3
votes
1answer
59 views

Invariance of canonical Hamiltonian equation when adding the total time derivative of a function of $q_i$ and $t$ to the Lagrangian

The following is exercise 8.2 in 3rd edition (and exercise 8.19 in 2nd edition) of Goldstein's Classical Mechanics. Adding the total time derivative of a function of $q_i$ and t to the Lagrangian ...
1
vote
2answers
152 views

When is this integral zero?

I have a particle with total energy $E$ confined in a potential $$U(x) = -\frac{\cos^4x}{2} - m \cos x - f \sin x. $$ The constants $f$ and $m$ are both in the range (-2,2). The energy is such that ...
0
votes
2answers
81 views

Electrical force between two objects

I tried to solve the following problem: There are 2 objects . The object m1 with charge q and the object m2 with charge q.(same charge).The object m2 is connected with a rope to the ceiling. at the ...
2
votes
2answers
105 views

What's wrong with my calculation of gravitational potential for a uniform sphere?

This is really embarrassing, but I'm not quite sure where I'm going wrong here... Why is this calculation of the gravitational potential inside a sphere with uniform mass distribution incorrect? ...
6
votes
1answer
73 views

Curvilinear Coordinates and basis vectors

In these notes, $\frac{\partial \vec{r}} {\partial q_i}$ is stated to form a basis set for the vector space. How does this happen? Also, how does one justify this equation from Goldstein's ...
1
vote
0answers
42 views

How to show $ \epsilon_{iab}\epsilon_{jcd}(x_ap_d\lbrace x_c,p_b \rbrace+x_cp_b\lbrace x_a,p_d \rbrace) = x_ip_j-x_jp_i$ [closed]

If $ \lbrace f,g \rbrace $ is Poisson bracket and $\epsilon_{ijk}$ is Levi-Civita symbol, how to show that $$ \epsilon_{iab}\epsilon_{jcd}(x_ap_d\lbrace x_c,p_b \rbrace+x_cp_b\lbrace x_a,p_d ...
1
vote
1answer
78 views

How can I derive this Hamiltonian?

I have a Lagrangian $L$, a momentum $p$ and a Hamiltonian $H$: $$L=\frac m 2(\dot z + A\omega\cos\omega t)^2 - \frac k 2 z^2$$ $$p=m\dot z + mA\omega\cos\omega t$$ $$H=p\dot z - L=\frac m 2 \dot ...
0
votes
2answers
49 views

How is the velocity not constant?

A bead is moving along the spoke of a wheel at constant speed u , the wheel rotates with uniform angular velocity w radians per second about an axis fixed in space , at t=0 the bead is in the x ...
1
vote
1answer
41 views

How can I find the motion equations of the 2-dim harmonic oscillator?

First of all: I am no physicist, so I am rather helpless. I need to find the moving equations of the 2-dim. harmonic oscillator. If it is possible it should be rather elementary, because, as I said, ...
1
vote
0answers
41 views

Tension on an object [closed]

According to a website, $T_3 = T_2 + T_1$. Also, the rope and pulley device are mass less. But I don't really understand this. Let me try and explain how I see the problem. $M_2$ receives tension ...
0
votes
1answer
31 views

Lifting an Atwoods machine from the ground? [closed]

If we have an Atwood machine where masses $m_A$ and $m_B$ rest on the ground, then we apply an upwards force $F$ to the Atwoods machine. What is the acceleration of the blocks when $F=124N$, $m_A = ...
0
votes
2answers
51 views

Rocket towing an object

I'm not sure if my question makes sense, but I don't know where to start. A crate of mass $m_2$ is connected by a massless rope of constant length $l$ to a rocket of mass $m_1$. We take into account ...
1
vote
0answers
30 views

Lagrangian for a system of particles [closed]

If a system of particles attracting each other under inverse square force, then prove that $$ 2<T> + <V> = 0.$$
-1
votes
1answer
43 views

Initial velocities of a collision [closed]

This is the question: A car of mass 900 kg and a van of mass 1300 kg collide at a crossroads. Investigation into the collision discloses that the car was travelling south east and that the van was ...
3
votes
1answer
51 views

