Questions tagged [angular-velocity]

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

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Kinematics: Circular Motion

What is the difference between angular velocity and angular speed? Is angular velocity after one complete rotation zero? Is the magnitude of angular velocity always equal to angular speed?
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Time taken by a round object inside rotating cylinder to exit from a hole

I want to know the time taken by a round object of sphericity of 0.85 inside a rotating cylinder to exit from a hole. The below figure will explain my query in a simple way. The notable points are: 1. ...
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The units when calculating Gyroscopic precession rate don't make sense [on hold]

I was doing a problem set for my physics course and I ran into some odd units for calcualting the gryeoscopic precession rate. As it is the angular velocity of the wheel around the axis, it should be ...
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How do I derive the formula for radial acceleration when there is no uniform circular motion? [duplicate]

My lecturer states that $a_r=\dfrac{v_t^2}{r}=\omega^2r$ where $v_t$ is tangential velocity, he also wrote that this is derived the same way that radial acceleration is derived in uniform circular ...
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Impulse on a pivoted rod holding two point masses on its ends

So, I'm studying for an entrance exam and came across this question. We hit the bottom block of mass $M=2.5 kg$ with a hammer. This block is attached to a massless rod of length $\ell=0.6m$, pivoted ...
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Velocity in circular motion, $v = r × \omega$ or $v = \omega × r$?

I know it might sound silly to ask, but is the relation between linear velocity and angular velocity of an object undergoing circular motion $ v = r × \omega$ or $v = \omega × r$? I didn't notice it ...
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Angular velocity in Body-fixed frame and space-fixed frame

When we solve for a free symmetric top we find that in body fixed frame, the angular velocity precesses. My confusion is regarding the calculation of omega in body frame. When i am in the body fixed ...
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Why do I get a non-zero Coriolis acceleration for a reference frame that moves in a straight line without rotating?

When you have a stationary reference frame $\{O', (\pmb{e}'_1, \pmb{e}'_2, \pmb{e}'_3)\}$ and a moving reference frame $\{O, (\pmb{e}_1, \pmb{e}_2, \pmb{e}_3)\}$, my textbook defines the Coriolis ...
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Will there be any radial velocity in absence of centripetal force and angular acceleration?

In the question it is stated that there is a ring which can move along a smooth rod. The rod itself is rotating in a horizontal plane with one fixed end with uniform angular velocity. Initially the ...
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Angular velocity in curved space (2d manifold)

In 3d Euclidean geometry, the velocity of any point of a rigid body is given by the cross product between its angular velocity and the position vector which links the instantaneous rotation center to ...
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Finding Direction of Angular Velocity

Suppose I have a 3D rigid object on which some external forces act at various points located on it. The resulting motion would, in general, be the translation of center of mass plus rotation about the ...
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What are the limits of spin speed on a graphene ribbon?

In my previous question, link below, I asked what are the limitations on spinning an object with the goal of achieving relativistic speeds at the edge of the spinning object. In the comments, someone ...
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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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Why are angular mometum and angular velocity not necessarily parallel, but linear momentum and linear velocity are always parallel?

I have read that it's not necessary for angular momentum and angular velocity to be parallel, but it is necessary for linear momentum and linear velocity to be parallel. How is this correct?
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Application of angular velocity to Euler angles

According to a post here Angular Velocity expressed via Euler Angles you can express angular velocity from euler angles. If I choose Y-Z-Y as a rotation sequence the expression becomes. $\theta_r, \...
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Angular velocity vs angular frequency clarification

I can't seem to find a satisfactory answer on stack exchange for this question, so I will present an example which I would appreciate some clarification on. Let's say we have a pendulum with mass $m$ ...
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Angular momentum and angular velocity

The angular velocity $\vec{\omega}$ lies along the axis of rotation. And the angular momentum $\vec{J}$ is the cross product of $\vec{r} \times \vec{p}$. Which according to me should also lie along ...
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What are the necessary conditions for relative angular velocity to be defined? [closed]

