Questions tagged [angular-velocity]
The time derivative of angular position used when studying rotating objects or systems.
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Why can't angular velocity be a scalar quantity in 3D?
Angular velocity can be represented as a scalar quantity in 2D.
In this case we have magnitude and sign of angular velocity that show direction of rotational motion (clockwise or counterclockwise).
In ...
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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
$$\dot{C}(t) = C(t)\ \Omega(t) \...
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3 objects in circular motion , must they meet if they have different angular velocities?
If we have three particles going around in the same circle with different starting positions and different constant omegas (the particles can overlap, and do not collide), is it a must that all three ...
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A paradox of the precession of a stick
I can see that a heavy flywheel around an axis experiences precession. But when I look at the equation:
$$ \dot{\omega} = (I \omega) \times \omega + \tau ,$$
where $\omega$ is angular velocity in the ...
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Proof and meaning of $\vec{v} = \vec{\omega}\times\vec{r}$
Elementary question but I'm slightly confused about the statement $$\vec{v} = \vec{\omega}\times\vec{r}.$$ I know that $\vec{\omega}$ is simply the time derivative of $\theta$, which, to make things ...
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Does the moment of inertia of a body change with angular velocity?
In the wikipedia of Moment of Inertia wiki-page:-
Let 𝑅 be the matrix that represents a body's rotation. The inertia tensor of the rotated body is given by:
$$\textbf{I}=\textbf{RI}_0\textbf{R}^T$$
(...
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Why is Angular momentum conservation used to explain the velocity of an electron in a specific orbit?
According to Bohr's Atomic Model, the formula for finding out the angular momentum of an electron, rotating in any particular orbit, i.e:
$$mvr = \frac{nh}{2\pi} \ ,$$
where $n$ = number of orbit, ...
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Instantaneous axis of motion
I'm currently studying rigid body kinematics, I'm using a book called "Analytical mechanics" (translated from italian) by Fasano and Marmi. In section 6.3 it is told the following theorem:
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$v=r\omega$ derivation confusion
A derivation of $v = r\omega$ is below, but I am sort of confused because the derivation is saying that $dL/dt$ is velocity, but $L = 2\pi rn$, which is distance travelled. So how can distance/time be ...
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Question on Angular Velocity - Exercises from the Feynman Lectures Problem 15.25
** NOT ASKING FOR SOLUTION **
I was able to solve the attached question from the Exercises from the Feynman Lectures. My solution set-up the conservation of angular momentum between the initial ...
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Velocity Formula For a Particle Inside a Rotating System
I'm having a bit of trouble really understanding the formula of velocity for a rotating and accelerated system.
Let $S$ be the inertial System with origin $O$ and let $S'$ be the rotating system with ...
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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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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 ...
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Is angular momentum only conserved about the centre of mass?
I was solving this problem.
And here's how I approached :
Initial Angular momentum of the system is : $mvr$ and the final angular momentum is $I \omega$ where
$$I = mR^2+mR^2 = 2mR^2$$
This gives, by ...
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Constant angular velocity of a rigid body
So, I was reading about rotational kinematics, on rigid body rotation about a fixed axis. And I came across a statement that states: "here we have assumed that the body is rigid, so that all ...
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