Rotational Friction

This is the question- Consider a cylinder of mass $M$ resting on a rough horizontal rug that is pulled out from under it with acceleration $a$ perpendicular to the axis of the cylinder. What is $F$ ...
0
votes
1answer
97 views

Acceleration of masses hanging from a system of two pulleys

"Masses $M_1$ and $M_2$ are connected to a system of strings and pulleys as shown. The strings are massless and inextensible, and the pulleys are massless and frictionless. Find the acceleration of ...
0
votes
0answers
50 views

Center of mass coordinates in Lagrangians and Laplacians

Is there a quick nice and easy way to write Lagrangian's and the classical/quantum Laplacian operator in terms of center of mass coordinates? The algebra is so involved and it has me confused about ...
1
vote
2answers
87 views

Damped Coupled Oscillations

I'm currently revising for a vibrations and waves module that I am taking as part of my physics degree. One of the our final questions involved finding equations for the displacements of the two ...
2
votes
0answers
23 views

Normal modes of two wires fastened together

The problem is to find the normal frequencies of the system formed by two fastened wires of length L, and different mass per unit length. I already wrote the boundary conditions, but I need to know ...
5
votes
5answers
220 views

Euler-Lagrange equation for continuous systems

I'm having a little trouble with wrapping my head around a part of a method which is fairly 'new' in some fashions to me. I imagine it should be fairly obvious, but I am not seeing something at the ...
0
votes
1answer
56 views

What can cause a change in wave's shape - One dimensional wave

what can cause a change in wave's shape of one dimensional wave moving through a rope? It's velocity ? or the wave's length ? What can cause him change his shape.
1
vote
0answers
29 views

Criteria for stable equilibrium [closed]

A homogeneous wooden bar of length 10 cm, thickness 4 cm and weight 1 Kg is balanced on the top of a semicircular cylinder of radius R as shown below. What is the minimum radius of the semicircular ...
3
votes
2answers
828 views

Sum of torque from a sphere

A sphere (grey color) turn in rotation at $\omega$ rd/s. There are 2 walls that prevent sphere to escape. Walls can only turn around center of rotation. The sphere turn only at $\omega$ rd/s too. The ...
0
votes
2answers
102 views

Inertia matrix of a rod rotating about an axis [closed]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
0
votes
1answer
41 views

A pearl that moves in a smooth vertical hoop

I wanted to ask about the situation of a pearl that moves in a smooth vertical hoop in circular motion as described in the following sketch. According to a simulation found in the internet , a ...
0
votes
1answer
39 views

A pearl that moves in a smooth vertical hoop (Circular motion) [closed]

I couldn't understand something about the situation of a pearl that moves in a smooth vertical hoop in circular motion. When the normal force equals 0 , the pearl didn't disconnect from the smooth ...
2
votes
4answers
80 views

Acceleration and Circular Motion

Lets assume that there is a force that makes our body moves in circular motion. We know that the acceleration of a body that moves in circular motion is Velocity ^ 2 / Radius . How is it ...
1
vote
1answer
61 views

Speed of liquid being blocked at end of pipe

How fast would water go if at the end of of a 1 inch diameter pipe was closed by a valve? The system is as follows: 5 meter high source of water that feeds a 1 in pipe. The pipe goes straight down ...
5
votes
1answer
115 views

Is there a systematic way to derive constraint equations?

There's this problem in Goldstein's (Classical Mechanics) derivations section: 5. Two wheels of radius $a$ are mounted on the ends of a common axle of length $b$ such that the wheels rotate ...
0
votes
1answer
34 views

A question about Hamiltonian phase flow

Show that if a one-parameter group of difeomorphisms of a symplectic manifold preserves the symplectic structure then it is a locally hamiltonian phase flow. Note that A locally hamiltonian ...
1
vote
2answers
118 views

How much force is required to compress air?

