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

Angular momentum without an axis of rotation?

A rigid body consists of particles of masses $m_i$ at distances $r_i$ from the origin, having linear momentum $p_i$. My teacher defined $∑r_i×p_i$ as simply the angular momentum of the system. But in case of rotation of a body about an axis, he…
Not Euler
  • 3,079
0
votes
2 answers

Mechanics - Hooke's law and energy conservation

Been doing some advanced mechanics questions and stumbled upon one i can't wrap my head around. It goes as follows: One end of a light elastic string of stiffness /l and natural length is attached to a point O. A small bead of mass is fixed…
HoplessStudent
  • 3
0
votes
1 answer

Math in Mechanics

I thought $\frac{d}{dx}, \frac{\partial }{\partial x}$ are basically the same thing and whenever it occurs in a problem I used just $\left(x\right)^{'}$. But recently my professor has been using $\int \:$ for $\frac{d}{dx}$. Why is that so? What…
Amarrraa
  • 1
0
votes
0 answers

Derivative of position and velocity in generalised coordinates

Consider $q_m$ to be the generalised coordinates where m = 1,2,3.... in Cartesian coordinates $x(q_m, t)$, we can express the velocity as $$\dot{x_{p,i}} = \dfrac{\partial x_{p,i}}{\partial q_m} \dot{q_m} + \dfrac{\partial x_{p,i}}{\partial t}…
Raptor
  • 109
  • 1
  • 1
  • 9
0
votes
1 answer

Tension in strings, when 2 strings hold 1 object

The question: In a different arrangement, the string is cut so that the lengths of the two parts are $0.5m$ and $2.3m$. Describe how the block hangs in equilibrium in this case and state the tensions in the two strings. My attempt: I used $a^2 =…
Sonny Da Silva-Peters
  • 316
0
votes
0 answers

Suppose we have a rigid body of mass $M$ . What Moment of Inertia do I use?

Let $O$ be a fixed point of the body and suppose that $O, \underline{e_1},\underline{e_2}, \underline{e_3}$ form principal axes for the body with principal moments of inertia $A, B, C $. The body is free to rotate about the point $O$ about the axis…
Connor Davies
  • 65
0
votes
1 answer

Frictional forces and their directions

Recently I asked a question regarding frictional forces at math stack-exchange(because its basically part of maths syllabus) and I drew some conclusions. If A and B are in rough contact and are in limiting equilibrium, then there exist two…
mathnoob123
  • 1,373
0
votes
0 answers

Perpendicular axis theorem on a particle

Is perpendicular axis theorem (inertia) applicable to a particle? If no, Why not? If yes, then in the question A uniform circular disc has diameter AB, mass 2m and radius a. A particle of mass m is attached to the disc at B. The disc is able to…
mathnoob123
  • 1,373
0
votes
2 answers

Inertia of a particle

The inertia of a ring is $I$. The ring is on the point $B$ of a rod AB of length 2a, having negligible inertia. The inertia of the particle at A is $I+4Ma^2$ where $M$ is the mass of the ring. However I use a different approach to calculate inertia…
mathnoob123
  • 1,373
0
votes
1 answer

Finding the critical point of Reaction on a plane

The answer scheme tells that C is the critical point and the the inequality $Reaction>0$ should be used over C. How is this point C decided? Why not B or midpoint of BC? Is there a way to formula a function whose stationary points will indicate…
mathnoob123
  • 1,373
0
votes
1 answer

Find the approximate Lagrangian when $\theta \approx \theta_0$

I'm given the Lagrangian $$L=\frac{1}{2}R^2\dot{\theta}^2(m+M)-mg(l-R\theta)+MgR\cos\theta$$ for a pulley system and I'm told that it has an equilibrium at $\theta_0=\arcsin(m/M)$. I'm asked to find the approximate Lagrangian when $\theta \approx…
MHW
  • 2,940
0
votes
1 answer

Use conservation of energy to justify where the maximum speed of the sphere occurs

Suppose a solid sphere of mass $M$ rolls along the surface given by $z=x^2/2-R$ without slipping. Also suppose that it is released from height $h$ and that the centre of the sphere remains in the $x-z$ plane. I have found that the kinetic energy is…
MHW
  • 2,940
0
votes
0 answers

Find the constraint force acting on the plane

An inclined plane of mass $m_1$ inclined at an angle $\theta$ lies on the $x$-axis. Let $(x,0)$ denote the position of the plane. A spring with spring constant $k$ is attached to the right of the plane. The spring is horizontal and unstretched when…
MHW
  • 2,940
0
votes
1 answer

Magnitude and sense of the force applied at A to reduce the reaction at B to zero.

A light horizontal beam $AB$, of length $9m$, supported at its ends by a force $S$ acting vertically and a force $R$ acting at an angle α to the line of the beam. A force of $30N$ is applied to the beam, at an angle of $30^o$, $3m$ from $B$. The…
J132
  • 307
0
votes
3 answers

Relation between the angles of two projectiles landing in the same spot

Given that two projectiles are fired at the same velocity, from the same spot, and land at the same point following different trajectories, how can I find the difference between the two angles of projection and the times taken for the projectiles to…
Plato
  • 2,332
1 2 3
…
22 23