Questions tagged [rotation]

Circular motion about a central point or axis

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139 views

Rotations of eigenstates of $S_z$

I have a question regarding the rotation of spinors in a spin-1/2 system. We have a Spin generator $\hat{S}$ for rotations of spinors. A rotation around the axis $\vec{n}$ with the angle $\phi$ is ...
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1answer
138 views

Lever question rotation torque

If I have a lever and fulcrum and I am applying 1 pound of pressure 12 inches from fulcrum on one side to lift a 2 pound stone 6" from fulcrum on the other side. Question is why does the fulcrum have ...
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2answers
374 views

Doppler shift and speed of rotating objects in space

I understand the concept of how we can use the doppler effect to know if an object is spinning, in the sense that the part of the object spinning towards us will exhibit a blueshift, and the part ...
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1answer
78 views

How to show that a hollow planet is rotating?

So i have this question that is bothering me for a while. Suppose you are inside a hollow planet with no contact with the exterior. How do one show that the planet is rotating? I've been thinking ...
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1k views

Calculating acceleration, etc. of a gear train with multiple driven gears

I'm writing a basic gear train simulation, where it is possible for every gear to be attached to a source of torque/angular friction. All the online resources I've found only deal with systems where a ...
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1answer
411 views

Why spherical harmonics are related to certain rotations (and not others)?

Let's take a direction eigenket $|{\bf\hat{n}}\rangle$ in 3-dimensional space oriented with angles $\theta\in\left[0,\pi\right]$ and $\phi\in\left[0,2\pi\right]$ in spherical coordinates. Next take ...
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0answers
248 views

What are the 3 Euler angles?

I am currently reading up on inertial measurement in aircraft systems. Euler angles are one of the concepts I am a bit confused with. In an Euler angle-rate matrix there seem to be 3 parameters: p, q, ...
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1answer
898 views

What is the purpose of torque in projectile motion?

Torque, $\tau$ is defined as: $$\vec{{\tau}} = \vec{r}\times\vec{F}$$ Intuitively, it's the rotational effect of force. However, using the above definition of torque we can calculate the torque ...
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1answer
227 views

Non Uniform Circular Motion and How External Force Affects The Motion

If there is a force angled inwards acting on the object in circular motion counterclockwise, and the force is split into 2 components, the tangential and the radial, how does each component force ...
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1answer
422 views

Laplace equation azimuthal and non azimuthal symmetry

In general we can say that if the potential is specified in the surface of a sphere with azimuthal symmetry $(m=0)$ has a solution: $$ \Phi(r,\theta)= \sum_{l=0}^\infty \left[ A_lr^l + B_lr^{-(l+1)}\...
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2answers
609 views

How to calculate resisting torque due to moment of inertia

I'm trying to determine whether a motor is suitable for an experiment. I know the motor's torque and the moment of inertia of the disk it will be turning. I was able to find the angular acceleration. ...
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2answers
565 views

Axis of rotation and Euler's theorem in rigid body dynamics

Euler's theorem of Rotation for rigid body states that In three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single ...
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1answer
47 views

Direction of rotation in transformation

If we rotate the set of axes in counter-clockwise through 3 Euler's angles to get the transformation matrix, then what about the direction of rotation to get direct transformation instead of the ...
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1answer
88 views

How should I understand rotational kinetic energy?

I am looking at problem 26 of the physics 2001 GRE and am faced with the following problem: A thin uniform rod of mass M and length L is positioned vertically above an anchored frictionless pivot ...
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2answers
140 views

multiple 3D rotations on one object

I'm working on a 3D space game with no gravity but multiple engines at the spaceship. My problem is collecting the different rotations and put them together. For example, this is the prototype of my ...
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1answer
29 views

Representing a vector in rotated frame

If $R \in SO(3) $ is a rotation matrix defined from body fixed frame to the inertial frame such that $e_1, e_2, e_3$ are the basis of inertial frame and $b_1, b_2, b_3$ are the basis of body frame, ...
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1answer
310 views

Transition Probability between Spin 1/2 States (rotated axes)

