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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What does net mechanical efficiency mean?

I often see the term "net mechanical efficiency" used in literature, but I am not quite sure what it means, and what the difference is between it and "normal" efficiency. Take this sentence for ...
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2answers
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Problem of Landau, Lifshitz - Mechanics - Integration of the Equations of motion [closed]

I'm studying Landau, Lifshitz - Mechanics. Could someone help me with this problem ? =) Problem 2 (Page 27 3rd Edition) Determine the period of oscillation, as a function of the energy, when a ...
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2answers
733 views

Is there any case in physics where the equations of motion depend on high time derivatives of the position?

For example if the force on a particle is of the form $ \mathbf F = \mathbf F(\mathbf r, \dot{\mathbf r}, \ddot{\mathbf r}, \dddot{\mathbf r}) $, then the equation of motion would be a third order ...
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1answer
426 views

How much (usable) potential energy is stored in a compound bow?

I have done a bit of reading about the energy stored in bows, but I haven't seen anywhere a description of how much energy actually is stored. Clearly there are many factors, bow design being ...
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147 views

all the 1-dimensional problems in newtonian mechanics are solvable?

i mean given a system with a conserved Energy in one dimension $$ E= \frac{p^{2}}{2m}+V(x) $$ then the 'solution' to this problem is implicitly given by $$ t(x)= \frac{1}{2m} ...
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715 views

Is there any case in classical mechanics where Newton's (strong) third law doesn't hold?

Is there any case in classical (non relativistic) mechanics where the strong form of Newton's third law does not hold (that is, reaction forces are not collinear)? For example, if we consider a system ...
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Lagrangian of pendulum with pivot point rotating about a circle [closed]

I just would like to know If I am on the right track with this stuff. I have scanned the work I have done, sorry if it is a little messy. Disregard the top most $\ddot x$ A disk of radius ...
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248 views

Question about non-holonomic geometric constraints

Suppose a point particle is constrained to move on the curve $y=x^2$. This would then be a non-holonomic geometric constraint since the particle has one degree of freedom and requires two coordinates ...
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Total Mechanical Advantage

How do you find the net Mechanical Advantage (MA) of two joint machines. Do you add or multiply the individual MA? Suppose I have two sets of wheel and axle connected by a fixed pulley. Each of the ...
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1answer
270 views

In which direction is the acceleration directed in a non uniform circular motion?

Acceleration is directed towards the center of the circle in a uniform circular motion. Is it same for the non-uniform circular motion?
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4answers
2k views

Is there a Lagrangian formulation of statistical mechanics?

In statistical mechanics, we usually think in terms of the Hamiltonian formalism. At a particular time $t$, the system is in a particular state, where "state" means the generalised coordinates and ...
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465 views

Translation Invariance without Momentum Conservation?

Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec ...
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1k views

Calculating projectile range from known maximum height and time traveled

I've been stuck on this problem for many hours and I think I'm onto the right solution but I'm uncertain about my math. I've got a projectile that I know its maximum height and it's hang time and I ...
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0answers
57 views

Fading transition and rotation of and object in 2D

I'm looking for sources about I guess dynamics subject. The model I'd like to solve is reduced to a question of: How does a force applied on a certain point of an object results in both fading ...
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1answer
266 views

What is actually a resonating vibration and resonance?

What is actually a resonating vibration and resonance? I have searched many books and made Google search too but couldn't understand it clearly.
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2answers
453 views

Hamiltonian and non conservative force

I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is $ \vec {A}= B/2 (-y, x, 0)$. I know that $$H=\sum_i p_i \dot q_i -L$$ where $p_i$ is ...
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1answer
146 views

Can a bracelet fitted to hand, slip off and stay connected? [closed]

Hello I have a bracelet in my hand with a clip that holds it connected. The bracelete can not slip off my wrist, it is not loose. However while I was standing, it felt from my hand and I found it ...
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1answer
448 views

Clarifications about Poisson brackets and Levi-Civita symbol

I need some clarifications about Poisson brackets. I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic ...
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1answer
2k views

What amount of force is needed to topple a person?

Assuming no sliding and that the shoulder is 1.2m from the feet, what force is required to topple a person weighing 70 Kg standing with his feet spread 0.9 m? If possible, please include an ...
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2answers
625 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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1answer
335 views

Speed of sound in air

Quick question. I thought that the speed of sound in air was constant, say in the right conditions of pressure and temperature, and humidity... 300 m/s. Now, if I have a sound source that moves ...
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0answers
30 views

Dual methods in structure optimization

I am studying Structure Optimization, and the teacher took a few weeks to detail dual methods, but I don't get why it is useful. From an optimization problem with ...
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3answers
1k views

Extended Rigid Bodies in Special Relativity

I was reading Landau & Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct". For example, if you consider a rigid ...
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0answers
377 views

How to find angular velocity of a point inner a circumference

Let's consider a cicumference that have the center in the origin of axes and rotates around x-axes. Let's stick a bar in a point $A$ of this circumference and at the end of the bar let's stick a mass ...
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3answers
243 views

Is there a mathematical relationship here or am I looking for relations when there are none?

When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. This lead me to think about the two situations depicted above. Left: Shows two balls of equal mass ...
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573 views

Writing equation for amplitude of driven harmonic oscillator in Lorentzian form

This harmonic oscillator is driven and damped, with the form: $$\ddot{x} + \lambda \dot{x} + \omega_0^2 x = A \cos(\omega_d t)$$ Now, I have used the ansatz (guess): $x(t) = B \cos(\omega_d t + ...
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1answer
5k views

Rolling bowling ball with slipping

If a bowling ball is moving with some initial velocity while slipping, how far will it move before it begins to roll once it experiences static friction? $\ddot{x} = \mu_{kf}g$ And there is also a ...
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3answers
764 views

Why does motion help you balance on ice skates?

