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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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Simple mechanics question - trapeze

A woman of mass 50kg swings on a light trapeze, i.e. a light seat suspended from a fixed point by a light rope. Her centre of mass, G, moves on the arc of a circle of radius 9m and centre O. Initially the woman is at the point A, where OA is at…
Pie
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Moment of inertia of a disc

In my mechanics textbook there is a derivation of the moment of inertia of a disc of mass $m$ and radius $r$ about an axis through its centre and perpendicular to its plane surface, which goes something like this: The mass per unit area is…
user85798
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Mechanics Question I do not understand

A particle starts from rest and moves in a straight line with constant acceleration. In a certain 4 seconds of its motion it travels 12 m and in the next 5 seconds it travels 30m. The acceleration of the particle is? The velocity of the particle at…
Xplane
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Evaluating space curves

What does it mean to evaluate a function on a space curve? Eg for the following question Consider the space curve defined by the following position vector: $$r(t) = \cos t \ i + \sin t \ j + t \ k$$ and the scalar valued function: $$V (x, y, z ) =…
user127700
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Harmonic Oscillator Homework, Require Verification

A particle of unit mass movies on a straight line under a force having potential energy $$V(x)=\frac{bx^3}{x^4 + a^4}$$ where a,b are positive constants. Find the period of small oscillations about the position of stable equilibrium. So, I…
Vladimir Nabokov
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Terminal Velocity Equation

A ball of unit mass is dropped. How do I work out it's terminal velocity when the ball has air resistance proportional to the square of the velocity?
Vladimir Nabokov
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Particle starting from rest

A particle starting from rest so that its velocity varies as the nth power of the distance described from the commencement of the motion. Prove that $\mathbb{n <= 0.5}$. I know we need to express $\mathbb{v = k(x-a)^n}$ and need to prove that a…
subrat verma
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How to find the angle of elevation and launch speed?

A particle is projected from a point on level ground with a speed of $u$ meters per second and an angle of elevation $\theta$. The maximum height reached by the particle is $42$ meters above the ground and the particle hits the ground $196$ meters…
Pranoy Bhatnagar
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For the following setup, what is the second holonomic constraint to limit the bead to one dimension?

We have a bead sliding along a smooth wire in the shape of a cycloid with equations, $$ x=a(\theta-\sin\theta),\space y=a(1+\cos\theta), $$where $0\leq\theta\leq2\pi$. To find the number of coordinates required to describe the motion of the particle…
Kian31
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What's the mathematical/physical reason this equation is true?

$$-\sum_i \frac{dx_i}{dt} \frac{\partial V(\{x\})}{\partial x_i} = - \frac{dV}{dt}$$ where $x_i$ is the coordinate of a configuration space and $V({x})$ is the potential energy function. I have only started learning multivariable calculus and don't…
244529
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Spivak, Classical Mechanics: rolling disc

In page 231 of his brilliant classical mechanics book ("Physics for Mathematicians 1"), Spivak considers the setting where we have a disc rolling on a planar floor such that the plane of the disc is always perpendicular to that of the floor (i.e.…
Plemath
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The particle flies into a strongly elongated ellipse and moves according to the law "angle of incidence == angle of reflection".

We need to find the period of motion and the regions inaccessible to the particle. I would like to at least understand how to solve it ideologically, otherwise I have no thoughts at all...
S4D7 F128
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Two particles on a lever. One of them can slide along the lever.

This is exercise 4 page 202 from Spivak's book on mechanics. Two particles of masses $m_1,m_2$ are attached to a lever of negligible weight, and are at distances $d_1,d_2$ from the fulcrum, like this: Suppose we start the lever making an angle…
Plemath
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calculate conjugate momentum p for a lagrangian

For the Lagrangian $2L=\dot{q}^2-q\dot{q}+q^2$ (A) $q+\dot{q}$ (B) $q-\dot{q}$ (C) $q\dot{q}$ (D) $\dot{q}-q$ I have a doubt here. in fiew books $p$ is said to be generalized momentum. Does these generalized momentum and conjugate momentums are…
user118413
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Is possible to define velocities for different bodies such that they will never be at the same point simultaneously?

I'm working on a school project and would like to discuss some ideas. First, let's imagine that there are two lines, each line has a length x. In each line there is a "runner", so to speak, and when the runner arrives at the end, he is transported…
Henrique Rick
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