Questions tagged [angular-velocity]
The time derivative of angular position used when studying rotating objects or systems.
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Can a GPS system detect the decline in the rotational velocity of the Earth?
From Wikipedia: Rotation in Angular Velocity of Earth
Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's ...
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Friction on a Spinning Platform
I do not understand at all why, if an object is sitting on a spinning platform, the friction force is towards the center. I understand the need for a centripetal force during circular motion, but ...
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Adding angular velocity vectors
We know we can add two angular velocity vectors to get a total angular velocity. Whereas I more of less understand the basic principle and the mathematical formulation, I have problems in visualizing ...
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Is centripetal acceleration the same as angular acceleration? [closed]
I know that the centripetal acceleration changes the direction of the tangential speed. But can I calculate it as the derivative of the angular speed with respect to time? Or are these different ...
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How to find tangential/radial/angular velocity for motion in any curve? [closed]
Is the radial velocity responsible only for changing distance between objects and the component perpendicular to it only for change in direction? If so why?
Please try to give a different explanation ...
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Ambiguity in angular velocity? Two different possible angular velocity vector assignments for the motion of a particle?
To simplify things, consider a particle moving in circular motion counterclockwise from the $+z$ position looking down at the $xy$-plane, so the position is $\vec{r}(t) = (a\cos ct, a\sin ct, 0)$.
One ...
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Why does angular frequency of a particle in SHM does not change when it's velocity is changed
$V = A \omega \sin(\omega t + \theta)$ gives velocity of a particle in SHM at time $t$. But, why does the value of $\omega$ doesn't change when $V$ is changed?
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Angular velocity as $r \to 0$
I know that angular velocity is defined as the rate of change of angular displacement and is related to tangential velocity via $$\omega = \frac{r\times V}{|r^2|}$$
My question is what will be the ...
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How do you travel in a circular orbit around a massive body?
I am trying to figure out how an object could achieve a perfectly circular orbit. Given a mass for the planet or other body the object is orbiting and a distance from the center of mass, how fast ...
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The Kerr metric applied to a solid rotating body
Can the Kerr metric be used as an exterior solution to analyse the vacuum outside a rotating solid body or does it only apply to a rotating black hole? If it can't, is there an alternative exterior ...
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Angular velocity calculation
The statement of the exercise is as follows: The system in the figure consists of a disk of radius R and a bar AB of length 4R, with no slipping between them. The disk rolls and slides on the floor, ...
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The relationship between velocity of centre of mass and angular velocity of a rigid body
Consider a rotating object with mass $m$, moment of inertia $I$, along an inclined plane of vertical height $h$. Then simply speaking the following conservation law holds.
$$\frac{1}{2}(mv_{CM}^2+I\...
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Why doesn't $v_T = \omega r$ involve the direction of its variables?
We derived $v_T = \omega r$ by the following procedure, and it's said that $v_T = \omega r$ "is a relation between the magnitudes of the tangential linear velocity and the angular velocity". ...
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Change in direction imply angular acceleration
Does direction change imply angular acceleration. When a non-point mass object changes direction (like a block sliding down a hill of changing slope), why do we not account for rotational $K.E$ when ...
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Is angular velocity in space frame same as that in the body frame?
The angular velocity of a rotating body can be expressed either in the space (fixed) frame, or in a frame fixed with the rotating body, as explained in this answer. Also, I understand how the angular ...
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How do I find the linear components of acceleration in a pendulum?
I have managed to derive the equation of motion of a simple pendulum under the influence of gravity using the Lagrangian, but since that only tells me what the angular acceleration is, I now want to ...
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Angular velocity formula for a particle?
I know that when the motion of a particle is circular about the origin then:
$$\vec v=\vec \omega \times \vec r$$
But that this does not hold for any motion with a radial as well as tangential ...
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When does the 'standard' angular velocity formula not hold?
I have read that the formula for angular velocity:
$$\dot {\vec r}=\vec \omega \times\vec r \tag{1}$$
does not hold in some situations, but the book does not specify what situation so please could you ...
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Why does this model fall apart when angular velocity is small?
I'm doing a physics problem in which a marble spins around a spinning bowl and both have angular velocity $\omega$. It rotates with radius $r$ around the central axis and the hemispherical bowl has ...
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Having trouble understanding how the centrifugal force works
I thought that I understood the centrifugal force earlier, but I can't seem to grasp how it interacts when considering that everything is relative?
Let's imagine that you are the only one in the ...
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Appearing To Reverse Object's Rotation
Can it be done, and if so, how does one you explain mathematically the ability to cause a rotating object to appear to change the direction of rotation? I believe it has something to do with angular ...
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Angular momentum equations
I do not understand this because angular momentum is $L=I\omega$ ($I$ is moment of inertia;$\omega$ is angular velocity) but it I have also seen equations where $L= rmv\sin(x)$. I do not understand ...
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Merry go round physics problem?
So I have the following statement.
"A merry-go-round is spinning with a fixed angular speed. As a person is walking towards the edge, the force of static friction must increase in order for the ...
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Physical pendulum: axis of rotation
Why is the angular momentum always considered to be parallel to the angular velocity in physical pendulum problems, as if the axis of rotation were a principal axis always? I don't see the ...
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What is the reason for so many of uniform circular motions even after so many irregularities in phenomena like motion of planets?
A body remains in uniform circular motion around another body due to the centripetal force between them, when the first body keeps moving with a specific velocity.
This is more possible in an isolated ...
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What does $\vec{\omega}\times\vec{r}$ equals to in circular motion?
I know that $\vec{v}=wr\hat{\theta}$ in uniform circular motion. This equation looks like a result of a cross product.
Yesterday, I started to learn Basic Dynamics of Rigid Bodies. My teacher wrote $\...
