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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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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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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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: $$\... 1answer 50 views 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 \... 1answer 66 views 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. 1answer 31 views 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 ... 2answers 33 views 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 ... 1answer 50 views 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 ... 1answer 163 views 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 (... 1answer 102 views 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 ... 1answer 23 views 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 ... 1answer 36 views 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 -... 0answers 62 views 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 ... 1answer 156 views 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 ... 2answers 44 views 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 $\ddot y$, ...
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 ...