Circular motion about a central point or axis

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1answer
22 views

Noninertial frame-rotation

$$de_2=[cos(d\theta_1)e_2+sin(d\theta_1)e_3]-e_2=[e_2+d\theta_1e_3]-e_2=d\theta_1e_3$$ I can't see the intuition behind this from here. Shouldn't the change in $e_2$ be just this $de_2=cos(d\theta_1)...
1
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0answers
26 views

Calculating resultant force along vertical axis when using smartphone accelerometer [on hold]

I'm making an app which is using accelerometer to automatically detect damages on the route while driving. To estimate if damage occurred or not I'm using accelerometer (acceleration along vertical y ...
4
votes
1answer
555 views

Angular velocity relative to different frames

In Goldstein it is said "It is intuitively obvious that the rotation angle of a rigid body displacement, as also the instantaneous angular velocity vector, is independent of the choice of origin of ...
2
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0answers
95 views

Determination of Euler angles from known angles between the axes of two coordinate systems

Suppose there is a unprimed coordinate system XYZ, tilted w.r.t. a primed coordinate system but their origins coincide. Let the angle between $X,X^\prime$, $Y,Y^\prime$ and $Z,Z^\prime$ are ...
1
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2answers
66 views

Time dependent ODE involving cross product

Let $\vec{A}$ be any time dependent vector quantity, and $\vec{\alpha}$ any constant vector. I was told that a solution to the differential equation $$ \dot{\vec{A}} = \vec{\alpha}\times\vec{A} $$ is ...
3
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1answer
58 views

Finding rotation axis of an operator on Bloch sphere

I would like to find the action of an operator $V$ on the Bloch sphere. The matrix representation of $V$ is $V=\sqrt{\frac{i}{2}}\begin{pmatrix} i &-1 \\ -1 &i\end{pmatrix}$. $\rightarrow |\...
0
votes
1answer
54 views

Does adding mass to the fan blades affect its max velocity?

If I replaced fan blades with congruent blades, the only difference being the second set has a higher density, would that affect the speed cap on the spin? I know it would affect acceleration, but I ...
2
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4answers
188 views

Rotation of a vector

Is a vector necessarily changed when it is rotated through an angle? I think a vector always gets changed because its projection will change, and also its inclination with axes will always change. ...
0
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1answer
16 views

Population Decay Model and the Rotating Wave Approximation

The paper which I'm reading mentions the following: The Hamiltonian, $$ \frac{\varepsilon}{2}\sigma_z + \sum_k \omega_k b_k^\dagger b_k + \sum_k (\sigma^+ g_k^* b_k + \sigma^- g_k b_k^\dagger), $...
1
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3answers
64 views

Rotation matrix for aligning x-axis in an arbitrary direction

I want to align the x-axis of my coordinate system, with an arbitrary direction in space $\hat{n}$. About which axis should I rotate? Ceratinty rotation about x-axis or $\hat{n}$-axis will not serve ...
4
votes
3answers
1k views

What is the formal definition of a stellar day?

I'm having trouble understanding precisely what a stellar day is. Neither the USNO nor the IERS sites provide a definition. And Wikipedia's description as the "rotation period relative to the fixed ...
9
votes
3answers
256 views

Coupling between galaxy spin and central black hole spin

What is the relationship between the spin of a galaxy and the spin of its corresponding black hole? Associated questions: Do they always have the same axis of rotation? Do they always spin in the ...
0
votes
2answers
275 views

Need help understanding angular acceleration due to gravity

The question asks what the angular acceleration of an uniform disc of radius $R$ rotating about an axis passing through its edge if it is released from rest with its center of mass at the same height ...
1
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2answers
59 views

How can you explain a paraboloid in a rotating liquid without centrifugal force or gravity?

