All Questions
Tagged with physics solution-verification
85
questions
1
vote
1
answer
39
views
What is the fault in this method of finding second moment of area of a circle
I am trying to find the second moment of area of a circle about a diameter using first principles.
Place the centre of the circle at the origin of XY-plane. Now consider a tiny circular sector with an ...
- 141
1
vote
1
answer
325
views
Pendulum hanging on a spinning Disk
It is a problem found in Physics. From the edge of a (in distance r to the center) disk a (mathematical) pendulum is hanging. The disk spins with a velocity w, which also stimulates the hanging ...
- 119
0
votes
1
answer
124
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Error in finding a solution for the acceleration in a pulley system
So based on the diagram here's what I've attempted:
Note: $\bar{g}$ is the Earth's gravitational constant and $T$ is the tension force acting on the Blocks.
$a_1,a_2,a_3$ will be the acceleration ...
- 321
4
votes
2
answers
349
views
Tilted rectangle falling down
Rectangle $ABCD$ is tilted such that its base $AB$ makes an angle of $\theta$ with the horizontal floor. It has its vertex $A$ in contact with the horizontal floor, and the rectangle is released from ...
- 24.4k
0
votes
2
answers
84
views
Where Did I make a mistake in my deviation for the Period of a Pendulum Formula
Imagine a Pendulum with String Length L, and Angle θ, which forms arclength S (Will be used later in the derivation.)
First V = $\sqrt{2gh} $ (Height is measured straight down) KNOWN TO BE A ...
- 37
4
votes
0
answers
163
views
Harmonic oscillator differential equation question
Consider a harmonic oscillator subject to a frictional force proportional to velocity: $$\ddot{x}+2\gamma\dot{x}+\omega^2x=0.$$
Here $\dot{x}$ and $\ddot{x}$ are $\frac{dx}{dt}$ and $\frac{d^2x}{dt^2}....
6
votes
2
answers
161
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In what time $\tau$ will the particle reach the point $x=0$?
A particle of mass $m$ capable of moving along the $x$-axis, is acted upon by a force $F(x) = -\frac{k}{x^3}$. At the initial time moment $t=0$, the particle is at the point $x=x_0>0$, and its ...
0
votes
1
answer
75
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Find the Pauli vector's eigenvalues
Question:
Find the eigenvalues of $\hat{a} \cdot \vec{\underline{\underline{\sigma}}}$.
My answer:
1- First let's note that $ (\hat{a} \cdot \vec{\underline{\underline{\sigma}}})^2 = \hat{a} \cdot \...
- 719
0
votes
0
answers
271
views
Integrating with respect to time: $dx/dt=a$
If $a$ is a constant and $dx/dt=a$, then integrating with respect to time gives $x = x_0 + at$. How do we show that?
Is my reasoning correct?
$dx/dt=a \implies \int_{0}^{t} dx(t) = a\int_{0}^{t} dt \...
- 716
3
votes
1
answer
334
views
Prove Kepler's second law of planetary motion
An object moves in $\mathbb R^3$ it's position $r(t)$ satisfies $$r''(t) = s(t)r(t)$$ for some scalar function $s$ (a central force field, in which all acceleration is directly towards or opposite the ...
- 4,450
1
vote
0
answers
65
views
Non-homogeneous wave equation, retarded potentials and causality
Consider the non-homogeneous wave equation in three dimensions with homogeneous initial conditions:
$$
\begin{align}
& \square f(\underline{x}, t) = g(\underline{x},t), \hspace{3mm} \underline{x} \...
- 1,179
4
votes
1
answer
70
views
Linear system $Ax=y$ with partially known $x,y$ and non singular $A$
PHYSICAL INTUITION
While proving the equivalence between the Dirichlet problem (i.e. the potential is known on the surface of every conductor) and the mixed problem (i.e. the potential is known on ...
- 1,179
3
votes
3
answers
183
views
Real part of the solution is not a solution?
Take for example this very simple differential equation with complex coefficients:
\begin{equation}\tag{1}
f'(t) = - i f(t)
\end{equation}
where t is a real variable. The solution is $f(t)=c e^{-i t}$...
- 61
4
votes
1
answer
229
views
Dynamics pulley question - Clarification of answer. (SOLVED)
I need some direction in solving this simple pulley problem.
Two masses of $m$ and $2m$ kg are connected by a light inextensible string passing over a smooth pulley. Find the acceleration of the ...
- 469
1
vote
1
answer
80
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Correct solution for dynamics problem (F=ma)?
Any help appreciated with this problem.
A train consists of a railway engine of mass $M$ tonne coupled to two trucks, each of mass $m$ tonne. Initially the train is at rest and each coupling is slack ...
- 469