I have certain doubts related to the definition of relative angular velocity .My textbook defines it in the manner given below:- $$\omega_{AB}=\frac{v_{AB}}{r_{AB}}$$ $\omega_{AB}$ is the relative ...
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Relative angular velocity

Two bodies are in circular motion with A at one diameter and having velocity tangentially downwards and B at other end of diameter tangentially upwards. Find angular velocity of particle A wrt B if ...
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Forces in washing machine

I have two front-loaded washing machines, when I wash shoes, in one of them the shoes seem to stick to the walls while it's spinning, but in the other I can hear them falling down now and then. What ...
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Angular velocity of thrown object?

I was reading this and came across the statement After releasing the knife, it will fly forward and continue to rotate around its center of gravity with the same angular velocity it had during ...
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Why can we observe further than that?

Why can we, as earth habitats, observe stars further than the speed of light /earth's rotational angular speed? I think it should be in the order of 10^14 m? As, relative to us, stars further than ...
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A peg moving on a ring [closed]

A thin but rigid semicircular wire frame of radius r is hinged at O and can rotate in its own vertical plane. A smooth peg P starts from O and moves horizontally with constant speed v0, lifting the ...
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Choosing motor speeds for an omnidirectional robot given desired linear and angular velocity

Below is an example of an "omnidirectional robot" with four wheels. Each wheel has rollers on it so it can only exert a force along the line parallel to its face, coincident to the ground, and ...
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What actually is the vector of angular momentum?

If an object spins around a central point, it gets angular momentum which is a vector with an orientation dependent on whether its clockwise rotation or anticlockwise, i get that. But what the vector ...
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Linear and angular speeds of a train

I am using Radar sensor in a train. Sensor is in the front part of the train to detect object and avoid collision. It needs vehicle motion data to calculate objects longitudional and lateral speeds....
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Understanding angular velocity in spherical polar coordinates [duplicate]

I'm a first year physics student and i've just learnt this equation for angular velocity in spherical polar coordinates: $\omega=\dot{\phi}\mathbf{e_z}+\dot{\theta}\mathbf{e_\phi}$ The diagram i ...
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Angular velocity of a pendulum in Cartesian coordinates

Hello I have a problem how to write down equations for the pendulum correctly. Say I would use Cartesian coordinates $x, y$ representing the position of the mass. Then the velocities would be usually ...
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Does moment of inertia only work for special cases?

I was looking into the moment of inertia expression for angular momentum. The angular momentum of a group of particles can be expressed as a linear transformation of the angular velocity vector. This ...
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Rotation matrix product and angular velocity

I'm solving the following problem from the book "Analytical Mechanics for Relativity and Quantum Mechanics" by Oliver Davis Johns: Let $R(t)=R_a(t)R_b(t)$ be a rotation matrix. Show that the ...
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Angular momentum w/ changing moment of inertia

A man of mass m1 is standing on a disk with radius R and mass M at a distance r The man starts walking around the disk with constant angular speed w1 and as a result the disk begins to rotate in the ...
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How to calculate the viscous damping coefficient of a viscous layer between an inner sphere and an enclosing outer sphere?

In this article by Rahn and Barba, a flat-spin transition manoeuvre is investigated. For this it is assumed that a rigid spacecraft contains a spherical, dissipative fuel slug of inertia $\boldsymbol{...
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Angular velocity formula in a precession motion

I find out that in the specific case of a precession motion of a constant in magnitude vector $\vec{A}$ we can say that: $\frac{d\vec{A}}{dt}=\vec{\omega}$x$\vec{A}$. Where $\vec{\omega}$ is the ...
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How does changing radius (constant mass) affect rotational kinetic energy?