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Why angular velocity is a vector quantity? [duplicate]
Angular displacement isn't a vector quantity (according to some websites) then how angular velocity can be a vector? shouldn't it be a scalar?
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Is angular frequency the same as angular velocity or are they different?
I know there are duplicates. But the answers seem to disagree and also I have more specific questions related to this title.
First of all, most questions on this site which ask this question have ...
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Would rotating a large asteroid be a structurally viable way generate 0.3 Earth gravity?
This question is based off something I have seen in science fiction. The TV series The Expanse is known for having realistic physics when it comes to artificial gravity (i.e. no Star Trek gravity ...
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Velocity of the points of a rigid body
The most general motion of a rigid body is a roto-traslation.
Firstly is it correct that any point (let's call it $O$) of the rigid body can be seen as the point through which passes a istantaneous ...
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Does Earth's rotation change at a constant rate?
Follow-up to
Is Earth's orbit altered by recoil from take-off/launch/recovery of aero/space vehicles?
How much meteoric/space dust does the moon accumulate daily?
Is the length of the day ...
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What is this $\frac{1}{r^2}$ factor added to the definition of $ \boldsymbol{\omega} = \mathbf{r} \times \mathbf{v} $?
$ \require{enclose} $
The relation between angular velocity and linear velocity is given by this equation (from openstax: angular velocity):
$$ \mathbf{v} = \boldsymbol{\omega} \times \mathbf{r} $$
I ...
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Is the object's angular velocity changed when the centripetal force becomes kinetic friction?
Consider a situation like a coin slips off a rotating disc due to the lack of static friction. Is the object's angular velocity changed when the centripetal force becomes kinetic friction at the ...
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Can there be any change in angular velocity without internal torque if angular momentum is to be conserved?
Also, why is angular momentum defined only for one body but linear momentum for a system of bodies?
Coming back to my first question, angular momentum is conserved when no external torque acts on it....
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Addition of angular velocities
I'm trying to understand an argument in Taylor's Classical Mechanics section 9.3.
Consider two frames, 1 and 2, and a body, 3. Let $\mathbf v_{21}$ be the relative velocity of frame 2 w.r.t. frame 1, ...
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Euler's equation for a rotating frame when the inertia tensor is non-diagonal
Wikipedia's entry for Euler's equation states:
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a ...
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Rotating Cone - Finding Energy and Momentum
I think I've a conceptual lacuna that needs to be filled, when it comes to a rigid body possessing angular velocities along more than one axes.
Here's my doubt -
Consider the following solid cone (...
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Angular acceleration in rigid bodies
This is a concept which is bothering me a lot. I'm sure there are other duplicates to this question but on seeing a few such duplicates, I haven't yet obtained an answer.
My question is, for a rigid ...
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Kinematics for Non-Uniform Circular Motion
I'm trying to understand how kinematics for non-uniform circular motion. I know that you can represent the net acceleration of an object in non-uniform circular motion with the following equation:
$$...
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Why are angular velocities of double pendulum small in small angle approximation? [duplicate]
In the lagrangian for double pendulum for small angles, the term $\dot{\theta}_1\dot{\theta}_2 \left [ 1-\frac{(\theta_1-\theta_2)^2}{2} \right ]$ is replaced with $\dot{\theta}_1\dot{\theta}_2$, ...
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Acceleration of spacecraft with thrust
I am reading the following paper:
http://web.mit.edu/larsb/www/iee_tcst13.pdf (p.3, equation (1))
By(1), we have the following:
$$\ddot{r}=-S(\omega)^2r(t)-2S(\omega)\dot{r}(t)+(g +\frac{T_c(t)}{...
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Angular velocity of a rigid object about an axis outside of the body
I know that for a rigid body rotating around a fixed axis, the angular velocity of any point with respect to any other point is the same. As a result, the angular velocity is the same for any choice ...
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Collision penetration problem
I'm implementing a 3D engine but I am having some problems with the physics. Sadly my education on this area is not that extend and i would love some help to solve this problem.
Let's say we have a ...
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Intuitively and in layman terms, Why does velocity increase when we reduce the radius for angular momentum?
I understand angular velocity increasing since the distance becomes shorter but why does the actual angular velocity increase? There is no force being applied perpendicular to the centripetal force so ...
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If $\omega = \frac{v}{r}$, why do we need torque?
If $\omega = \frac{v}{r}$, then why do we need torque and angular acceleration? The velocity v can be found just by Newton's second law of motion $F = ma => a = F/m$ and $v = v_0 + at$ . Then we ...
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Time derivative of angular velocity in rotating reference frame
I am going through a section in a textbook regarding the Newton Euler equations for a system of rigid bodies (robotics text). There is a particular line in the derivation I don't understand, I've ...
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How do the units for angular velocity come out of $\omega = \sqrt{k/m}$?
I'm confused about an exercise of a book. I understand that the units for angular velocity is $\text{rad/s}$; but I don't understand, how can I get it from the relation $\omega=\sqrt{k/m}$.
Solving ...
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Understanding angular velocity $\omega$ as a vector
I would like to validate my understanding of angular velocity as a vector.
Suppose we have a particle $P$ moving around in $3D$ space in some arbitrary way. At any given point in time, we would like ...
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Equivalent Characterizations of Rigid Bodies & Angular Velocity Interpretation
In rotational kinematics, there seem to be two common characterizations of a rigid body:
A rigid body is any collection of particles with position vectors $\textbf x_1,\textbf x_2,...$ such that the ...
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Is there a nice physical interpretation of this formula?
As a trivial example in our vector analysis class, we did the following computation.
Let $\overrightarrow{\omega} = (\omega_1, \omega_2, \omega_3)$ be the angular velocity and $\overrightarrow{r} =(x,...
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