How does a rotating container with liquid in it cause a paraboloid to form? My physics teacher says that it is incorrect to use Centrifugal force and Gravity, but after reading though many forums on ...
1
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1answer
146 views

2d pool collision with rotational motion

I'm trying to calculate a collision between two 2d disks with rotational motion. The collision is perfectly elastic: the sum of translational and rotational energy is conserved. In the instant of the ...
1
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2answers
220 views

Rigid Body Dynamics - Calculating Rotation of an Object

I've looked everywhere and I can't quite find a concise answer, especially due to my limited knowledge and understanding of terminology. I found something called Rodrigues' Rotation Formula that ...
1
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1answer
214 views

How can angular velocity be constant even when there is a torque by friction?

A cylinder at rest lying on a rough ground is given an impulse which imparts a translational velocity (no angular velocity) to it. The question goes ahead with finding time after which rolling starts ...
0
votes
1answer
37 views

Can rotational velocity be transformed into directional movement?

If I attach a weight to a string, and spin it, I notice that the faster I spin it, the more it pulls away from me. So, I imagine what would happen if I arranged a very large machine, designed so that ...
2
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0answers
40 views

Electromagnetic field transformations under rotations

If you have magnetization vector in vertical magnetic field, it starts precessing. If you do a transformation to rotating coordinate system you obtain a stationary magnetization. Is there a direct ...
2
votes
1answer
193 views

Rotation motion like the number 8

I'm a college student majoring in culinology and I'm trying to find out the reason or method of the number 8 motion. Responses doesn't have to be in culinology examples, but that would be a great help ...
1
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1answer
34 views

Orientation from acceleration?

I have an object that has a sensor attached on it. This sensor calculates the acceleration in all axis and angular acceleration in all axis(Keep the gravity force in mind). How can I get the Pitch, ...
1
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0answers
29 views

Effect of atmospheric drag on earth's rotation

Okay, so I had a question answered regarding the earth rotating and planes flying east and west but one part of the answer talked about how the atmosphere is moving along with the earth (same angular ...
1
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3answers
79 views

Air flight and Earth's rotation

I read a response asking why flights of equal distance east and west take roughly the same time (disregarding wind actions). I have trouble visualizing part of the answer; "the speed of the rotation ...
0
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0answers
29 views

Is there a physical formula or equation to describe change in size of rotating tire?

I've heard that tires will actually grow larger when you are moving, and shrink back down when you stop. I was wondering if there is a way to calculate the size of a given tire, and what the variables ...
0
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0answers
22 views

What is the exact physics behind the heading indicator?

If I know right, the really basics of its functioning is that a quickly rotating gyroscope's axis of rotation moves into the north-south direction, due to the torque resulting from the tangential ...
2
votes
0answers
210 views

To prove uniqueness of the rotation tensor associated with rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and $j$...
13
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9answers
7k views

What is the difference between translation and rotation?

What is the difference between translation and rotation ? If this were a mathematics site, the question would be at best naive. But this is physics site, and the question must be interpreted as a ...
0
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2answers
39 views

Derivation of Specific Rotation formula?

This is sort of a weird question, so bear with me: I was reading about how chiral molecules rotate plane polarized light and decided to think of a "logical" formula for expressing the amount that ...
-7
votes
2answers
59 views

Why anticlockwise movement is present in the whole universe [closed]

Why electronic movement in its orbit and planet orbital movement along with milky ways have anticlockwise movement. is there any specific reason. The Sun is rotating anticlockwise from its axis as ...
1
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0answers
37 views

Dampening a swinging mass

Suppose a bar (black) sitting on a suspended ball (blue) has two rigid loads attached to it (red, green): Because the bar sits on a ball, the bar can swing clockwise or anti-clockwise. Suppose the ...
2
votes
3answers
65 views

Force at axis of spinning wheel

This is a newbie question, but I don't quite understand the forces at work when an object is rotating. So I've read that i can use my right hand to determine the direction of the force at the axis ...
-1
votes
1answer
58 views

Vertical circular motion(with gravity)

Let's say I have a stone tied to a string and swing it vertically upwards. Now, if I provide an initial velocity such that the velocity of the stone = 0 at an angle greater than 0 from the horizontal(...
1
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0answers
31 views

A point on a disc travelling at the speed of light [duplicate]

This might be a duplicate of this. I had an interesting thought experiment: suppose that you have a disc of a 1 m radius, where a point P2 inside the disc travels at the speed of light. You have a ...
0
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0answers
7 views

Pointer to reference for rotational dynamics for large torques?

