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 angular velocity parallel to axis of rotation?

I'm reading the Wikipedia page on angular velocity. It says here of the angular velocity vector in three dimensions that “[t]he magnitude is the angular speed, and the direction describes the axis of ...
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1answer
49 views

Rate of applied force versus material failure?

Question: Does the rate at which a force is applied to an object determine the maximum force reached that mechanically fails the object? If so, what are the concepts that need to be understood to ...
0
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1answer
61 views

How does a pop pop boat work?

I have been reading about the pop pop boat on wikipedea. What I don't understand is after the hot water is ejected the vacuume gets created, so when the same amount of water will be sucked in the boat ...
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2answers
75 views

Simple Plane pendulum

So, I am having a lot of troubles visualizing the following system. The point of suspension of a plane simple pendulum of mass m and length l is constrained to move along a horizontal track and is ...
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0answers
27 views

Integral of Forces is the Velocity

I am self learning classical mechanics. I have the following problem: At time $t$ we have a force $f(t)$ acting on a particle with mass $m$ that is at distance $x(t)$ from $0$. We also assume ...
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2answers
24 views

Torsion and twist in solid cylindrical beam

Well given a beam (as shown), a solid cylinder with radius R. A Torque $T$ applied to it, I need to solve the angle of twist ($\theta$) at the position where the torque is applied ($z$). The basic ...
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0answers
42 views

An object on a conveyor belt

Let's say a bag (30kg) is sitting on a moving conveyor belt and at the end of the conveyor belt, there is a wall. Since the belt is moving at a constant speed (say 2.0 m/s), when the bag hits the ...
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0answers
45 views

What does the Hamilton-Function have to do with conservation of Energy in Lagrangian Mechanics?

I am currently doing Lagrangian Mechanics and I am having difficulties with deriving conservation laws from the Lagrangian. I have tried to understand this by reading the explanation in three ...
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0answers
31 views

How much torque would it take to tip over a Christmas tree?

I had an, ah, incident in the house last night (need I say more? That has led to me wondering about how much torque I would need to apply to tip over a tree to the point where gravity causes the tree ...
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1answer
45 views

Force Exerted on a Rocket

I am reading Spivak's "Physics for Mathematicians". He has the following setup up: We let $m(t)$ be the mass of a rocket and its fuel at time $t$. And, we let $q(t)$ be the velocity at which the ...
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1answer
24 views

What is the effect of torque transmitted through a gear system to the angular acceleration of a flywheel?

For a school project, I am trying to design a system that will spin a flywheel at a high rpm to store energy. My initial idea was to accelerate the flywheel via a compound gear train with an ...
2
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0answers
61 views

What is “Accumulated plastic strain rate” in Current yield Norton law?

I'm doing FEA of steel under high strain rates and using Elasto-ViscoPlastic material model, with Von-mises yield criterion along with Isotropic hardening. The strain rate sensitivity is addressed by ...
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2answers
58 views

Is this an error?

The teacher wrote the following: There is a dot missing where the green arrow is, right? After applying Euler's theorem, the term in brackets becomes $x_j$, but we need it to be $\dot{x_j}$, don't ...
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4answers
79 views

Relativistic acceleration in sinusoidal electric field

Consider a relativistic charge $q$ moving with an oscillating electric field $E_z$ with phase velocity $v_p=c$ in direction $\hat{z}$ (e.g. radially polarized laser coprogating with electron). What ...
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0answers
52 views

A mysterious conserved quantity for a central potential

In teaching a course in classical mechanics and I have come across (from my predecessor) a to me mysterious conserved quantity. We are considering a gravitational (or electric) potential with the ...
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1answer
36 views

Will a permanent dipole placed in a uniform external electric field exhibit periodic motion if it is displaced from equilibrium position?

Because at equilibrium position, the dipole is aligned along the direction of electric field and since it is a uniform electric field ,there will be no force on the dipole but it can still experience ...
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2answers
301 views

Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...
2
votes
1answer
67 views

Volume as a choice of measure in phase space

For equilibrium systems, we expect the Liouville theorem to hold. This theorem states that the density function of the states of the system is a constant of motion, which in turn can be translated ...
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1answer
51 views

Deformation of an elliptical ring

How will it deform when I compress an elliptical ring along its long axis? For simplicity we could consider that the ring is homogeneous, elastic, has no internal stress at the beginning, and its ...
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0answers
34 views

How Newton measured inertial mass of an object?