How much force (Newtons) is required to compress normal air in a chamber to 2 atm? For example, if I had a sealed piston pump, how much force would need to be exerted in order for the air to be ...
0
votes
0answers
77 views

More on the closed-form for a simple pendulum

I've learnt about the simple pendulum, and while the regular curriculum only uses the linear approximation of $\sin\theta$ to obtain $\ddot\theta+\omega_0^{2}\theta=0$. I tried to find out about a ...
2
votes
1answer
94 views

Lagrangian to Hamiltonian

I'm having some problems with an assignment where I have to state the Hamiltonian from the kinetic energy $T$ and potential energy $U$. These are as follows: ...
-1
votes
1answer
54 views

Can someone explain the solution (provided) of this conical pendulum work problem [closed]

In the image, it looks like the tangential direction is always 45 degrees away from the string, not 90 degrees. Is it not the circular path that the solution is talking about?
1
vote
2answers
86 views

How do I properly write Newton's second law for a particle with drag?

A heavy particle is projected at speed $U$ at an angle $\alpha$ to the horizontal. The particle is subject to air resistance which is experimentally found to vary proportionally to the square of ...
1
vote
1answer
98 views

Spring Damper System for a Vibrating Motor

Good day people of SE I have a friend that has a final year project and is stuck. He has a motor with a small weight at the end of the shaft that causes vibrations. This motor is on a thin plate. ...
1
vote
0answers
69 views

2d pool collision with rotational motion

I'm trying to calculate two 2d disks' collision with rotational motion. The collision is perfectly elastic: the sum of translational and rotational energy is conserved. In the instant of the collision ...
2
votes
1answer
71 views

Find Angular Momentum about any point

How do I find the angular momentum of a body about any point? We know that $L=I\omega$ for a body rotating in space, where $L$ denotes the angular momentum, $I$ denotes the moment of inertia and ...
7
votes
2answers
224 views

Find the minimum value of velocity [closed]

Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$. Details and assumptions $R=2m$ $g=9.8m/s^2$ Neglect air resistance. All ...
0
votes
3answers
163 views

In what situations do water levels not reach equilibrium?

I have been taught that water levels will always equal out. However, now I find that sumps and some other setups allow for water not to become equal. What other arrangements allow for the water levels ...
0
votes
1answer
36 views

Two masses collide on a ramp [closed]

M1 slides down a frictionless ramp and collides with M2 They both compress the spring. How far is the spring compressed? What is the final velocity of M1 on the rebound up the ramp? I was thinking ...
1
vote
1answer
918 views

How to calculate the moment of inertia of a solid cube

How do I calculate the moment of inertia of a uniform solid cube about an axis passing through its center of mass? I also wanted to know if the moment of inertia ...
0
votes
2answers
84 views

Angle rotated by a rod when it's hit by a pendulum

Consider a pendulum of length $h$ with a bob of mass $m$ it is held horizontally at and angle of $90^{\circ}$ with the vertical. A rod of mass $M$ and length $h$ is pivoted at its upper end and this ...
0
votes
2answers
53 views

Homework Question involving Momentum [closed]

I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: You are at Lowe’s shopping for bricks ...
1
vote
1answer
252 views

Modeling a 2-dimensional mass spring system

First of all, I am unfortunately not an expert in physics, so please be indulge with me. I am trying to model a $2$-dimensional mass-spring system with $1$ mass and $3$ springs to solve a dynamics ...
1
vote
1answer
73 views

$\cos^{2}(\phi)$ in the kinetic energy term of the Lagrangian is one?

I'm doing some homework in Classical Mechanics, and is about to write out the Lagrangian of a system. But, when I check the answer from my teacher, something is missing. The kinetic energy I'm using ...
1
vote
1answer
113 views

From Lagrangian to equations of motion [closed]

I have a given Lagrangian: $$L= e^{st}\cdot\frac12\cdot(mv_y^2-ky^2)$$ And are asked to identify the equations of motions, the constants of motions and physical system. Without the exp-time-term, ...
3
votes
3answers
151 views

A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$ [closed]

I have complications to do the following problem: A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors. My first idea was ...
5
votes
1answer
114 views

Pendulum with a rotating point of support from Landau-Lifschitz

I found this problem in Landau-Lifschitz vol.1 (Mechanics) A simple pendulum of mass $m$, length $l$ whose point of support moves uniformly on a vertical circle with constant frequency $\gamma$. ...
0
votes
1answer
70 views

Power and speed [closed]

I'm asked to calculate how much POWER a 1210kg car needs to drive with a 85 km/s speed up a 655 meter long slope of 4.5°. I can find how much energy and work is required to do this, but isn't ...