Questions tagged [angular-velocity]

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

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Angular velocity in body frame [on hold]

I am reading about IMU and getting confused in term "angular velocity of body frame with respect to Inertial frame introduced in body frame". It is said in text it is measured by IMU. If someone ...
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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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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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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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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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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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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 ...
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How can a magnetic field exert a torque that causes a disc to rotate?

I'm confused about the premise of this homework problem: A thin, non-conducting horizontal disc lies in the $x$-$y$ plane. The disc has a mass $m$ and a total charge $q$ distributed uniformly over ...
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How to distinguish between angular frequency $\omega$ and frequency $f$

The relation between the "regular" frequency $f$ and the angular frequency $\omega$ ($\omega = 2\pi f$) is clear to me. However, every time I see "rotations per second" I really get confused as to ...
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Angular Dispacement, velocity, acceleration [closed]

What is the effect of angular velocity and acceleration on circular motion as they both have direction so what is its effect?
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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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Centripetal Acceleration as a Cross Product

Is it fine to express the centripetal acceleration as a cross product? a=v X w (where a is centripetal acceleration, v is magnitude of velocity, w is angular velocity) And is it v X w or w X v? ...
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Is natural frequency of an LC circuit equal to angular frequency? Why don't the units match?

When I was reading the LC circuit in my textbook I came across the derivation of equations of instantaneous charge and current. Which is no problem, but when I got to the derivation to current . It ...
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Definition of angular velocity vector of $B$ in $A$ - Strange notation

I found the following definition of angular velocity vector of B in A at page 49 of the book "Thomas R. Kane, Peter W. Likins, David A. Levinson - Spacecraft Dynamics - McGraw-Hill (1981)": The ...
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Deep concept of Rotation Dynamics

If angular velocity about axis of rotation passing through COM is × then why value of angular velocity remains same( i.e ×) If we assume axis of rotation anywhere which parallel to the original one?
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How to define signs for angular velocity, acceleration and torques?

I get confused how to define signs of angular velocity, acceleration and torques in the cases like the following. We have a disk with radius $r$ and center of mass at point $CM$ shifted $d$ from the ...
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Does conservation of angular momentum break conservation of momentum?

Say we have a spinning ring of mass $M$, rotating at $W_0$, at a radius $r$ from some pivot point. This ring has massless spokes extending out to a length of $2r$. From this, we can calculate the ...