It's my understanding that when dealing with rotational dynamics (e.g., a gyroscope like at time=2155 seconds of https://youtu.be/N92FYHHT1qM?t=2155) that the equation for relating the speed of ...
1
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0answers
57 views

Why does a fan blade appear to spin backwards when spun really fast?

This a phenomenon which I notice everyday but never really took an interest in. Why does a fan (or any other rotary object), when spinning really fast, 'appear' to slow down, upto a certain rpm, then ...
1
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2answers
106 views

Pauli Matrices & 2D Rotation Operators?

I was doing a strange calculation with my teacher the other day: find the eigenvalues and eigenvectors of the 2D rotation operator. Intuitively, there should be no solution to this problem in $\mathbb{...
5
votes
2answers
487 views

How is Chasles' Theorem, that any rigid displacement can be produced by translating along a line and then rotating about the same line, true?

Chasles' Theorem in its strong form says: The most general rigid body displacement can be produced by a translation along a line (called its screw axis) followed (or preceded) by a rotation about ...
1
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0answers
40 views

Are there characteristics that distinguish our universe?

Are there any defining characteristics of our universe that could be different for other universes (or "instances of our universe") that operate under the same laws of physics? And which, if any, are ...
0
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0answers
30 views

Rotation operation on spin-1/2 particles

How does rotation operators work on a particle? What does it do on the particle conceptually? Also does particles spin on its axis?
3
votes
3answers
54 views

Why does a pot start rotating when coffee is stirred inside?

I usually make Turkish coffee as my morning coffee. I have a small somewhat rounded pot with handle on one side. I noticed that when I pour water in and start stirring, pot has a tendency to start ...
0
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3answers
60 views

Axis of rotation and rotating rigid body [closed]

We know that angular momentum of a solid disk rotating with angular velocity $\omega$ is given by $I\omega$ about its center. Now if I chose any axis (parallel to above), will it have same magnitude ...
0
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3answers
94 views

Rolling dynamics of round objects down an incline

If a cylinder is rolling down an inclined plane with inclination $\theta=30^\circ$ (with coefficient of static friction between cylinder and the plane $\mu_s=0.8$) without slipping and it has mass $...
4
votes
1answer
194 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
0
votes
3answers
96 views

Direction of deflection of Coriolis force on Earth

I'm a bit confused about Coriolis force direction on Earth. The observed deflection is to the right in the northern emisphere and to the left in the southern one. But what about an observer in the ...
0
votes
2answers
32 views

How to calculate the acceleration, if the mass-center is not on the force-vector's line (2D)

In a 2D plane there is an object, whose center of mass is at the $P$ point. The mass of the object is $m$. We apply a force $\vec F$ at the point $A$. If the center of mass is on the line, defined ...
4
votes
0answers
40 views

Why rotating reference frames are not inertial? [duplicate]

Let's say I'm standing on the equator, and that there is no other reference point in the sky. If the planet is rotating, then I measure my weight to be lower than if it is not. But given that I have ...
1
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5answers
120 views

Rolling without slipping taking the contact point as pivot

I'm confused about this "rolling without slipping" kind of situation. Or better in this case the object is rolling and slipping, just use the label "rolling without slipping" to identify the kind of ...
0
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1answer
23 views

Moment of Inertia for objects moving in a circle?

I have been treating objects moving in a circle as a hoop, where $I=MR^2$ and it's been working but I feel like it works for a different reason from what I'm thinking. How do you actually find the ...
0
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1answer
29 views

For a rolling object, is the tangential velocity the same as the velocity of the center of mass?

For example, a solid disk rolling down a hill would include both rotational and linear kinetic energy. For the rotational kinetic energy ($\frac{1}{2}I\omega^2$) the angular velocity becomes $v/r$ but ...
0
votes
2answers
36 views

Why does the angular speed formula end up in radians per second?

So, in my homework I am given the radius and also the tangential speed $v$, the measurement for radius is meters; the measurement for $v$ is $m/s$. I don't understand how by after calculating the RPM ...