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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Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
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187 views

Do we need infinite energy to make 2 similar charges touch only in theory?

By Coulomb's law, say if we have 2 point particles each having a charge of +1C then by the formula, F = k/(d)^2 if we need to make the distance between them zero, clearly y the formula, we need to ...
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3k views

What force does bathroom scale measure?

When you stand on a bathroom scale, I know that the force displayed is the normal force. Since it is the normal force, then technically the force displayed would actually be Fg= (mass)(acceleration) ...
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672 views

effect of atmospheric pressure on reading of a weighing scale

Let us consider a completely sealed weighing scale such that the air pressure above and below the pan of the scale are equal and is equal to 1 atm. pressure. The scale initially reads zero. Now if ...
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187 views

Energy of a cylinder rolling down a path

Problem statement: A cylinder rolls without slipping down a hill. It is released from height h. What is its speed when it come down? The cylinder mass may be completely concentrated on the radius R, ...
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590 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.
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132 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 ...
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2k views

Stopping distance of two objects with equal Kinetic Energy

I'm working on a problem regarding two objects with the same kinetic energy. Two objects with masses of $m_1$ and $m_2$ have the same kinetic energy are both moving to the right. The same constant ...
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575 views

FWHM in resonance amplitude square derivation

Consider a linear harmonic oscillator subject to a periodic force: $$ \ddot x + 2 \beta \dot x + \omega _0 ^2x = f_0\cos \omega t$$ The solution tends to: $$A \cos (\omega t - \delta)$$ where: ...
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967 views

How do you tell what forces do no work?

The total mass of the children and the toboggan is 66 kg. The force the parent exerts is 58 N (18 degrees above the horizontal). What 3 forces/ components do no work on the toboggan? I said the ...
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413 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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1k 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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299 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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80 views

How to show that if two masses($m_1$ and $m_2$) are connected($r_1<r_2$) with a string moving around a point A, they move with same angular velocity?

How to show that if two masses($m_1$ and $m_2$) are connected($r_1<r_2$) with a string moving around a point A( circular motion), they move with same angular velocity? In this special case if ...
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333 views

By how much will water resistance and upthrust slows down a fully submerged object?

Consider the following example: While running, I do work and I have a certain velocity and acceleration. When I'm in a pool (my feet are touching the bottom), I do the same work but, I have less ...
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128 views

Non-relativistic Kepler orbits

Consider the Newtonian gravitational potential at a distance of Sun: $$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$ I write the classical Lagrangian in spherical coordinates for a planet with mass ...
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558 views

Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
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818 views

Energy used to stop / slow an object

I'm trying to workout how much energy (if any), I use (imagining me as an efficient machine rather than a complex bio-mechanical human) when I lower or catch a weight. I understand that when I push it ...
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206 views

Horsepower achieved with multiple motors

Scenario I'm planning to build an electric motor for fun (not for any practical purpose). I recently purchased a shapeoko CNC mill kit and intend to manufacture most of the parts housing, stator etc. ...
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239 views

Having Trouble With The Principle Of Conservation Of Momentum For a Multiparticle System

I'am reading John Taylor's Classical Mechanics chapter 1 page 20 where he proves the principle of conservation of momentum which states "If the net external force $F^{ext}$ on an $N$-particle system ...
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Does effective potential for a gravitational force have a maximum below $E=0$?

The relevant figure is below (taken from Goldstein's Classical Mechanics). This figure plots the effective potential for a gravitational force. Does the effective potential $V'$ go flat below $E_2=0$? ...
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90 views

Showing $ \textbf{F} \cdot d\textbf{s} = -dV$ is equivalent to $ F_s = -\frac{\partial V}{\partial s}$

Can someone please explain how the following $$ \textbf{F} \cdot d\textbf{s} = -dV$$ is equivalent to $$ F_s = -\frac{\partial V}{\partial s}$$ using some intermediate steps. I don't follow this ...
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401 views

Angular velocity $\omega$ by $v$

We have two girls, with mass ($M$). They become close to each other in speed of $V$. The distance between them is $3L$. I was asked to calculate the Angular velocity ($\omega$) of the two girls. So ...
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98 views

Explain moving lightbulb [closed]

An acquaintance of mine, while being home alone, saw that the light bulb in the room which was hanging from the ceiling with wires having a pendulum motion which was more than noticeable. He says that ...
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377 views

How does solar activity affect the ISS?

Currently the sun is launching some intense solar flares. http://www.guardian.co.uk/science/2011/feb/17/solar-flares-northern-lights-uk Th article I've linked also mentions how a "coronal mass ...
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2k views

Impulse - distance question [closed]

What impulse should be applied to an object of mass m, having a known coefficient of friction u to get to a distance d ? Thanks! Update 14.02.2011: I still wasn't able to find an answer to this. ...
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42 views

Hamilton-Jacobi problem

In analytical mechanics by Fasano and Marmi they consider the Hamilton-Jacobi equation for a conservative autonomous system in one dimension with the following Hamiltonian, \begin{equation} ...
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19 views

What can I say about a graph depicting orbit a particle has gone through? Acceleration VS friction

I have an orbit in which a particle is told to have gone through. There is a straight part, and a curved part. I am asked to mark the right statements, which are: a. Without any further data, there ...
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38 views

Holonomic constraints and degrees of freedom?

