Questions tagged [rotation]
Circular motion about a central point or axis
1,120 questions
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What does it mean when physicists say: "An object rotates around any point you choose"?
I say that the Earth rotates around its center of mass (CoM), but physicists tell me "Earth rotates around any point you choose".
I do not understand how an object’s rotation can be ...
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Why can we calculate a time-dependent rotation matrix by integrating the angular frequency matrix over time?
The report "An introduction to inertial navigation" says that
In order to track the orientation the attitude algorithm must solve the differential equation
$$\dot{C}(t) = C(t)\ \Omega(t) \...
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Is angular velocity parallel to the axis of rotation when it is changing in time?
I am studying some material about rotating frames and I need to compute the following quantity: $$\frac{d}{dt}R(t)=\frac{d}{dt}e^{\vec{\theta}(t)\cdot \vec{J}}$$ where $\vec{J}$ is the 3-tuple of the ...
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Examples of where utilizing theory of infinitesimal rotations is helpful
The group of rotations of a rigid body is not commutative. I understand that the so called infinitesimal rotations commute (up to first order, aka with the help of a group contraction); that is all ...
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Can a floating object achieve any arbitrary submerged volume fraction by rotation if fluid density is unrestricted?
I'm studying buoyancy and am curious about how much control one has over a floating object's orientation and the fraction of its volume that lies below a fixed horizontal plane (the "waterline&...
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How do we actually define the unitary rotation operators from their rotational matrices, and is this a map between representations?
The way I understand it, $SO(3)$ is an abstract group, which has a 'convenient' representation in the $\mathbb{R^3}$ real vector space: the $3 \times 3$ special, orthogonal (rotational) matrices, let'...
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Understanding Rigid Body Tumbling
The algorithm for rotating a rigid body around an angular velocity $\vec{\omega}$ with an inertia tensor $\mathbf{I}$ is the following.
The apostrophe (') mark means the old state with respect to my ...
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Infinitesimal vs finite symmetries in the Kepler Problem
I have been studying the Lie symmetries of the Kepler problem from this paper by Prince and Eliezer but I am struggling understanding the manner they explain the angular symmetry of the problem.
Using ...
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Moments of forces acting on a rigid body that is rotating
The lower end of a homogeneous rod of mass 𝑚 m and length 𝑙 is placed in a socket, while the upper end is connected to a fixed vertical axis by a light, inextensible string, such that the string ...
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Can a rotating object have more than one axis of rotation? [duplicate]
If an object is observed as rotating at high speed around one axis, and slowly rotating about another, can this be expressed as a single rotation about an axis which is some combination of the two ...
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Does converting IMU Euler Angle outputs to Quaternions avoid gimbal lock? [closed]
I am working with an Inertial Measurement Unit (IMU) that outputs only in Euler Angles. I want to avoid gimbal locking, but I am not sure if I should get an IMU that works with quaternions out of the ...
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Why do we need (or prefer?) $SU(2)$ rather than $U(2)$ to perform rotation of 3d Pauli vectors?
In order to rotate the usual 3d vectors (Written as Column vectors), We start with the idea that Rotation perserves lengths, which leads us to the group of $O(3)$. But Reflections also perserve length,...
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Units of angular velocity and frequency
I was recently studying for an exam and had a small argument with my teacher when I said that the angular velocity of something was in hertz.
The way I see it: $dim(ω)=\frac{rad}{s}$ but radians are ...
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What does it actually mean for quantum phase to be "uncertain" in the number–phase uncertainty relation? $\Delta \phi \cdot \Delta N \gtrsim 1$
I’m trying to get a clearer physical and intuitive understanding of the number–phase uncertainty relation in quantum mechanics, especially in quantum optics.
$$\Delta \phi \cdot \Delta N \gtrsim 1$$
I ...
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Why is the direction of angular velocity or angular momentum perpendicular to the plane where the circular motion actually occurs? [duplicate]
I always thought that it was just a mathematical thing (as we can't use something like a curvy vector) and has no real life physical significance. However, i saw the working of a gyroscope which ...
