Questions tagged [angular-velocity]

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

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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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How are the tipical values of the Columbus and viscous friction torque?

I am mathematically modeling a motor and I want to calculate the constant columbus and viscous friction torques. The forumula I found was: where a is the voscous friction torque and b is the ...
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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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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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Calculating the wattage of an appliance with radial velocity of domestic electrical meter

There's a heater who's wattage I want to work out. I notice when it is not plugged into the mains socket, the dial on the electric meter for the house spins at x rpm. When it is plugged in, it spins ...
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Rolling motion, sliding, contact point, friction

I have a question about rolling motion. So suppose we throw a bowling ball with no initial angular velocity, only linear velocity $v_0$. At first it will be sliding on the ground. Let the kinetic ...
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Determining orbital height of a satellite just by observing angular velocity

A few days ago I obervered a satellite with my telescope. But when I later looked at Stellarium (after adding all available satellite databases), there was no satellite passing the spot that I ...
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Can a particle make a turn in space without accelerating? Does the size of the turn it makes, make a difference?

Is it possible for a particle to have angular velocity but no angular acceleration? Even if the angular velocity does not change, does there always need to be a centripetal / centrifugal acceleration ...
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How to add angular velocity vectors?

I was reading David Morin's mechanics book and came across this problem. And here is the solution provided: I am just wondering why you can express the total angular velocity of the coin with ...
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Why is the angular speed at the axis of rotation of a rotating disc equal to the angular speed at any other point on the disc?

I was just reviewing classical mechanics problems on Khan Academy and got the following question: I knew that the angular speeds at points II, III, and IV must be equal, but I'm not sure how you'd ...
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Angular velocity and banking angle

In a swing ride in an amusement park, the angle and speed of a seat in circular motion can be modelled by the banking angle equation: $$\tan \theta=\frac{r\omega^2}{g}$$ Since tan of $90^{\circ}$ or $\...
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Can Wavelength also be used as Circumference?

Could Lights wavelength be the result of the electron orbits and its distance? Could this be why wavelength and orbit circumference measurements are the same? This would imply that wavelength radius ...
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Question about the value of angular displacement [closed]

Can angular displacement be greater than $2\pi$ radians? Is $5760$ radians correct here or should we do something like this: $\frac{5760}{2\pi} = 916.732472209$ $0.732472209 \cdot 2\pi = 4....
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Why does the angular velocity use $r$ instead of $R$?

I am calculating final velocity of a Maxwell wheel rotating and translating down due to gravity with energy. I split the kinetic energy into translational and rotational kinetic energy. I am little ...
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Does in 3D rotations angular velocity about any point can be taken as same as any other point?

In 3D rotations suppose we have two different angular velocities one for spinning and other for revolution about a point like lets say this figure so here one can see the angular velocity of disc to ...
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Does the height a person jumps from onto a rod, affect the rotational height of a rod?

I was explained in a lecture that if lets say, I jumped from height h and grabbed onto a vine, I would reach y height at the tip of the swing. But if I were to jump from 2h, I would still reach the ...
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Net angular motion of a body in two cases

So here I have two questions and both have nearly the same structure but the method used for both of them is different, not method exactly but formula. So here is the first question, So here is the ...
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Differece between torque $\tau$ and angular velocity $\omega$

The title is a weird question, i know. But hear me out: Take the equation that relates the tangential velocity $\vec v$ and the angular velocity $\vec \omega$ of an object moving on a circle with ...
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Does the mass moment of inertia stay the same for a particular spinning object?

A solid disk of mass m and radius r spinning about it's central axis would have a mass moment of inertia, I = (1/2)mr^2. But according to the conservation law of angular momentum, the initial angular ...
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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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Angular Velocity via Extrinsic Euler Angles

I am wondering if the angular velocity of a rotating coordinate system, if expressed through extrinsic Euler angles, is $(\dot{\alpha},\dot{\beta}, \dot{\gamma})$ since extrinsic Euler angles are ...
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Tangential velocity - Spherical coordinates

In a spherical coordinates system ($r$, $\theta$, $\phi$ ), assuming an angular rotation $\omega_z$ around the z-axis, the tangential velocity of a point can be expressed as: $$V_x = -\omega_z R \sin\...
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Does there exist a point from which you can observe a body in an eliptic orbit having constant angular velocity?

Consider an eliptic orbit where a smaller body orbits a larger body located at one of the foci of the ellipse. All bodies are coplanar. Due to keplers second law the angular velocity about the larger ...
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Why does this setup fix a specific angular velocity?

First let me clarify that this is not a homework type question as I am not seeking any solution rather I am confused about the question itself. Question: Find the angular velocity of rotation. My ...
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Connecting Linear and Rotational Velocty

I'm was watching the MIT open courseware classical mechanics and don't understand why the presenter did what she did to equate liner speed to rotational speed. I was wondering if anyone would be able ...
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Change in angular velocity of an initially non-rotating spherical object after a collision

In the theoretical scenario below: Will the object rotate? My first thoughts on this were: The initial angular velocity is $0$. This means it does not have any angular momentum (right...?) and it ...
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