and swung in a vertical circle. I understand the total work done by both the tension in the string and ...
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22 views

Moment of area and centroid

What actually is moment of area? I know area into distance definition but what is its physical interpretation.When I say moment of area of two objects are different then what the difference I eill see ...
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92 views

Why is the trajectory of the alpha particle in a cloud chamber almost straight?

This question baffled me since high school. Presumably, the alpha particle has collided with macroscopically large number of molecules when it makes a macroscopically large displacement. One would ...
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Sinusoidal variation of a generalised coordinate with its conjugate momentum

The hamiltonian of a system with 2 degrees of freedom is given by: H= 0.5(p12q14+p22q12-2aq1) where 'a' is a constant. I am to show that q1 varies sinusoidally with p1. My attempt was to write down ...
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What is the link between D'Alembert's principle and the Lagrange equation of the first kind?

I have just gotten into Lagrangian mechanics. So far I have only been using Lagrange equations of the first kind i.e: $$m_n\ddot{x}_n=F_n+\sum_{\alpha=1}^{R} \lambda_{\alpha} \frac{\partial g_{\alpha ...
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69 views

Inverse Lorentz transformation confusion

I've been tripped up for a very long time by this question. I hope that someone can explain it for me once and for all. My question is that when does one use the Lorentz transformation and when does ...
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66 views

Equations of motion for double spherical pendulum simply?

I am attempting to simulate a double spherical pendulum, i.e. a combination of the spherical pendulum and the double pendulum. I understand that the equations of motion can be derived via the ...
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50 views

2 men support a uniform horizontal beam at its 2 ends .If one of them lets go ,the force exerted by the beam on the other man will?

A) remain unaffected B) increase C) decrease D) become unequal to the force exterted by him on the beam This was a question in one of my books for mechanics, they solved the question using ...
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37 views

Formula - Bounce height with respect to time

I'm trying to graph a bounce with respect to time. I have these formulas: $\frac 12 mV_2^2 = mgH_2$ and $H_2 = \frac{1}{2} \frac{V_2^2}{g}$ I will have a series of $H(t)$ formulas as I know how to ...
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70 views

Where does the spring's energy go?

I have learned that ideal spring has no mass. Suppose, I attach a ideal spring (spring constant $K$) to a wall and pull it a distance $x$ it will have a potential energy $U = \frac{1}{2}Kx^2$ and if I ...
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88 views

Is the Hamiltonian conserved or not?

The question is the very last sentence at the end of this post. In this post, I'll first show that the Hamiltonian is conserved since it does not have explicit dependence on time and then show that ...
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Explaining conservation of angular momentum with a disconnect

A probe is rotating in space and an instrument comes loose and disconnects. I need to explain why the angular velocity $\omega$ of the probe does not change. This equation describes how the angular ...
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Relation between force and torque for a set of gears/bicycle

If there are 2 gears meshed together and they are of different sizes, then rotating the smaller one will make the larger one spin with a smaller angular velocity but with more torque. And the opposite ...
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223 views

What are the boundary conditions associated to this lagrangian?

Suppose that $L(q^i, \dot{q}^i)$ is a standard and well behaved lagrangian associated to some Dirichlet boundary conditions : $q^i(t_1) = q_1^i$ and $q^i(t_2) = q_2^i$. Now I have this new lagrangian ...
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86 views

How does a cyclist moves the center of mass of the cycle-cyclist system?

Consider the image shown below, In the left diagram the centre of mass of the system lies upon the perpendicular from the point of contact. But in the right diagram the centre of mass has shifted ...
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61 views

What is the difference when we measure torque/angular momentum about a point and about an axis?

When do we measure torque about an axis and when do we measure torque about a point?Whats the difference? I tried searching this on google but did not get satisfactory answer.
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31 views

Physical significance of direction of rotational variables

When discussing rotational quantities, the direction of such vectors corresponds to the axis of rotation, and not he actual direction of rotation(for example, while we use torque in clockwise and ...
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What's the point of hamiltonian mathematical formalism of classical mechanics? [duplicate]

Just what the title asks. What are the applications of it?
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Which has the larger change in momentum [closed]

This is a concept question in my physics class, It isn't for marks, its just to gauge your understanding of the subject. I'm not sure if I have the right idea. since the mass of block A is 4 times ...
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Hemisphere moment of inertia with varying density

Find the moment of inertia through axis of symmetry of a hemisphere given by $x^2+y^2+z^2 \leq R^2$ and $0 \leq z$ with density $\rho = \alpha \sqrt{x^2+y^2+z^2}$ Since the density is radius ...
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269 views

Why do we obtain classical physics by taking the limit of Planck's constant to zero?

