Questions tagged [angular-velocity]

The time derivative of angular position used when studying rotating objects or systems.

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How is angular velocity defined in this case (and why)?

Suppose we have two particles with trajectories $\vec{r}_{1}(t) = (\cos ct, \sin ct, 1)$ and $\vec{r}_{2}(t) = (-\cos ct, -\sin ct, -1)$. On one hand, we could say the angular velocity of the two ...
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An object is being swung around in a circle, attached by a string. If the string breaks, does the angular velocity instantly drop to zero?

If an object attached to a string is being swung around in a circle, then when the string breaks, the object will continue in a straight line at a constant velocity, per Newton's First Law. If I ...
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Where is the reaction force of an object that has just flung out from a circular motion?

An object in a circular motion will fly out tangentially when released. As per Newton's Third Law of motion, there is a reaction in every action. The moment the object is released, where is the ...
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Experimentally determine the Moment of Inertia of a complex (mathematically indescribable) object

I'm a high schooler that's trying to design a robot for a physics project. The robot is a catapult; it will calculate a trajectory and shoot at a certain speed and angle using a large motor. I'm using ...
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Circular motion of two bodies: how to determine when they meet up again?

Let's say that there are two satellites, one of them moves in the red orbit and the other one in black one. At the time t0 they start together on the green point. How can I set equations to deduce ...
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What is the angular velocity of a wheel as a function of time as it is spun up by a DC motor?

For the sake of concreteness, let us consider a brushed DC motor. I am trying to predict how much a wheel spins up when it is connected to a DC motor for a certain amount of time $t$. Let's say I ...
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Angular velocity of a coordinate system in General Relativity

In the textbook, The Classical Theory of Fields (Landau & Lifshitz), the authors express the line interval of the 3-dimensional absolute-space in the form $$dl^2=\gamma_{\alpha\beta}dx^\alpha dx^\...
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Circular motion at a fixed angle [closed]

An equal amount of white solution of AgCl was taken in 3 test tubes. One test tube was centrifuged at a 0-degree angle, one at a 180-degree angle, and the other at a 45-degree angle. Will the result ...
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How does a particle have torque and angular momentum?

I'm aware similar questions have been asked, but I didn't understand the answers. Can a particle experience torque? What about angular velocity and/or acceleration? Assuming a particle is a body ...
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Do stars lose spin angular momentum, to planets, radiation, or gravitational waves, or in some other way get a longer period?

A spinning star is throwing off stellar wind, and electromagnetic radiation, which might be carrying away angular momentum, so that the star loses angular momentum, and its angular momentum per unit ...
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Calculate Angular Velocity (Spin) From Trajectory Parameters

I am trying to determine (roughly) the RPMs of a tennis ball based on it's trajectory parameters. I have Vo (initial velocity), ø (trajectory angle from horizontal), d (total distance travelled), t ...
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Ballerina Universe Paradox [closed]

Imagine a ballerina spinning with angular velocity $\omega$ on the ground, you will see her arms opening due to the centrifugal force. Now think of the same ballerina but she is the only thing in 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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Angular velocity at a general point

I have been reading circular motion for a while and the magnitude of angular velocity is defined as component of linear velocity (perpendicular to the position vector) divided by position vector. But ...
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Magnitude of the time derivative of angular momentum

This is a problem involving a stick of mass m and length l which spins with frequency ω around an axis, as shown in the figure below. The stick makes an angle θ with the axis The goal was to find the ...
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Direction of angular velocity vector VS angular momentum vector

I understand that angular velocity and angular momentum velocities don’t need to be parallel to each other. However, I’m confused what these vectors even represent. So I have 3 questions about this: ...
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Is it possible to change the speed at which a wheel is freely spinning by moving only its axle?

Suppose we have a wheel spinning on a perfectly lubricated axle. Is it possible to change its angular velocity about that axle, by moving only the axle? Due to the wheel's symmetry about the axle's ...
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Finding motorcycle turning radius based on lean angle

I have been implementing a basic motorcycle physics model and have been predicting the turning circle of both wheels based on the current angle of the front wheel. However, this fails to predict the ...
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Rotating a lever — small end has more force but less speed?

Suppose I have a massless lever with two masses at the ends and a fixed pivot as depicted below. Assume no gravity in this scenario. Further, let's say object $B$ is closer to the pivot, so $r<R$. ...
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Angular Acceleration of Spinning Body About a Rotating Axis

How would you find the angular acceleration of a body spinning about an axis that is itself rotating? Specifically, how would you find the angular acceleration in question 1.58 of Irodov's physics ...
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Velocity and Angular Velocity Equations for Cue-Ball Interactions

I'm trying to create an eight-ball pool simulation in Python, and I'm trying to simulate the interaction between a cue stick and a cue ball. Suppose I thrust a cue stick with mass $m_s$ at a velocity $...
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Integrating Angular Velocity Vector using Rodrigues' Rotation Formula

My understanding is that Rodrigues Rotation Formula can be used to explicitly compute an exact rotation associated with a constant angular velocity vector over a given time step. How do you derive the ...
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Why does relativistic rotating rod bend?

Let's consider two inertial reference frames S and S', S' moving with velocity V relative to S (velocity V to the right with respect to S considered stationary, in X-axis direction). We have a ...
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Does the angular velocity of a rigid body equal to the angular velocity about an axis plus the angular velocity of the axis?

If so, how to prove that relation?
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Angular velocity along a fixed rotational axis in space

I've been having some trouble getting my head around angular velocity and it's tangential movement, From what I think I understand the angular velocity has always a direction which is perpendicular to ...
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Will a radioactive ball conserve its angular velocity?

