All Questions
Tagged with homework-and-exercisesclassical-mechanics
1,359 questions
0votes
0answers
76views
Are collision underdetermined? [closed]
Imagine we have the following scenario: A collision between two different balls. (I'm drawing the system as if I have no clue of the resultant directions after the collision) Stating the equations ...
- 1,821
0votes
1answer
82views
Trying to find nonlinear wave equation for a string by abusing notation (algebraically manipulating differentials)
I derived the wave equation for a string of mass density $\mu$ with an equal tension $T$ being applied at both ends at an angle $\theta_x$ relative to the $x$-axis by taking an infinitesimal length of ...
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-1votes
0answers
27views
Shape Evolution of an Inflating Balloon Before Tautness [closed]
Consider an ideal spherical balloon made of homogeneous material. And consider the following process: Start from a deflated balloon (i.e. with 0 tension on its surface) of arbitrary shape, slowly ...
0votes
0answers
37views
How can I tell if a ball rolling on a treadmill will stay rolling? [closed]
Basically, I am in the process of planning my Physics IB IA, which means I am looking for some topics to pursue. One of these topics is rolling resistance, in which I have a number of steel chrome ...
6votes
5answers
618views
Formulating the catenary problem as a variational problem
I am interested in studying the curve a string follows when fixed by two points and subject to a (uniform) gravitational field. Say the string has a constant length $L$ and is fixed on two points A, B ...
- 2,164
-1votes
2answers
97views
Potential energy of a bead attached to a massless rotating hoop
When calculating the Lagrangian for a bead on a massless hoop of radius $R$, spinning along an arbitrary $z$-axis with angular velocity $\omega$, one has to use its potential energy. In this case, it ...
5votes
5answers
472views
Derivatives of conjugate momenta wrt generalised coordinates in Lagrangian mechanics
I am struggling understanding the validity of the solution that my professor gave to the following exercise. A heavy symmetric top rotating about a fixed point has Lagrangian: $$ \mathcal L=\frac{I_1}...
2votes
0answers
57views
How can I use physics to distribute a 3.6 kg load over multiple nails using a string? [closed]
I'm trying to solve a practical problem with what feels like should be basic physics. I've guessed that this problem might be about vectors, pulleys and trigonometry, but it's knowledge which I lack, ...
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1vote
1answer
51views
Why does body spin when released from other spinning body? [closed]
the situation is following: In space - no gravity, no air resistance - there is a spinning disk with angular velocity and mass. This disk is spinning around axis perpendicular to its face. On this ...
1vote
1answer
55views
Potential Energy graph of a bead on a rotating ring [closed]
Consider a ring of radius $R$ and negligible mass with a small bead, that can be treated as a point object, on it. The two have no friction between them. When the ring revolves around its diameter, ...
- 124
-1votes
1answer
43views
How does scaling a wire frame affect the frequency of a bead's periodic motion? [closed]
A bead is released from one end of a frictionless rigid wire frame fixed in a vertical plane, as shown in the diagram. The bead slides periodically due to gravity. The following details are given: The ...
1vote
0answers
39views
Small oscillation of by brute force expansion without first modifying potential [closed]
I am not arriving the same answer as Thornton's text He arrive this by modifying potential setting reference point $U(\phi_0)=0$ but could our frequency be equivalent? Which means $$g\sqrt{(m_1+m_2)(...
- 135
1vote
1answer
97views
Second question of Problem 2.6(a) - David Morin's Introduction to Classical Mechanics [closed]
Problem 2.6(a) of David Morin's Introduction to Classical Mechanics reads as follows: A disk of mass $M$ and radius $R$ is held up by a massless string, as shown in Fig. 2.12. The surface of the disk ...
- 188
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1answer
53views
Why does calculating acceleration of different bodies differently in free body diagram yields the wrong answer? [closed]
I was reading the Fundamental laws of Mechanics by Irodov and encountered a problem [Problem 2.2] Here I went on to solve by my method: Net force on the block $m_1$: $$m_1 g-T$$ Net force on the ...
0votes
1answer
77views
Two methods to obtain the Hamiltonian equations of motion but they ain't the same
Given the Hamiltonian $$H=\frac{1}{2}m (\dot{r}^2 +(r\dot{\theta})^{2}) - \frac{k}{r},\tag{1}$$ And the Lagrangian $$L=\frac{1}{2}m (\dot{r}^2 +(r\dot{\theta})^{2}) + \frac{k}{r},\tag{2}$$ its ...