For Spin 1/2 particles, the spin operator along an arbitrary axis defined by the normalized vector $\vec{n}$ is given by a weighted sum over the pauli matrices: $$S(\vec{n})=n_x \sigma_x + n_y \...
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1answer
181 views

How do the radian have a unit? [duplicate]

The radian is defined as the ratio of the circumference and the radius. Both are measured in meters. So there should not be a unit for that. But we use 'rad' as the unit of the radian value. The ...
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1answer
99 views

Constraints on the factorization of a unit quaternion rotation operator

In Jack B. Kuipers' Quaternions and Rotation Sequences page 194-195, section 8.7.1 explains how to decompose a tracking sequence quaternion $q = q_0 + \vec{i}q_1+\vec{j}q_2+\vec{k}q_3$ into two other ...
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1answer
719 views

Calculate force between rotating objects

For a physics engine I need to calculate the force that results from rotating objects colliding with each other. I need to get the force that applies to a defined point ($x,y,z$ - coordinates) with a ...
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1answer
421 views

What's the EM field inside a rotating magnetized sphere?

I'm looking for the analytical expressions of the magnetic and induced electric fields inside a rotating uniformly magnetized sphere. If the sphere isn't rotating, the electric field is 0 everywhere, ...
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1answer
79 views

Conservation of linear momentum when impulse is given to a free rod to set it into general rigid body motion

Why can't we use conservation of linear momentum when an impulse is given to a free rigid body (e.g. at one end of the rod) and the rod is set into general rigid body motion (translation plus rotation)...
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1answer
299 views

Rotational motion activity for physics of sports class

I'm looking for a really solid rotational motion lab for a physics of sports class I'm teaching for younger students (HS Freshmen mainly). It should be something that the students can gather data ...
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Superluminal Thought Experiment [duplicate]

If I had a weightless, indestructible rod that was 1,145,915,590 meters long and I moved it 15° would the end of the rod go faster than the speed of light? (Assuming it's path is unobstructed.) ...
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1answer
23 views

Experiment to determine cyclette power

I have a cyclette with 8 resistance levels set magnetically using a knob (a magnet is moved near the rotating disk thereby increasing its rotating resistance). The distance from the pedal to the ...
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2answers
153 views

Why is the distance travelled by a non-skidding rolling object equal to the arc length?

I'm having a hard time linking the rotational movement of a rolling object (like a tire) and the horizontal displacement in my head. Is there any way to prove that the distance travelled is exactly ...
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1answer
236 views

Why is the Galilean group not commutative?

As I understand it, the Galilean transformation is a matrix $$ \left[ {\begin{array}{ccccc} R_{11} & R_{12} & R_{13} & v_x & a_x\\ R_{21} & R_{22} & R_{23} & v_y ...
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172 views

About the aerodynamic force on a rotating maple leaf seed

Every matured (ready to fall), wing-shaped seed of the maple leaf tree ends up in a rotating motion, no matter what it's initial position is (the seed follows the path of least action, or in more ...
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1answer
129 views

Matrix of any special unitary transformation in two dimensions

I want to show that every special unitary transformation in two dimensions can be written as the matrix $$ U = \left(\begin{array}{cc} e^{i(\delta + \varphi)}\cos\theta & i~e^{i(\delta - \varphi)}...
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1answer
113 views

Queries about rotation in QM for spin $s = 1$ system

I am interested in how to do a rotation about the $x$-axis in QM for spin $s = 1$ system. In an answer to the post we have that for a general rotation in QM where spin $s = 1$ we have the equation: \...
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1answer
71 views

Why is 24h (angle) equivalent to 360°?

Why is 24h (angle) equivalent to 360°? The earth does not spin 360° in 24h. When giving astronomical coordinates, my GCSE study guide says right ascension is measured in hours where 24h right ...
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1answer
916 views

matrix of rotation for quantum states [duplicate]

For the two-level quantum system, we have the bloch sphere representation, and for a rotation we have the exponential operator: $$\text{exp}(\frac{-i \sigma \cdot \hat{n} \phi}{2})$$ where $\sigma = (\...
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1answer
93 views

Can any object or thing spin in two directions at once? [closed]

Can anything spin in two directions at once, separately? If so, how? For instance, could an object spin sideways and up and down at the same time, separately?
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1answer
1k views