Can we see that a constraint can decrease the degrees of freedom of a system if and only if it is holonomic. Either way please can you explain why?
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38 views

Which of the Physics textbooks would you recommend I read this quarter (Analytical Mechanics)? [duplicate]

My Analytical Mechanics class this quarter has one required textbook: "Classical Dynamics of Particles and Systems" by Thornton & Marion and three recommended readings: "Mechanics" by Landau ...
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56 views

Why does the following contradiction arise in Lagrangian Formalism?

If we look at the Lagrange's equation $\frac{d}{dt}(\frac{\partial L}{\partial \dot{q_i}})- \frac{\partial L}{\partial q_i}=0$ It is clear that Lagrangian is invariant under a Transformation $L ...
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58 views

Does it take more effort to move against earth's rotation?

I know that if we stand still, we are traveling at 0 m/s relative to the Earth. But if we move against the rotation of the Earth we lower our speed, so, wouldn't we have to fight against the ...
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22 views

How to visualize the holonormic constraint $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0

A holonormic $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0 appears in Goldstein's Classical Mechanics Pg 12. Where $i$, and $j$ are particles, however $c_{ij}$ is not defined. How someone deduce the ...
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53 views

Lagrange equation and a force derivable from a generalized potential

I was reading the solution of this exercise and I have a doubt: A point particle moves in space under the influence of a force derivable from a generalized potential of the form $$U(r,v) = ...
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56 views

Showing time-invariance of Lagrangian with time-displacement operator

I am trying to show that the time-invariance of the Lagrangian of a simple one-particle system implies energy conservation for that system. The first step is, well, to show that the Lagrangian is ...
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55 views

Euler-Lagrange equation with torsion, question on derivatives

Consider a mechanical system, the Lagrangian of which is: $$-L(u,\dot u)=\int\left(\dfrac{\partial^2 u}{\partial x^2}\right)^2\mathrm{d}x$$ This would correspond to a system in torsion, for example. ...
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81 views

Mathematical pendulum in accelerating frame of reference [closed]

An aquintance of mine, who is a first year physics student was given a simple task as a homework-like task, which is about determining the ratio of periods between two equal-parameter mathematical ...
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104 views

Taking moments about two different points in a system of forces

If you have a system of forces and you take moments about two different points will the moment be the same?
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48 views

How to calculate the deceleration of two trains moving with the same velocity? [closed]

Two trains travelling on the same track are approaching each other with equal speeds of 40m/s. The drivers of the train begin to decelerate simultaneously when they are just 2km apart. If the ...
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155 views

How much force can bolt cutters exert?

What's the mechanical advantage of an ordinary, let's say, 3 feet long bolt cutters? How many pounds can they exert? I'm asking because I have a lock which is apparently immune to over 9 tons of ...
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261 views

Rolling without slipping and friction

When a ball rolling without slipping along an inclined plane reaches the bottom, it has a linear velocity $v$ and angular velocity $\omega\ =v/r$ at the bottom. Then it continues its motion on the ...
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64 views

What are the necessary/sufficient conditions for a system to be Hamiltonian/non-Hamiltonian?

I searched for a definition of Hamiltonian system on Huang and Tuckerman text but have not found anything precise. So intuitively I suppose: Hamiltonian system= a system which admits a complete ...
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132 views

Find angular velocity of motor

I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong. Basically ...
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1answer
43 views

What am i doing wrong here(dynamics)?they should give the same answer [closed]

So a body $m$ is on a uniform circular motion ($\omega = d\theta/dt = \text{constant}$), it is suspended by an inextensible rope with negligeable mass: First picture so: $$ -mg + T \cos \alpha = ...
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1answer
143 views

Torque and Car parked on slope [closed]

I have a homework question in which a car of mass $M\ kg$ is parked on a hill inclined at $25^o$ The car is facing up the hill and I am told that the wheels are $3\ m$ apart and the centre of mass is ...
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242 views

Why is angular velocity of any point about any other point of a rigid body always the same?

I have the following question regarding an ideal rigid body. Firstly, is it always true without any exceptions that the angular velocity of any point about any other point on a rigid body is always ...
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80 views

determining phase constants in SHM [closed]

A particle moves along the x axis. It is initially at the position $x$ of $0.300 m$, moving with velocity $v$ of $0.070 m/s$ and acceleration $a$ of $-0.330 m/s^2$. Suppose it moves with constant ...
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50 views

Questions about basic jump physics

This is a problem a friend and I are working on for an undergrad reading course. Our goal at the end is to make an accurate two-dimensional model of the human jump using Processing by the end of next ...
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85 views

Gravitational work

As far as I know gravitational work is independent from the path of the object, and I have an object that goes up on a inclined plane to a certain height, and than, after the object reaches the edge ...