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Questions tagged [angular-velocity]

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

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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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1answer
20 views

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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27 views

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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1answer
40 views

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
19 views

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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1answer
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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
26 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 ...
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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
37 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 ...
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1answer
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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
81 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 ...
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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 ...
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1answer
27 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 -...
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0answers
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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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1answer
60 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 ...
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2answers
27 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 $\ddot y$, ...
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2answers
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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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2answers
158 views

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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3answers
168 views

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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1answer
33 views

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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34 views

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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117 views

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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1answer
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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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1answer
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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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2answers
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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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2answers
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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 ...
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0answers
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Basic doubts about dynamics of a rod [closed]

I have few doubts in the given solution. It says there is no force along the plane but $mgcos\alpha$ is acting along the plane ? As given, $A$ is used as orgin. Then how come x-co-ordinate of $G$ is ...
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Why are the units of angular acceleration the same as that of angular velocity squared?

According to this answer, the units for angular velocity squared are $\mathrm{rad}/s^2$. The units for angular acceleration are also $\mathrm{rad}/s^2$. Why is this the case?
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Velocity And Angular Velocity Of A Sphere Rolling Down A Ramp

I was given a question on a recent test that asked me the following: A sphere is allowed to roll down a smooth inclined plane (No Friction), as it rolls down does its velocity remain constant, and ...
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2answers
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What properties must a smoothly spinning toy top have?

It would seem that there is some open source software that would allow you to create objects of a certain volume, even with arbitrary shape (I'm thinking blender and some of it's addons.) Now, I know ...
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2answers
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Rotating object on table: from sliding to rolling

A object which is rotating around a horizontal axis is placed on a surface, and starts sliding (with kinetic friction). After some time, it starts rolling without sliding through the table. The goal ...
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2answers
53 views

Velocity of earth due to the rotational motion of the earth moon system about the center of mass

I calculated the location of the centre of mass of Earth-Moon system using $$\frac{\sum m_ix_i}{M} = \frac{mx}{M}$$ where m is the the mass of the Moon $= 7.35\times10^{22} kg$, x is the distance ...
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If the Sun moves across the ground at 0.25 nautical miles per second, why do shadows move very much slower? [closed]

This title has been discussed previously on this site here. Question: Shadows from the sun moves fairly slow across the ground. Maybe a centimeter per sec. however, I calculated that the sun is ...
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0answers
49 views

Angular momentum, velocity and center of mass

I have a small question. Assuming I hold a given stick A with weight mA, which has a Weight B with mass mB attached to it, start rotating and release at any point. The general movement would be ...
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1answer
45 views

Why does bike trip on the opposite side when turning the handle?

It can be observed on a stationary bike and also on a moving bike that on giving a jerk on the handle the bike leans to the opposite direction in which the jerk is given. Is it due to angular momentum,...
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3answers
60 views

Coriolis force decomposition of angular velocity [closed]

I can’t for the life of me understand how the $\omega$ in this is decomposed to $$\vec{\omega}= \omega (-\sin(\theta),0, \cos(\theta))$$ Any help would be greatly appreciated!
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1answer
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Does the centre of mass of a circular object such as a cylinder or sphere rotate? [duplicate]

Say I pushed a cylinder to roll on a flat surface with velocity v, the point at contact with the floor will have zero velocity in order for the cylinder to not slip - which implies the point at ...
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1answer
24 views

angular and linear velocity of an object let go of while spinning

Can someone explain to me what exactly happens when let’s say you are holding an object like a 1 ft x 6 ft piece of wood. When you are spinning every part of the wood is spinning at a different ...
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1answer
90 views

Integrating rigid body equations for a game engine simulation

I'm a mechanical engineer who's trying to implement a physics engine for a 3D game simulation, so I apologize for being incorrect or simply ignorant of some aspects of computation. I'm implementing ...
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1answer
45 views

Gymnastics angular velocity help

I was confused by another equation again. Would appreciate it if anyone sheds light for me! Consider the following question: A teacher demonstrates a giant pirouette (legs fully extended, body ...
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2answers
156 views

What is the physical interpretation of dividing $2\pi$ by a variable?

Looking at the angular wavenumber eqn: $$k = \frac{2\pi}{\lambda} = \frac{2\pi\nu}{v_p} = \frac{\omega}{v_p}$$ I'm curious what it means to divide $2\pi$ by the wavelength and why $2\pi$ was chosen....
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1answer
86 views

Relation between rotation vector derivative and angular velocity when the rotation angle is constant

$\def\va{\vec{\alpha}} \def\vw{\vec{\omega}} \def\vn{\vec{n}}$Let $\va(t)$ be a rotation vector such that its direction is the rotational axis and its length $\alpha=|\va|$ is the angle describing the ...
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1answer
50 views

Angular velocity by velocities of 3 particles of the solid

Velocities of 3 particles of the solid, which don't lie on a single straight line, $V_1, V_2, V_3$ are given (as vector-functions). Radius-vectors $r_1, r_2$ from third particle to first and second ...