Mixing intrinsic and extrinsic 3D rotations

I am struggling with mixing two types of rotations; after much reading, I still feel a little confused. I am trying to mix intrinsic and extrinsic rotations. I have three pieces of hardware that have ...
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0answers
189 views

Modelling rotation of angular momentum eigenstate in Python [closed]

Consider an angular momentum eigenstate $|j,m \rangle$, what would be the simplest way to model a rotation of this state in Python which starts out in a state where $m = j$ and is acted on by a ...
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1answer
439 views

Orbital speed of moon considering everything else stationary

(Edit:Please see the comments, for they would change the meaning of my question) How can one calculate the pure orbital speed of the moon around Earth by removing the effect of the Sun and keeping ...
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126 views

How would I explain why a top wobbles to someone who has never taken a physics course?

I found this this website that explains the precession of a top, but obviously, it is not comprehensible to a younger student. I am not referring to why tops stay up, just why they make circles that ...
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2answers
869 views

Irreducible form of Spherical tensor operators

In the section on spherical tensors in Sakurai, he introduces the idea of going from Cartesian tensors to irreducible spherical tensors. He states the following: A spherical harmonic can be written ...
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4answers
426 views

Why is circular motion circular?

I'm interested in a purely mathematical argument as to why when I have a constant velocity perpendicular to a constant force, that it produces uniform circular motion? If I was given this information,...
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1answer
146 views

Barrel Rolling on concrete reverses its direction of motion

While reading my textbook I came across an activity which told : Try rolling a barrel from concrete onto grass, what happens does the barrell reverses its direction of motion ? Is this because of ...
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1answer
1k views

How to find the angular velocity and tension in the string?

A light string with a particle of mass $m$ at one end, wraps itself around a fixed vertical cylinder of radius $a$. The entire motion is in the horizontal plane(neglect gravity). The angular speed of ...
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1answer
297 views

Why multiply the infinitesimal generator for a rotation $R$ by $i$ when constructing $U(R)$?

I'm sure this is a silly question, but I can't figure out the answer. Current I'm reading chapter 4 in Weinberg's Lectures on Quantum mechanics. Earlier in the book, he asserts that unitary operators ...
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1answer
1k views

Minimum speed needed for a gyroscope to precess

I was reading about gyroscopes and their precession. Based on the text, the angular speed of precession is: $\omega_{precession}=\dfrac{\tau}{L}$ But intuitively, if the wheel of the gyroscope is ...
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2answers
470 views

Motion of an object spiraling outwards on a rotating disk with friction

I recently came across the following problem: A spinning disk has an object initially located at radius R. The object is moving with the same angular velocity as the disk (which I will call ω). ...
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1answer
58 views

Rotation of tennis ball getting reversed on striking the ground. Reason?

When a person throw a tennis ball in downward direction towards the surface with an anti-clock rotation, then when it comes up after striking to the surface the rotation is reversed. Why is that?
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227 views

Rotational Kinetic Energy

So I'm having a bit of an issue in solving equations that involve rotational energy and how to distinguish it from mechanical. For instance, how to set up the energy equation of an atwoods machine, ...
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3answers
378 views

Conceptual angular velocity question

Suppose we have a person sitting on a rotating chair,he is rotating with angular velocity w(omega) .Then he extends his arms outside,this changes the angular velocity to w'. My question is which force ...
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0answers
303 views

Calculate a two wheeled robot wheels rotation velocity for different movement [closed]

Consider the following situation. I have a two-wheeled robot like that I have required information: size of a robot, radius of wheels and so on. Also I have an object that the robot should pass ...
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0answers
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Is the rotational velocity of a vortex consistent across its height?

I am trying to locate information about calculating the rotational velocity of a vortex. Is the velocity at the vertex maintained across the entire vertical height of the vortex? As the radius ...
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1answer
128 views

Rotations of spin eigenstates in QM

If you have a state $| \psi \rangle = | \uparrow \rangle$ which is the spin eignstate of the spin operator $\hat{S}_z = \frac{\hbar}{2} \hat{\sigma}_{z}$ then if you view this state as a vector in the ...