Questions tagged [rotation]

Circular motion about a central point or axis

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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 ...
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 ...
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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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 ...
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 ...
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 ...
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, ...
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 ...
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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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 ...
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 ...
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 ...
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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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)...
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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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 ...
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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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: \...