All Questions
26
questions
1
vote
1
answer
73
views
The square of the center of mass [closed]
In the book Classical Mechanics by Goldstein, there is an exercise related to the square of the position of the center of mass of a free particle. I must prove that
$$M^2R^2 = M\sum_i m_ir_i^2 - \...
0
votes
1
answer
35
views
Center of Mass calculation in configuration of $3$ pennies inscribing equilateral triangle [closed]
I'm working on a problem that is asking me to solve the moment of inertia about the center of mass of a $3$ penny system where the edge of each penny is touching the edge of the others and the ...
0
votes
1
answer
241
views
Rotating reference frame - Taylor Problem 1.27 [closed]
I'm having trouble understanding how to think about Problem 1.27 in Taylor's Classical Mechanics. I want to be able to solve similar problems qualitatively when it comes to changing reference frame so ...
- 177
0
votes
1
answer
149
views
Problem 6.3 from David Morin (classical mechanics) [closed]
I get the lagrangian for the system as
$$
\begin{align}
\mathscr{L} = \frac{m}{2}(\dot{x}^2 + l^2\dot{\theta}^2 + 2l\dot{x}\dot{\theta}\cos \theta) + mgl\cos\theta
\end{align}
$$
Where $\theta$ is the ...
- 23
0
votes
2
answers
176
views
Lagrangian of inverted physical pendulum with oscillating base
An inverted physical pendulum is deviated by a small angle $\varphi$ and connected to an oscillating base with oscillation function $a(t)$. The pendulum's mass is $m$ and its center of mass is $l$ ...
0
votes
1
answer
67
views
Find the equation for the angle $\theta$ in which the particle leaves the semicircle. No Friction [closed]
I think I missed something in this mechanics problem.
We're given a polished (no friction) and homogeneous hemicircle which has mass $M$ and a particle of mass $m$ laying on the top of it.
There is ...
- 153
1
vote
1
answer
150
views
Lagrangian formalism for non-inertial reference frames
I was solving the exercise where the massless ring with radius $R$ is rotating around axis (shown in the picture) with angular velocity $\omega$. On the ring is a point-object with mass $m$ which ...
0
votes
1
answer
126
views
Using reduced mass to solve problems
A small block of mass $m$ rests on the bottom of a big box also of mass $m$. If the small block is then given a velocity $V$ to the right, how far has the box moved once the block has come to rest ...
- 67
0
votes
1
answer
422
views
Kinetic Energy of pendulum with moving support
I am trying to calculate the kinetic energy of a pendulum with moving support. I have come across two ways that could be used to calculate the kinetic energy, and although I know that the first of ...
- 29
6
votes
6
answers
692
views
Validity of rotational Newton's second law in a changing instantaneously inertial frame
A standard textbook question is to ask about some rigid body (say, a 2D disk) rolling down an incline without slipping (cf. John Taylor's Classical Mechanics, Problem 3.35).
The standard approach is ...
- 1,095
1
vote
2
answers
752
views
Equation of motion of a particle inside a rotating tube [closed]
I'm trying to solve a problem but I don't know even where to start.
The problem is about a smooth hollow cylinder of mass $M$ rotating about an axis in one of the extremes of the pole with an initial ...
3
votes
0
answers
98
views
Path of a bead on a rod with external torque [closed]
Imagine a bead, free to move along the length of a horizontal rod, pivoted at one end. The system is initially at rest, with the bead at some distance from the end. Now, a constant torque is applied ...
- 1,076
2
votes
1
answer
344
views
Find COM velocity with respect to laboratory reference frame [closed]
I'm trying to solve the following homework question.
Suppose that in the laboratory frame of reference we have $2$ particles. Particle "$a$" is at rest with total energy $E_a$, while ...
- 207
1
vote
2
answers
288
views
In general, conservation laws do not hold whenever the center of mass of the system is moving?
I am currently studying Classical Mechanics, fifth edition, by Kibble and Berkshire. Problem 3 of chapter 1 is as follows:
Consider a system of three particles, each of mass $m$, whose motion is ...
- 899
1
vote
2
answers
557
views
What does the Problem 14 from Goldstein's book on classical mechanics chapter-7 (special relativity) really mean?
I am having difficulty in understanding problem number 14 in Goldstein's Classical Mechanics, 3rd edition, chapter 7 on special relativity. Here is the problem ---
A rocket of length $l_0$ in its ...
- 1,088
0
votes
2
answers
158
views
Acceleration-Meter [closed]
I encountered a Physics Olympiad problem:
A ball bearing rests on a ramp fixed to the top of a car which is accelerating horizontally. The position of the ball bearing relative to the ramp is used as ...
- 1,047
6
votes
3
answers
231
views
Inconsistency of PE to KE conversion in moving reference frames [closed]
Here's a nice trick question to keep you amused over the weekend.
A trolley of unit mass with light frictionless wheels is released to roll down a ramp onto a smooth level surface. The PE lost equals ...
- 26.4k
0
votes
1
answer
354
views
Banked curve problem in another frame of reference
How would you set up Newton's equation of motion for this problem (rolling without slipping in a circular path) using the frame of reference shown in the figure:
- 145
1
vote
1
answer
474
views
Picking the Right Reference Frame
A space vehicle travelling at $3860 \ \text {kmph}$ w.r.t Earth sends its exhausted rocket motor backward with a speed of $125 \ \text{kmph}$ w.r.t the command module. The mass of the rocket motor is $...
10
votes
3
answers
3k
views
Lagrangian equations of motion for ball rolling on turntable
The equations governing the motion of a ball of mass $m$, radius $R$ rolling on a table rotating at constant angular velocity $ \Omega $ which are derived using Newton's laws are: (I present these for ...
- 145
0
votes
0
answers
404
views
Re: Susskind and Hrabovsky: Should the Lagrangian of a particle referred to a rotating frame omit the velocity dependent "potential"?
My question pertains to Lecture 6: Exercise 4 in The Theoretical Minimum by Leonard Susskind and George Hrabovsky. A suggested solution has been posted here: http://www.madscitech.org/tm/slns/
The ...
- 2,015
4
votes
1
answer
1k
views
Lagrangian of rotating springs
I'm trying to construct the Lagrangian for the following scenario. A turntable of radius $R$ is rotating at angular velocity $\omega$, maintained by a motor. Two springs with Hooke's constant $k$ are ...
user138458
2
votes
2
answers
189
views
Take derivative to a cross product of two vectors with respect to the position vector [closed]
I'm doing classical mechanics about Lagrange formulation and confused about something about vector differentiation.The Lagrangian is given:
$$\mathcal{L}=\frac{m}{2}(\dot{\vec{R}}+\vec{\Omega} \times \...
- 103
0
votes
2
answers
493
views
Uniform circular motion & relative velocity
Consider a car moving along a straight horizontal road at constant speed, $v$.
Also consider one of the tyres/wheel of the car. On it, there are two particles of dust $A$ and $B$ (as shown in the ...
- 1
4
votes
2
answers
599
views
Work done changes between reference frames?
(This is not homework; a friend shared with me this puzzler and neither of us can figure it out.) Suppose you are in a plane traveling at velocity $v_1$ relative to the ground. The flight attendent ...
- 43
1
vote
1
answer
166
views
kinetic energy of the stone
Suppose we have a man traveling in an open car (roof open) with speed $v$ towards right (man faces right). He throws a stone (mass $m$) towards right, in his frame-forward with speed $V$.
In the ...
- 834