All Questions
24
questions
0
votes
2
answers
50
views
Properties of the Center of Mass
My students are currently going through the rigid rotor and hydrogen atom unit in their quantum physical chemistry course and I found myself at a loss on how to justify what seems a natural way to ...
- 3,202
2
votes
4
answers
227
views
Is angular momentum conserved on a spinning sphere, specifically Earth [closed]
Specifically in relation to meteorology. I was wondering if the angular momentum an object, lets say a parcel of air has due to the roation about the earths axis. Is it conserved if moved to a ...
0
votes
5
answers
160
views
Torque Intuition [duplicate]
We are all taught that the torque $\boldsymbol{\tau}$ is given by $\boldsymbol{\tau} = \mathbf{r}\times\mathbf{F}$ so that torque increases with the lever arm length. What is the physical intuition ...
- 223
0
votes
2
answers
61
views
Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples?
Inertial accelerations like the Coriolis effect are well known. Are there also 'inertial jerks' and what are some examples?
My guess would be that it would look something like:
$$ j=-3v_r \omega^2 e_r ...
- 2,035
0
votes
2
answers
115
views
When to apply $I_c \underline{\omega} = \underline{M_c}$?
I was solving an exercise the other day, about a rolling cylinder on an inclined plane. Initially the cylinder slides, but then it begins to roll and the problem wanted to know the velocity of the ...
- 402
0
votes
1
answer
89
views
Time derivative relation between two rotating frames
I know that the time derivative of some quantity $r(t)$ in a rotating frame which rotates with angular velocity $\Omega(t)$ is related to the derivative in a fixed (i.e. inertial) frame by
$$
\Big(\...
- 15
1
vote
2
answers
264
views
Finding latitude of landing of projectile in Rotating Earth
Assuming that the Earth is a uniform sphere of radius $R$, rotating about its axis with a uniform angular velocity $\omega$. A rocket is launched from the Equator in a direction due North. If it keeps ...
- 23
6
votes
6
answers
690
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
2
votes
1
answer
332
views
Understanding Euler's Rotation equation for rigid bodies (Frames Of Reference)
$$
\tau_b=I_n\dot\omega_b+\omega_b\times I_b\omega_b
$$
Now in the above is Euler's famous rigid body rotation equation, in the body frame of reference ..... this does not make sense to me. How can a ...
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
0
votes
2
answers
182
views
Relating torque and time rate of change of angular moment when an object isn't rotating about its center of mass [duplicate]
My book "Fundamentals of Physics" by Halliday, Resnick, Walker says:
The net external torque acting on a system of particles is equal to the time rate of change of the system's total ...
- 105
0
votes
3
answers
195
views
Having trouble taking derivative of a cross product when finding Lagrangian to find force equation for rotating non-inertial frame
I've been working on a problem for my classical mechanics 2 course and I am stuck on a little math problem. Basically, I am trying to prove this equation of motion with a Lagrangian:
$$m\ddot{r} = F + ...
- 17
8
votes
9
answers
2k
views
Different coordinate system as opposed to different reference frame
I'm having a hard time getting the difference between the two. In Euler's equations of rotating bodies for example, we have:
$$ \mathbf{\dot{L}}+\mathbf{\omega} \times \mathbf{L} = \mathbf{\Gamma},$$
...
- 1,038
3
votes
2
answers
2k
views
Why does a body not rotate if force is applied on the centre of mass?
The definition of centre of mass on Wikipedia is given as
This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration.
How can I prove that such ...
- 517
0
votes
3
answers
570
views
Find angular momentum using center of mass frame
Suppose I have a square-shaped plate getting hit by a ball as shown in the picture below (notice how the force vector applied by the ball is not parallel to the $r$ vector). Let's set the origin to be ...
- 147
3
votes
2
answers
934
views
Rotating Rod As a conical pendulum
Consider A Rigid Rod hinged at its top point Whirled around in a circle (similar to a conical pendulum). It is given that the angular velocity (and thus the semi-vertical angle) is constant. I am ...
- 1,295
2
votes
1
answer
332
views
Reference-frame transformation for the Lagrangian of a charged particle
The Lagrangian of a charged particle in a magnetic field reads:
$$
L=\frac{m}{2}\dot{\bf{r}}\cdot \dot{\bf{r}} + q\bf{A}\cdot \dot{\bf{r}}
$$
This is the Lagrangian in the reference frame $Oxyz$.
...
- 1,232
3
votes
2
answers
769
views
Confusions about frames of reference when deriving Euler's equation of rotational motion
I am getting confused about when torques should be frame independent. My understanding is that torque is the same in all frames that are rotating at constant angular velocity. However, this seems to ...
- 1,335
2
votes
1
answer
59
views
What is the physical argument for $d(G)_s = d(G)_b + d(G)_{rot} \quad ?$
In the book of Goldstein, Classical Mechanics, at the end of the page 171, it is stated that
A relation between the two differential changes in $G$ can be derived
on the basis of physical ...
- 2,283
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
2
votes
1
answer
124
views
Applied Force in a Non-inertial Frame
Let us consider two reference frames: $S$ and $S'$. $S$ is an inertial frame and $S'$ is a non-inertial frame as it is rotating wrt $S$ with an angular velocity $\omega$ about a fixed axis. The ...
- 3,023
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
18
votes
6
answers
9k
views
How can the centripetal force lead to objects flying apart?
I don't understand how the centripetal force, which always points to the center of our circular motion can cause this scenario:
We have a big stone which spins very fast, so fast that a part breaks ...
- 396