It's almost impossible to balance on a single ice skate if you're standing still. But give yourself just a little forward motion—it doesn't take very much—and it suddenly becomes easy. You can stand ...
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3answers
2k views

Aircraft Level Flight Trajectory

An aircraft climbs to 15000 feet and enters 'level flight' phase. My basic knowledge of physics says that forces on the aircraft at this time are balanced - as seen in this diagram. Would an ...
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1answer
2k views

Poisson brackets and angular momentum

I'm trying to find $[M_i, M_j]$ Poisson brackets. $$\{M_i, M_j\}=\sum_l \left(\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial ...
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2answers
360 views

Bowling ball on a rubber sheet

After reading a layman's guide to general relativity, I began to wonder what shape a bowling ball on a large rubber sheet would produce. For simplicity, I would like to assume that Hooke's law applies ...
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420 views

Normal modes of oscillation: how to find them

Are normal modes the eigenvectors of the matrix $(\omega ^2 T- V)$ where $T$ is the matrix of kinetic energy and $V$ is the matrix of potential energy? Is it the only way to express them? How can I ...
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122 views

Are Carnot engine efficieny and Fourier heat trasmission law related?

It just occured to me that the efficiency of Carnot cycles is $\eta= \frac{T_1 - T_2}{T_1}$, that is, the efficiency decreases as the difference between reservoir temperatures decreases. On the other ...
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Uniform chain falls off table Diff EQ

I really need some assistance setting up this problem. any assistance would be a Godsend: a uniform heavy chain of length a initially has length ...
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2answers
3k views

Ball Rolling in a Parabolic Bowl

I encountered a physics problem which inquired about a ball rolling inside a parabolic bowl (i.e. a bowl where any cross section through the vertex would make a parabolic shape given by $y = kx^2$). ...
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55 views

Cubic symmetry and a stiffness tensor [duplicate]

Possible Duplicate: Stiffness tensor Let's have a stiffness tensor: $$ a^{ijkl}: a^{ijkl} = a^{jikl} = a^{klij} = a^{ijlk}. $$ It has a 21 independent components for an anisotropic body. ...
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412 views

What is the angle of the string with the vertical?

A heavy uniform sphere of radius $a$ has a light inextensible string attached to a point on its surface. The other end of the string is fixed to a point on a rough vertical wall. The sphere ...
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3answers
257 views

Is $k_B \rightarrow 0$ the classical limit of stat. mech., as $\hbar \rightarrow 0$ is in QM?

I hear very often among my peers and seniors that just as how $\hbar\rightarrow0$ takes me to classical mechanics from quantum mechanics, $k_B\rightarrow0$ will take me to classical thermodynamics ...
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2answers
99 views

Quantum Conservation versus classical conservation

If energy is conserved in all quantum mechanical interactions, how are there classical interactions in which energy is not conserved, given that classical interactions are a macroscopic approximation ...
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1k views

Force through quantum mechanics

In classical physics force is: $$F=\frac {dp}{dt}$$ How about quantum mechanics? In Old Quantum Mechanics momentum is: $p=\hbar \cdot k$ so force will be: $$F=\hbar \frac {dk}{dt}$$ what does $\frac ...
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165 views

What happens at the end of Coriolis Deflection

Consider we launch a cannonball due south from a point at 45 degrees latitude in the Northern Hemisphere (e.g the point defined with the co-ordinate system on this diagram). The cannonball travels for ...
7
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1answer
634 views

Can a deformable object “swim” in curved space-time? [duplicate]

Possible Duplicate: Swimming in Spacetime - apparent conserved quantity violation It is well known that a deformable object can perform a finite rotation in space by performing deformations ...
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1answer
5k views

Why is an electric motor more efficient at higher loads?

My question is driven by the plot below. We see that acceptable operating range of a motor is between 50-100% of the rated load. Below 40% or so the efficiency of the motor drops off dramatically. ...
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1answer
118 views

GR limit with massless particles and strong fields

What the mechanics arises if to take limit of general relativity with massless particles interacting with strong fields? Suppose there a system of attracting particles that have zero rest mass. What ...
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14answers
4k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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1answer
2k views

Projectile Motion with Air Resistance and Wind

I am wondering how the general kinematics equations would change in the following situation. If an object were fired out of a cannon, or some sort of launcher, so that it had both an initial velocity ...
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1answer
909 views

Need for a side book for E.Soper`s Classical Theory Of Fields.

I am reading now E Soper Classical Theory Of Fields now and sometimes it is very hard to follow the equations.So I need a side book to read it comfortably.Landau`s book is not helping as its content ...
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0answers
146 views

Stiffness tensor

Let's have a stiffness tensor: $$ a^{ijkl}: a^{ijkl} = a^{jikl} = a^{klij} = a^{ijlk}. $$ It has a 21 independent components for an anisotropic body. How does body symmetry (cubic, hexagonal ...
2
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1answer
361 views

Euler-Lagrange Equation

A particle moving towards the origin has initial conditions $x(t=0) = 1$ and $\dot{x}(t=0)=0$ If the Lagrangian is L:=$\frac{m}{2}\dot{x}^2 -\frac{m}{2}ln|x|$ This should satisfy Euler Lagrange ...
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1answer
2k views

Meaning of negative frequency of sound wave

Suppose that Alice and Bob are both holding speakers emitting sound at a frequency $f$. Alice is stationary while Bob is moving towards Alice at twice the speed of sound. In the case of Alice, if I ...