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Questions tagged [classical-mechanics]

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question.

Wikipedia says:

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light.

For questions on classical mechanics from a mathematical standpoint. This tag should not be the sole tag on a question. Examples of other tags that might accompany this include , , and .

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Confusion about Legendre transform

So we if we have a function $A(x,y)$ and we want to get a function $B(x,z)$ where $B$ is the function $A$ that is dependent on z and independent of $y$. We define the Legendre transform as $$B(x,z) = zy - A(x,y)$$ and we say that for $B$ to be…
realanswers
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Conservation angular momentum under rotation, Theorem 12.2 Classical Mechanics by Gregory

I am trying to understand the following proof form the book "Classical Mechanics" by Gregory: Question What I do not understand is were the formula $\frac{\partial r_{i}^{\lambda}}{\partial\lambda}=k\times r_{i}^{\lambda}$ comes from. The…
Hans
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A mechanics question with "constant acceleration"

Main problem is with part (b). I got it right up to the accelerations with -11.6 and 4.4 respectively. Then I dont really see the reason why we have to break it up to two parts as given in the solution. We should be able just to use the constant…
CasperYC
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How to calculate mu on a rough inclined plane

I'm sorry that I can only give the question here but I have no idea how to calculate $\mu$. Question is as follows: A body is projected at $24\text{ft/sec}$ up a rough plane inclined at $\text{tan}^{-1} \frac{7} {24} $ to the horizontal. With what…
GR L
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Arnold's problem on central filed

I am reading Mathematical Methods of Classical Mechanics by Arnold. I got stucked on a problem about central fields. Usually in literature central fields are given by $\mathbf{F} = \Phi(r) \mathbf{e}_r$, where $\mathbf{e}_r$ is the radial unit…
gmirsan
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Two Planets with different radii, same mass and same angular velocity orbit a star on a straight line.

I tried to solve the following exercise in theoretical mechanics: Two Planets A and B with equal mass $m$and equal angular velocity $w_0$(constant) move around the sun $S$ with mass $M$ in circular concentric orbits with radius $r_1$ for Planet A…
Blue2001
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How to form equations in vertical motion under gravity questions.

I've been struggling with this for a while but despite my best efforts I have not been able to form suitable equations. Question is as follows: A stone is dropped from a cliff $160 ~\text{ft}$ high and $\frac{1}{2}$ second later another stone is…
GR L
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Find the expression for the work done in turning the cylinder through one revolution

A light cable connects two weights $W,w (W>w)$ and passes over a rough circular cylinder whose axis is horizontal. $W$ rests on the ground,and $w$ is suspended in the air. Find the least value of the coefficient of friction between the cylinder…
ALMEra
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True Vectors? Kleppner's Mechanics

Kleppner refers to the displacement vector as a 'true vector' in the sense that while it's coordinate values depends on the initial and final points in a coordinate system, the vector itself does not. What specifically does this mean? Is it merely a…
Lars
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CLassical Mechanics | Relative velocity and Acceleration

With distances measured in nm and velocity measured in knots, 3 ships $A,B,C$ are observed from a coast guard station. At noon they have the following position and vectors relative to the station. $\vec{r_A}=-\mathbf i+\mathbf j$ and…
Maranatha
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Why does it matter where you take moments, when its a lamina?

I've just been doing moments on laminas for the first time and I think I've missed something crucial. If I take moments around point X, I get: Clockwise: 30N with a perpendicular distance of 2m = 60Nm Anti-clockwise: 10N with a perpendicular…
harpomiel
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What is the point talking about work done by frictional force here?

https://www.youtube.com/watch?v=0jWwl0bt6aU&list=PLUl4u3cNGP61qDex7XslwNJ-xxxEFzMNV&index=128 In this class Professor talks about work done by frictional force. He talks about motion of the object as well. I know frictional force is force opposes…
Unknown x
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Is solution to this question partly incorrect, i.e. does the solution contain a typo?

This is another old O level applied mathematics problem regarding moments. It reads as follows: A rod $PQ$ is $5 ft.$ long. When a $1 lb.$ mass is hung from $P$ and a $3 lb.$ mas is hung from $Q$, the rod balances at a point $42 in.$ from $P$. When…
GR L
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basic forces question about the reaction force

For a object like this, is the upward force applied of 2000N counted as part of the total reaction force to gravity? or is it separate and therefore the object will motion upwards.
kmvfkmfv
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confusion about the calculation of power

A car of mass $1600$ kg is pulling a caravan of mass $800$ kg on a straight horizontal road. The car and the caravan, moving at a constant speed of $25$ m/s, are connected by a light rigid tow bar. The resistances to the motion of the car and…
borns
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