Why if we specifically set Planck's constant equal to zero (the limit of it) do we sometimes get classical physics? I mean, what does it mean physically to set the constant equal to zero? Or to say it ...
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Particle Disintegration Range of Angles (Landau& Lifshitz)

In the particle disintegration problem in the book by Landau and Lifshitz (pg 44 question 3), it is asked to find the range for $\theta=\theta_1+\theta_2$, where $\theta_1$ and $\theta_2$ are the ...
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Deduction of Lagrange's equations for non-conservative systems using Hamilton's Principle

Consider $\vec{F}$, as the total force applied on the system, $U$ the potential energy of the existent field, and $\vec{Q}$ a non-conservative force. We have that: $$F_k=-\frac{\partial U}{\partial ...
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A bead is threaded on a frictionless vertical wire loop of radius R

The question is the very last sentence at the end of this post. In this post, I'll demonstrate how I reach to a contradiction(the conditions mentioned in conjecture 1 should be satisfied by all ...
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Changing orbit of a space shuttle

In the figure here, a space shuttle is initially in a circular orbit of radius r about Earth. At point P, the pilot briefly fires a forward-pointing thruster to decrease the shuttle’s kinetic energy K ...
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Bead on a smooth rotating rod

Suppose a bead ($m$) is free to move on a thin rod in the otherwise empty space. The rod is made to rotate at constant angular speed $\omega$. Lets assume the initial position of the bead is $(r_o, ...
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41 views

System of potential energy

Is potential energy calculated between a system? More specifically, if we say 'potential energy of a ball with respect to earth', does it mean that the Earth + the ball is a system?
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1answer
81 views

Rotating disc problem [closed]

This question comes into my mind this evening. Suppose I have a rotating disc whose maximum rotation speed is $500$ rpm (say). On this rotating disc I have placed another small rotating disc with ...
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1answer
179 views

Moment of inertia of disk with off center hole [closed]

So I am given the figure shown below and told to find the moment of inertia if we have that the mass of the shaded region is $M$. I think I have to find the total mass without the hole and the mass ...
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22 views

how to reduce the order of the hamiltonian equation for electrical problem given below?

I am having my FYP in this Hamiltonian project to analysis the integrator for Hamiltonian system. Can anyone please guide me how to reduce the equations to first order using substitution method?
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21 views

How to reduce the order of Hamiltonian equation for electrical problem [duplicate]

I want to reduce the order of this Hamiltonian but I don't know how to proceed. The equations are given below: $$H(p,q) = \frac{1}{2} (kq^2) + \frac{p^2}{2m} $$ This is the Hamiltonian for a simple ...
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93 views

Full time-derivative, Poisson brackets and Hamilton's equations (classical mechanics)

While studying Poisson brackets in classical mechanics and the derivation of $\dot{q_j}=\{q_j,H\}$ and $\dot{p_j}=\{p_j,H\}$ form of Hamilton's equations I encountered a surpsing identity, which led ...
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Disregarding the claim of perpetual motion. Does this design have any merit at all?

I'm wondering, in reference to this youtube video Whether or not this design would actually make the wheel move. Any big brains out there wanting to help me out would be greatly appreciated
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Textbooks to teach myself physics [duplicate]

I'm currently studying mathematics in Switzerland and only have a couple hours of General Physics a week. I would like to teach myself physics at a more advanced level but I don't know what textbooks ...
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Graduate level orbital mechanics book

I recently finished an undergraduate course in classical mechanics and really enjoyed the subject, particularly the sections regarding the mechanics of orbits. I am considering pursuing a graduate ...
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Action for solution of general nth order differential equation [duplicate]

Suppose I want to find solution to a general nth order differential equation. (If I am right about the logic then) one might say that the solution $y\equiv y(x)$ is that function for which the ...