I'm trying to understand how rotational energy would change if radius shrinks but mass stays the same. The initial question was posed as follows: "The radius of a disk of matter forming around a ...
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1answer
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Wheel RPM measuring reference point [closed]

Attached is picture of a car wheel in 3D. Assume it is suspended and rotating in the air. If I put a nut + proximity sensor right on top of the nut within the red line to measure RPM, will the nut ...
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Why does $\sqrt{\frac km}$ represent angular velocity and not frequency?

When I break down $\omega = \sqrt{\frac km}$ (angular velocity for a simple harmonic oscillator) into its units, I get: $$\omega = \sqrt{\frac{kg * \frac {m}{s^2}}{kg *m}}$$ which simplifies to: $$\...
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Homework problem on pulling a rotating cylinder wrapped with massless rope [closed]

I am trying to solve the following homework problem on mechanics. The solution I attempted is as follows. Equations of motion for cylinder: $F=ma $ $\rightarrow$ $100N=20kg \times a$ $\...
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1answer
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How did moment of inertia affect the length of the day? Please try to explain briefly [closed]

How did moment of inertia affect the length of the day? Please try to explain briefly.
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1answer
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Angular Momentum and assymetric axis

The question I came across , If a semicircular disc rotates uniformly (const. angular velocity) about an axis passing through its Centre of mass , and prependicular to its plane , do we need an ...
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Calculating when the center points of two orbiting bodies will be at the same circumferential position

I'm working on a game idea that includes objects orbiting around a common center point. I would like to have some way of knowing (mathematically) when two given objects/bodies will be at the same ...
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1answer
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Minimum Angular Velocity

A bead is free to slide on a vertical circular frame of radius $R$ comes to equilibrium when $\cosθ = g/Rω²$. The minimum value of angular velocity comes out to be $\sqrt{g/R}$, which we can find out ...
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Why are angular velocity and angular frequency not measured in Hertz?

Recently, I was doing my homework and I found out that Angular Velocity and Angular Frequency can be calculated using $\omega=v/r$. This means the units of angular velocity and angular frequency are (...
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1answer
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Position vector from the axis of rotation in a rotating sphere

In Fluid Mechanics textbook, I found the following example: In the rotating sphere viscometer, a solid sphere of radius $R$ is suspended from a wire and rotates slowly at constant angular ...
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Is (velocity=angular rotation*radius) dimensionally homogenous? [duplicate]

I have been driving myself mad trying to prove it one way or the other, I understand how it is derived and how to use it etc. but it still seems to me to be saying that (m/s)=(rad/s)*(m) which I don't ...
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1answer
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Angular acceleration of a double compound pendulum [closed]

How can I calculate the angular acceleration of a double compound pendulum? I'd like to know what the angular acceleration of each of the pendulum's center of mass will face at any point in time. PS -...
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Angular acceleration as a function of angular velocity squared and angular displacement?

I was reading this on Quora which stated that angular acceleration $\alpha$ can be expressed as $ - \omega^2 \theta $ where $\omega$ is angular velocity and $\theta$ is the angular displacement. I’ve ...
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Rotating sphere and the velocity of particle at the surface

If a sphere is rotating with speed $\omega$ and has a radius $r$, then after one complete revolution what would be the velocity of a particle at the surface (neither at topmost or point of contact of ...
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What's the relation between acceleration, position and angular velocity?

I just encountered a problem involving lift and oscillations where I found the following differential equation: $$\ddot y = -\frac{ \rho gA}{m}y = -\omega^2 y$$ What's the relation between $\ddot y$, ...
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Angular velocity of a body observed from a frame of reference fixed on the body

I have a body and the reference frames, one is the inertial reference frame O-xyz, the other is a non inertial reference frame O'-x'y'z' fixed on the body. The angular velocity vector of the body ...
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How does changing the moment of inertia of an object being swung by a human affect the kinetic energy?

If a human swings a baseball bat with moment of inertia $I$ at velocity $\omega$, as hard as he/she can the swing has a given kinetic energy. If you increase $I$, then the human will not be able to ...