Consider a uniform spinning sphere in vacuum. In principle it should spin forever, because of angular momentum conservation. However, assume that the sphere is made of radioactive material: since it ...
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A dilemma regarding torque when a body moves in circular motion

Consider a mass 'm' tied to a rope and I am rotating it in a circular path with constant angular speed.One component of the tension balances the weight and the other component provides centripetal ...
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How do the inertia tensor varies when a rigid body rotates in space?

The inertia tensor is clearly constant the in a frame moving with the rigid body. But what is the simplest way to see why its columns can be considered rotating vectors in space with the angular ...
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Does an irregular rigid body can only rotate in three directions?

Suppose that at a certain instant the angular momentum with respect to the center of mass is not parallel to the angular velocity. Does this necessarily imply that the angular momentum is rotating ...
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Angular velocity of a ball if force is applied above its center

I am wondering what the angular velocity would be if you apply a force over time to a ball above its center (but not tangential). For instance, if a ball of was lying on a flat surface and you apply a ...
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Confused about the solution to the pendulum differential equation

So I’ve learned how to derive the exact solution to the pendulum differential equation (in respect to its period), $\ddot{\theta} + \frac{g}{l}\sin\theta=0$, where $g$ is gravitational acceleration ...
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Angular velocity and axis of rotation

If the angular velocity is along the axis of rotation, then why angular velocity has different components in space and body axis. Let's say $\boldsymbol{\omega}$ is the angular velocity, if it is in ...
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What is the angular momentum of a particle rotating around an axis in 3D?

What would be the angular momentum of the particle at position $r_i$ in the diagram above? The vector from the axis of rotation is $R_i$ and the tangential velocity is $v_i$ so the magnitude of ...
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Why does angular velocity changes as i strech my hands?

Suppose I am sitting on a turnable chair. I have given that turnable chair some angular velocity $\omega$ and it starts rotating around me as axis of rotation. Now at that instant suppose I expand out ...
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Rate of change of angular speed and tangential acceleration

My textbook gives the following equation $a_{tan} = \frac{dv}{dt} = \frac{d(r\omega)}{dt} = r\alpha$ Now, what exactly is $\alpha$? I says the rate of change of angular speed, but as it is written, it ...
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Acceleration of an instantaneous centre is always 0? [closed]

I came across the following question recently: My understanding of the question is that it wants us to show that end A is an instantaneous centre. The mark scheme does so by showing that A has no ...
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How to calculate velocity vector from scalar angular velocity and position vector in 2D?

I would like to know, if I have an angular velocity as scalar, how can I calculate the velocity vector. I know that the product of angular velocity and the length of the distance gives the speed, but ...
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1 vote
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How much percent of the speed of rotation of the solar surface at the equator is due to frame dragging effect? [closed]

Frame dagging effect is interesting and my particular interest is does this rotation could be compared with the law of motion of planets in a system similar to our Solar system and also can we measure ...
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What should be the correct way to write kinetic energy of this body?

This is not a homework problem. I only want to check my concept. The solution of the question given in my book goes like this: The angular velocity $\omega$ of body about its axis as shown in figure ...
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How does the angular velocity of the charged disk affect the magnetic field?

How does the angular velocity of the rotating charged disk affect the magnetic field?
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On the Critical Angular Velocity of Stars

I read on Wikipedia that if the Angular Velocity of a star is above its Critical Angular Velocity, it reaches hydrostatic equilibrium in the shape of a Jacobi Ellipsoid. But how exactly would I find ...
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How to derive the formula for angular velocity?

In my mechanics course, we entered rotational mechanics. We were previously introduced to the idea of angular velocity in 2-dimensions as follows, $$v=\omega r$$ Where $v$ stands for angular velocity....
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Physical significance of the angular velocity vector and its projections along different axes

Let's say there is a disk spinning at angular velocity $\omega$. If an observer looks down at the disk directly from the top, he will see the red marker spinning about the center of the disk at ...
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How to predict position with forward Acceleration(with angle) and angularAcceleration?

I'm working on predicting the path of a point in 2D space for a game; My point have a direction initial and I want to accelerate on this direction every times, the direction of point is computed with ...
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How to obtain the torque from a magnetic moment Lagrangian?

Consider a body with magnetic dipole moment $\vec m$ subject to a magnetic field $\vec B$. We know that the torque on the body will be given by: \begin{equation} \vec \tau = \vec m \wedge \vec B \end{...
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Does always angular momentum and angular velocity have the same direction?

I was studying how angular momentum is cancelled when it is transferred directly into the origin of the axis of rotation and during the lecture the professor did something and I was pretty confused. ...
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Relative angular velocity and linear acceleration of a fixed rigid body coordinate with respect to another moving rigid body coordinate

Let me describe a problem I currently have: The robot (orange box) moves around the object (green box) located in a fixed position. Odom keeps providing a homogeneous transformation (rotation and ...
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Angular momentum and torque meaning

I am trying to understand torque and angular momentum. I faced the following problems but couldn't find an answer in my textbook or internet: why is torque equal to vector product of force and ...
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Confusion in using angular momentum conservation to solve this problem

Suppose I have spherical shell kept on a rough horizontal surface. The radius of this shell is given as $R$. Let us call the center of the sphere $O$. At some height $h$ above the center of the sphere,...
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How do you find the angular velocity required to keep a constant distance $r_0$ between two unequal spherical masses?

I am having trouble coming up with this solution. Here is where I am at. I defined two variables, $r_1$ and $r_2$, where the former is the distance between $m_1$ and the center of mass, and the latter ...

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