How Newton measured inertial mass of an object when he gave 2nd laws of motion. As we were not advanced enough at that time to use harmonic motion method to determine inertial mass of an object.
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1answer
38 views

Time until next collision

I'm coding a simulation of a 2D gas (circles of radius R) and I need to find the time of the next collision between two specific particles. Since the particles move in a straight line between ...
0
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2answers
54 views

Mass hanging from spring: potential energy [closed]

I have encountered a problem with a mass $m$ hanging from a spring. I want to find the maximum distance it will be stretched from the spring's equilibrium. At the maximum distance the spring is ...
0
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2answers
51 views

Momentum Equation VS Momentum of Momentum Equation

Newton's second law states that the linear momentum ($P$) rate is equal to the net force: $$F=\frac{d}{dt}P \tag{1} $$ On the other side, there is a same expression for angular momentum ($L$): ...
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0answers
42 views

How would a motorcycle with a sidecar flip?

On what edge is a motorcycle with a side car most likely to flip with and without a passenger? Assume that side car is on the right side of the vehicle and has a single wheel. It looks like this: ...
0
votes
1answer
80 views

Infinite pulley system

http://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol43.pdf Hi, I've been trying to solve this question for a while, I understand the first solution and also the solution to the second ...
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0answers
125 views

Friction in Lagrangian formulation

We know the Lagrange equations are: $$\frac{\partial \mathcal{L}}{\partial q_i}-\frac{d}{dt}\left(\frac{\partial \mathcal{L}}{\partial \dot{q_i}}\right)=0.$$ Then, when we add friction in there, we ...
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36 views

How would you prove/verify that the real forces are independent of frame of reference?

How would you prove/verify that the real forces are independent of frame of reference?
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1answer
21 views

conditions for variable tension in string

Are below the correct conditions for a string to have variable tension 1. string has to be massless 2. String is un accelerated. I get the 1st one. I am not able to understand 2nd one. I have seen ...
0
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1answer
124 views

We cannot solve this inclined plane problem, right?

We drag a sledge along a snow-covered hillside with constant speed. Distance is 150m. The time it takes to reach the top is 300 secs. The sledge is 12kg. And the coefficient of friction $\mu$ = 0.04. ...
2
votes
1answer
64 views

finding velocity along a curve with kinematic equations using time

(i'm "not" looking for coding help. i need help setting up the math.) i'm writing a program for a physics class to find the velocity of an object across a random curve. where the only force acting on ...
3
votes
2answers
100 views

What will limit the speed at which one can play the piano?

I thought about this as a fun question. Suppose we provide a piano player that is limited only by the typical relativistic rules (i.e., hands and fingers cannot move faster the speed of light), so ...
2
votes
0answers
37 views

Safest place to store a laptop in a car? [closed]

I sometimes drive my younger brother to his robotics club meetings and he brings a laptop to work on. He weighs about 70 lbs (32 kg) and is about 5'3" (1.6 m) tall. The laptop weighs about 20 lbs (9 ...
0
votes
1answer
31 views

Plausibility of the distance estimation in a cycle ergometer gym exercise

A friend of mine pedaled for an hour on a cycle ergometer, a stationary bicycle in a gym. At the end of the ride the cycle computer reported a distance of $40\:\mathrm{km}$ and an average power of ...
0
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1answer
49 views

Procedure for finding integrals of motion

In some examples I have read that if you want to find the integral of motion for some equation of motion, say on the form $\ddot{x}+ax=0$ for some constant $a$, you multiply the EOM by $$\dot{x}=q(x) ...
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1answer
64 views

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 ...
1
vote
1answer
36 views

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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0answers
34 views

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 ...
0
votes
1answer
38 views

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 ...
2
votes
3answers
123 views

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)?
1
vote
2answers
92 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 ...
1
vote
0answers
70 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 ...
0
votes
2answers
44 views

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 ...
0
votes
1answer
48 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 ...
0
votes
1answer
24 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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vote
0answers
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 $$ ...
0
votes
1answer
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 ...
0
votes
0answers
32 views

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} ...
1
vote
1answer
54 views

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 ...
1
vote
1answer
60 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 ...
0
votes
0answers
21 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 ...