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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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Help with deriving angular momentum balance from position and momentum

I have no idea how to derive this! I've looked all over the internet and throughout two textbooks, and all I can find is very specific proofs, but none showing what I need. Any ideas?
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Will a spinning rocket induce an additional angular rate while ejecting a satellite?

A rocket spins with 30 degrees per second, and ejects a satellite into the space. From the experiment on the ground we know that the ejecter will give a satellite angular rate 5 degrees per second if ...
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23 views

Angular acceleration of a double compound pendulum [on hold]

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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30 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 ...
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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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Rotation of Compact discs (CDs) [closed]

Here's a problem on rotation of CDs: The (a) and (b) part are particularly easy to calculate but I'm having problem to start (c). What is the way to find the angular speed here? We are only given a $...
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30 views

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
121 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
58 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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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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25 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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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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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 ...
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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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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
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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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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
44 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
51 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
21 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
83 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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31 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
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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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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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48 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 ...
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145 views

Calculate Linear Velocity and Angular Velocity After Collision, in SceneKit [closed]

Here is an attached scheme which i want to write my own custom wall reflection method to simulate the ball collision having right (or left, or top/back) spin. As an example, i have created wall node ...
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1answer
164 views

Rotational Kinematics and Angular Velocity Vector Transformation

Say we have a rigid body with a body-fixed coordinate system XYZ and an inertial coordinate system (North - East - Down) XoYoZo. If we use the x-y-z convention and rotate the body fixed frame first ...
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2answers
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Speed of the rotating block [duplicate]

Problem: A block tied to a string is rotating with an angular velocity $\omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the ...
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2answers
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Is the right hand rule a trick to avoid tensors?

I have read in this answer that "to represent angular momentum as a vector you need to use a right hand rule. This is annoying, because physics at ordinary scales is reflection invariant but ...
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1answer
51 views

Proof regarding curl of a vector [closed]

I'm stuck in this problem where we need to prove that the curl of the velocity vector is twice the angular velocity of a rigid body in circular motion. How do I prove it? I am very new to the concepts ...
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1answer
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An interesting problem from circular motion [closed]

Consider this situation: Two individuals are seating side by side on a Merry-go-Round moving with angular velocity $\omega$) seats they are just seating next to one another. Now the person A is ...
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1answer
30 views

calculate the time elapsed for a robot to pass certain distance with a load [closed]

For a robotics project I wanted to find the optimal gear ratio for my robot to travel 10 meters. Unfortunately. the acceleration is nonconstant, and that proved to make my life much harder. I think I ...
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1answer
54 views

Calculating angular velocity of rolling object with just gravity?

From what I have learned, you can calculate what the angular velocity of an object will be based on its potential energy. Say there is a situation where: acceleration due to gravity = 10 m/s² ...
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0answers
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forward and angular velocity addition

I share some data here which is related to my question. ...
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1answer
76 views

How to calculate the radius of a curve based on vehicle wheel speeds of a car

I have data of the 4 differen wheelspeeds of a vehicle during driving time. Based on that I want to calculate the radius of a curve it is taking. The following are my current thoughts that seem to be ...
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2answers
57 views

Speed of two objects orbiting around a central axis

This question has been bugging me for quite some time and i'm not too sure if i'm missing out some important factor in the understanding of this scenario: Given two objects of equal mass and size ...
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3answers
101 views

rotation matrix in quaternion representation

is the the rotation matrix corresponding to the quaternion different from the rotation matrix corresponding to the quaternion error (between desired and actual value) ? Let $\mathrm{Q}$ be the ...
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0answers
111 views

Do symmetric angular velocities lead to symmetric axis of rotation observed in a fixed frame?

It has been observed that some insects with relatively small stroke amplitudes (such as mosquitos) take advantage of a translating axis of rotation to generate lift where insects with larger stroke ...
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1answer
89 views

Time derivative of vector in rotating frame with angular velocity about a rotating axis

In general, I know that if you have a vector $\vec{F}$ in a rotating frame, and the frame has an angular velocity $\vec{\Omega}$ that the time derivative of $\vec{F}$ in a fixed frame would be $$\frac{...