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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 .

2097 questions
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I'm unable to get a solution that agrees with the book.

This is another O level mechanics question that I've been struggling with for some time. It reads as follows: A uniform rod $AB$ $10$ $ft$ long and weighing $20 lb$ is hinged at $A$ to a point in a vertical wall and is kept in position by a string…
GR L
  • 329
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Kinematics stone thrown upwards past a point, show the following.

I know I should be able to do this, but I have tried for 3 hours and can't do it. I know its simple but it's driving me mad. A particle is projected vertically upwards with speed $ u_{0}$ and passes through a point that is a distance $ h $ above the…
wavey
  • 45
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Shifting of axis of rotation of disc

Image for following question Initially a disc is rotating about a point A on circumference with angular velocity $\omega$ . The point is then released and almost immediately point B is fixed on circumference. Show that the disc starts to rotate…
VGisHere
  • 58
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A-Level Mechanics Ladder Friction Question. Is the question wrong?

I received this question in one of my math homeworks. To sum the past couple months into a short sentence, this question has caused a lot of arguments: A uniform ladder, of weight 'W' and length 5m, has one end on rough horizontal ground and the…
Conor1102
  • 23
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Need Help With A Friction Problem (Mechanics)

Here is the problem: "A ring of mass $3\,\text{kg}$ is at rest on a rough horizontal wire. It is attached to a string that is at an angle of $60^\circ$ above the horizontal. The coefficient of friction between the ring and the wire is $0.7.$ Find…
Aven Riveri
  • 31
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How does author derives $\cos \theta = \frac{dx}{ds} \qquad \sin\theta = \frac{dy }{ds}, $?

In the book of Dynamics by Horace Lamb, at page 103, is it given that for a motion on a smooth curve, the equation of motion is given by $$mv \frac{dv }{ ds} = -mg \sin \theta \qquad \frac{ mv^2 }{r} = -mg \cos\theta + R, $$ where $\theta$ is…
Our
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Central force problem with relation to Kepler's law

The problem is: Consider a particle moving in $\mathbb R^3$ with location as a function of time described by the vector function $\mathbf r$(t). Assume that the motion is driven by a central force of unspecified magnitude in the direction $\mathbf…
big daddy
  • 103
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Finding the velocity of a trolley with spring on a slope

Can anyone help me see where my reasoning is wrong? My reasoning is as follows: Vertical drop in falling through distance b on slope of 30 degrees = $b\,sin\,30=b/2$ Equating loss in PE to gain in KE leads to: $\frac{mgb}{2}=…
gnitsuk
  • 217
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Given a body's initial and final velocity, find its maximum acceleration for a given power and mass

Stan is driving his $35 (metric) tonne$ truck on a horizontal road. Stand accelerates from $50 km h^-1$ to $65 km h^-1$, which is his maximum speed at $500kW$ power output. Find the maximum acceleration of the truck, assuming the total resistance…
Inquirer
  • 825
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Deriving $x=ut+0.5 a t^2$ in different ways

I was playing around with the equation in the title when I realized it isn't as simple as I thought. I basically changed the parameters in the derivation given in the book because I was wondering why $t=0$ in particular had to be the starting point.…
Raghib
  • 347
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Hamiltonian Approach

Solve the plane pendulum problem using the Hamiltonian approach and show that H is a constant of motion. Approach : Assuming it means simple pendulum by plane pendulum, I have calculated Hamiltonian as a function of $\theta , l$ (Length of…
user1611542
  • 93
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Inertia tensor for circular arc

I'm trying to calculate the inertia tensor for a circular arc, as shown in this image: It starts at the x-axis and lies entirely in the XY plane. It has a mass per unit length of $\rho$ and spans an angle of $\theta$ (which could be anything up to…
DoktorDemento
  • 21
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Bead on a smooth rotating wire.

I'm trying to solve the following problem: A bead $P$ of mass $m$ slides on a smooth wire. The wire lies in a horizontal plane, and its shape is given parametrically by $\mathbf{r}=(x(s),y(s),0)$, for $0\leq s \leq 1$, where $\mathbf{r}$ is…
H_Hassan
  • 807
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How far does a free-falling object fall in the $3$rd second?

The question: An object is dropped from a cliff. How far does the object fall in the 3rd second?" I calculated that a ball dropped from rest from a cliff will fall $45\text{ m}$ in $3 \text{ s}$, assuming $g$ is $10\text{ m/s}^2$. $$s = (0 \times…
Yusuf Abukar
  • 293
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When are two particles moving in the same or opposite direction?

Given that particles $P$ and $Q$ have velocities $a$i+$b$j and $x$i+$y$j, what is the condition that they are going in the same direction, and what is the condition that they are going in the opposite direction?
Plato
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