Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
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If we take a sufficiently large axle for a wheel then is it possible that the top of the wheel would have thrice the velocity of its axle?
I recently learnt that the top of a wheel has velocity twice that of its axle. In all such cases of why this is so the axle is always considered to be very small in comparison to the wheel. Thus, I ...
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Rotating Tank of Charged Liquid
Consider a long rectangular tank of dimensions a×b, where a≫b, that is rotating at a constant angular velocity and filled with an incompressible charged fluid. How would one find an equation ...
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Final velocity when accelerating down a rotating corridor [closed]
Lets say you have a wheel of radius 100m. The wheel has a corridor at its center, such that the top of the corridor is at the center of the wheel, while the bottom of the corridor is at the edge of ...
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Linear approximation of the magnetic dipole field
Summary: using 3 angles to represent a magnetic dipole's orientation is redundant because the rotation around the $z$-axis of the dipole does not change the magnetic field, there are only 2 DOFs for ...
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Does spinning the umbrella slow down the fall more?
Ignoring its structural weakness, if you jump from some height and use an umbrella to slow down the fall, would making it spin while you're falling affect the speed in any way?
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Relative motion between two points on a rotating disc
Consider two children A and B sitting on diametrically opposite points of a merry go round rotating about its centre. Suppose A and B are facing each other. As seen from A, B never seems to move and ...
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How can we show that $((\vec v · \vec r) \vec r )'$ corresponds to Coriolis force?
We have:
Position as $\vec r$
Velocity as $\vec v=(\vec r)'$
Acceleration as $\vec a=(\vec v)'$
Angular velocity as $\vec \omega = \frac{\vec r × \vec v}{r^2}$
Angular acceleration as $\vec \alpha = ...
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Angular velocity versor
I am going back through the definitions of good old Euclidean vectors and trajectories to see whether when i was younger i missed important concepts.
In my notes, and reference book, i found that for ...
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Kinetic energy of an ellipsoid
I am trying to solve the following exercise, taken from Landau's Mechanics:
Find the kinetic energy of a homogeneous triaxial ellipsoid, rotating around one of its axes (AB, fig. 44), while the ...
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Index notation for the generalized form of the velocity gradient with shear and rotation
Good day guys, I was studying fluid dynamics and came across the following equations (shown in the image):
When we have both shear and and rotation, they each contribute to the change in velocity ...
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The stupidest question ever on relative kinematics and angular velocity [duplicate]
I am scratching my head on a very basic formula whose meaning escapes my intuition.
On basically all texts of mechanics the following result is derived:
Suppose that a rigid body is moving with ...
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How is momentum conserved in this collision with loosely-connected spheres?
There are three identical spheres. B and C are loosely connected with a light inextensible string, and A approaches B directly at some initial velocity $v$. There is no angular momentum.
A and B have ...
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What is the moment of inertia $I$ when angular velocity $ω$ is zero?
$$I = \dfrac{L}{\omega}$$
What is the moment of inertia when $\omega = 0$? Is it just not defined or is the formula not valid when $\omega = 0$?
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Circular motion at relativistic speed
I am working on a personal hard science-fiction project but when I analysed the following situation, in the context of special relativity my conclusion seems counter intuitive and perhaps I am ...
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When a wheel begins to roll on a flat surface, is it due to fulcrum generated at the contact point by friction?
[Edit: What I'm trying to understand is how any wheel rolls on a surface, instead of just spinning in place. I know that friction provides the force to make the wheel roll, but I'm unsure about the ...
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