Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
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A question on the rotational motion of a metal drinking cup
When I rotate a metal drinking cup slowly it rotates normally. However, when I rotated the cup with a much greater speed, the cup's body started to rise and was rotating with a small portion of its ...
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Rate of change of heading in terms of normal acceleration and air speed
Let's say an aircraft is traveling with speed $|\mathbf v|$ with respect to an inertial frame. The aircraft is able to execute turns by producing an acceleration $\mathbf a$ that is normal to $\mathbf ...
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Is there a transport equation specially for two rotating frames?
The classical transport equations related vector derivatives between an inertial frame and a rotating frame, is this equation applicable to a set of frames where both are rotating? or does one always ...
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Rotations about a unit vector which doesn't pass through the origin in 3 dimensions
I am trying to understand how rotating a vector about an aribitrary axis which does not pass through the origin of the coordinate system $(x,y,z)$. Let the $\vec{r_{1}} $ and $\vec{r_{2}} $ be two ...
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Transverse speed of hamster in wheel as function of theta
i need help with conceptual understanding of how this system works.
A small animal is running in a wheel with radius R, (and 0 mass). When the animal is at an angle $\theta = \alpha $ measured from ...
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Gravity and rotating torus
Questions:
Would a spinning torus lose its weight?
Would a solid torus, spinning at 7,81 km/s radial speed completely loose it's weight on Earth-like object?
Would it 'fly away' at higher speeds?
{...
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Attitude quaternion from 2 vector measurements
I am using a method proposed by R. G. Reynolds to estimate attitude based on two vector measurements, taken from: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19990052720.pdf
Suppose we ...
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Does an object that's freely swinging about its pivot point have translational motion?
For example, a pendulum rotates about its pivot point, but does the pendulum also have translational motion?
I ask this because in the following link, the author assumed in his first equation that a ...
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Dynamics of Rigid Bodies (rotation, angular notions, etc) in quantum physics view
When I was studying the rotation of rigid bodies, I came to this notion of rigid body, and many other assumptions. However in the real world there is no rigid body. All bodies are composed of millions ...
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Computing angular acceleration of a composition of coordinate frame transformations
Given two coordinate frames $A$ and $B$, we can define the transformation between them by:
$[\vec r_{AB}]_A$, the vector from the origin of $A$ to the origin of $B$ (resolved in frame $A$), and
$q_{...
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Does Earth's precession rate change with the seasons?
As Earth's precession is caused by the differential solar, etc., attraction to its 'spare tire', then does the rate go to ~zero at the equinoxes and ~twice the average at the solstices? (preferred ...
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What is "first passage" in orbital mechanics?
Sometimes people talk about the "first passage" of an object falling in toward or beginning an orbit around a more massive object. I'm specifically thinking about this phrase in the context of ...
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Angular momentum of a 2-dimensional system in polar coordinates
Say I am studying a system who's motion is restricted to a 2 dimensional plane, for example, the two body problem in a central potential. We can align its angular momentum with the z-axis and then the ...
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Motor-powered gyroscope's precession speed
I was doing experiment about the gyroscope's precession speed and I made my own gyroscope, which is the one in the picture. It is the motor-powered gyroscope as I found out the one made with bearing ...
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Angular velocity in body frame to displacement in lab frame?
For the case of a freely spinning symmetric top (no gravity), I derived the following equations, where $\omega_i$ is the angular velocity about a body-fixed axis:
$$ \omega_1 = w_1 \cos (w_3 t) $$
$$ ...
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