Mathematics Stack Exchange
Mathematics Stack Exchange

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 .

2097 questions
0
votes
1 answer

Determine coefficients so that $f(x,y)$ is a conserved quantity

Given the function $f(x,y) = ax^2y + by + ct^2 $ with $x(t)=2t$ and $y(t)=3t^2$ I shall determine the coefficients a,b,c so that $f(x,y)$ is a conserved quantity. My approach is $$\frac{df}{dt} = \frac{\partial f}{\partial t} + \frac{\partial…
Christian
  • 1,781
0
votes
1 answer

Circular Motion and Conservation of Energy Question

A particle $P$ of mass m is connected to a fixed point $O$ by a light inextensible string $OP$ of length $r$ and is moving in a vertical circle, centre $O$. At its lowest point, $P$ has speed $U$. When the string makes an angle of $\alpha$ with the…
user140161
  • 1,363
-1
votes
1 answer

What's the relationship between KE, PE and WD against Friction in the Work-Energy Principle?

I'm struggling to understand the WE principle in its relationship to the gains/losses of both Kinetic Energy and Potential Energy. How do the formulas work? Does KE Gain + PE Loss = WD? Or does KE Gain - PE Loss = WD against Friction? The same…
mskr710
  • 31
-1
votes
1 answer

Position vector on rotating wheel

I'm working through mechanics questions and came across the following: Two identical particles P and Q, each of mass m, are attached to the ends of a diameter of a light thin circular hoop of radius a. The hoop rolls without slipping along a…
redknightofthesun
  • 45
-1
votes
1 answer

Using the conservation of energy with regards to a zero potential line

I have been trying to find the value of theta at which a string goes slack in a vertical circle, by letting the diameter of the circle be the zero potential My question is would the gravitational potential above and below the zero potential have…
Filthyscrub
  • 592
-1
votes
1 answer

Lagrangian and equations of motion on a pseudospherical surface

A particle of mass m oscillates up and down on a smooth surface of revolution parameterized as: $$(x= a \sin \phi \cos t, y= a \sin \phi \sin t,z= a(\cos \phi+ \log \tan \phi/2 )\;) $$ The $z$-axis is vertical up. $t$ is polar angle, $\phi$…
Narasimham
  • 40,495
-1
votes
1 answer

A cyclist's acceleration

A cyclist is travelling at a velocity of 10m/s when he reaches the top of the slope, which is 80m long. There is a bend at the bottom of the slope, which it would be dangerous to go around any faster than 11 m/s. Because of gravity, if he did not…
Shah21
  • 13
-1
votes
1 answer

High School Simple Harmonic Motion Question

Could someone please guide me through the following question. I honestly have no clue where to start. Thank you so much! A particle moving in Simple Harmonic Motion starts from rest at a distance 10 metres to the right of its centre of oscillation…
BooScout
  • 179
-1
votes
1 answer

Are the tension on the two strings that constrain a particle that is doing circular motion the same?

may I know whether the tension on the two strings are the same, the picture is attached. Thank you very much for your reply.
Henry Cai
  • 633
-1
votes
1 answer

Calculating Sumss Of Maths

I need to work out the total thrust on a vertical wall. The 1st part of the question: Imagine a pool having dimensions of (x)m x (x)m and it has a depth of (x)m The density is $(x)kg/m^3$ pmax + pmin / 2 pa x area will then equal the total thrust?
Diamonds
  • 59
-1
votes
1 answer

Central force and orbits

A particle moves in a plane under a force, towards a fixed centre, proportional to the distance. If the path of the particle has two apsidal distances $a,b$ $(a>b)$, then find the equation of the path. I came across this question on MSE. While…
Sharmi C
  • 419
-1
votes
1 answer

How to find their final speed in terms of their masses?

The answer is $\frac{1}{m_1}$ and $\frac{1}{m_2}$. I used the conservation of momentum (taking into consideration initial momentum is zero) , coefficient of restitution , and conservation of kinetic energy (since it is elastic collision) and did…
Powerful blaster
  • 23
-1
votes
1 answer

"Newtons laws applied to a train of 3 cars"

A train consisting of three cars of mass 'm' each is pulled with force 'F' by a locomotive in a straight, horizontal line. Assuming there is no friction, find the force on each car. How would I answer this question?
QuestionAnswer13
  • 93
-1
votes
1 answer

Circular Motion Question - fully algebraic

I'm sort of struggling with this problem, I've explained my reasoning so far below. This is the problem: A bend in the road is a horizontal circular arc of radius $\ r \ $. The surface of the bend is banked at an angle $\ a \ $ to the horizontal.…
Antonios
  • 25
-1
votes
1 answer

A rigid body having one point $ O $ fixed and no external torque

A rigid body having one point $ O $ fixed and no external torque about $ O $ has equal principal moments of inertia. Then the body must rotate with (1) angular velocity of variable magnitude (2) angular velocity with constant magnitude (3)…
MAS
  • 10,638
1 2 3
…
22
23