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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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How can we choose two different mass moment of inertias for the same momentum calculation?

I am working on answering part (a) and here is what I got: By conserving linear momentum, we have that $$mv_0 =(3M)v_f \hspace{3mm}\implies \hspace{3mm} v_f =\frac{1}{3}v_0$$ Now, in order to conserve ...
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Is this assumption about a vortex's angular velocity reasonable?

I am deriving a velocity flow function $\psi(r,t)$ that could be derived by (1) establishing the relation between two vortex area functions, $a(t)$ and $A(r)$, using the disk method of integration, ...
Tayler Montgomery's user avatar
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3 answers
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Two questions on the instantaneous centre of rotation

In one of the "Additional solved problems" in chapter 6 of Analytical Mechanics, an Introduction (Fasano, Marmi, 2006) the following is stated: Let $C(t)$ be the instantaneous centre of ...
ebenezer's user avatar
1 vote
2 answers
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Serway & Jewett's definition of rotational equilibrium

On p. 364 of Physics for Scientists and Engineers (9th ed.), Serway and Jewett define a rigid object to be in rotational equilibrium if it has an angular acceleration of zero. They then state that a ...
dontknowphysics's user avatar
1 vote
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Angular velocity versor

I am going back through the definitions of good old Euclidean vectors and trajectories to see whether when i was younger i missed important concepts. In my notes, and reference book, i found that for ...
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Kinetic energy of an ellipsoid

I am trying to solve the following exercise, taken from Landau's Mechanics: Find the kinetic energy of a homogeneous triaxial ellipsoid, rotating around one of its axes (AB, fig. 44), while the ...
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The stupidest question ever on relative kinematics and angular velocity [duplicate]

I am scratching my head on a very basic formula whose meaning escapes my intuition. On basically all texts of mechanics the following result is derived: Suppose that a rigid body is moving with ...
ebenezer's user avatar
3 votes
2 answers
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Angular frequency vector, when explaining the motion of a wave

The wave number $|k|$ results as the magnitude of the wave vector $k$. Is there an analogous vector from which the angular frequency $\omega$ results when the magnitude is formed? If yes, how can you ...
plantpot's user avatar
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4 answers
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What is the moment of inertia $I$ when angular velocity $ω$ is zero?

$$I = \dfrac{L}{\omega}$$ What is the moment of inertia when $\omega = 0$? Is it just not defined or is the formula not valid when $\omega = 0$?
Krishn Sharma's user avatar
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Does the direction of an angular velocity vector always stays constant with no force involved [duplicate]

Are there cases where there is a rigid body that rotates somehow and the direction of the angular velocity vector changes in the lab system?
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Is this the correct way to integrate orientation given torque and inertia tensor?

I am trying to develop a 3D rigid body simulation in C++ in which I had some conceptual doubts on how to integrate for orientation given the total torque applied to a rigid body, and it's initial ...
Kotetsu Chan's user avatar
2 votes
1 answer
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Centripetal acceleration of centre of mass towards instantaneous axis of rotation (IAOR)

When an object purely rolls on a horizontal surface, the centre-of-mass moves in purely circular motion, with respect to the instantaneous axis of rotation (IAOR). So does the centre of mass have an ...
Alex francis's user avatar
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2 answers
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Linear velocity on a circle

Consider a ball rotating around the z-axis with constant angular velocity $\vec{\omega}$, then the linear velocity $\vec{v}$ is given by $\vec{v} = \vec{\omega} \times \vec{r}$. It is easy to ...
Chuan Huang's user avatar
1 vote
3 answers
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Volume change of a deformable cylinder with a uniform spinning angular velocity

Consider a deformable cylinder without gravity with a uniform spinning angular velocity and the cylinder is not in contact with anything. In theory this cylinder shouldn't change its cross sectional ...
feynman's user avatar
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2 answers
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Angular velocity vs Angular frequency

Are these two omega same? (angular frequency of a current oscillating loop and angular velocity of a rotating body)
Shreyansh Kabir's user avatar
3 votes
6 answers
160 views

Why can't rotations in general be associated with vectors?

In my textbook, there's a question: A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be ...
archthegreat's user avatar
2 votes
2 answers
57 views

Physical pendulum: axis of rotation

Why is the angular momentum always considered to be parallel to the angular velocity in physical pendulum problems, as if the axis of rotation were a principal axis always? I don't see the ...
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2 answers
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Angular velocity relative to some frame

In "Introduction to Robotics" by John Craig, we have the following statement: The vector ${}^A \Omega_B$ describes the angular velocity of $B$ with respect to $A$, and ${}^C({}^A \Omega_B)$ ...
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Circle to Polygon & Circle to Circle Velocity Resolution

I current am working a 2d physics engine, but have recently hit some bumps in the road. Polygon to polygon collision and velocity resolution works without issue, but I am struggling to get working ...
TrippR's user avatar
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3 answers
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Understanding the meaning of the directions of $\vec\omega$ and $\vec{L}$

I'm struggling with some basic intuition regarding the angular velocity $\vec\omega$ and angular momentum $\vec{L}$ vectors, for any arbitrary motion. Specifically, I'm trying to figure out what the ...
Aviv Cohn's user avatar
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6 votes
2 answers
326 views

Radian unit mystery (damped oscillator)

I would be extremely grateful for any help that anyone could offer here. I am interested in solving the optical bloch equations for the excited state population Rabi oscillations with damping due to ...
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Definition of angular velocity in rotational motion of a non-rigid body? [closed]

Consider a particle in rotational motion with radius r and angular velocity w both varying with time, what is the relationship between the displacement u and w of the particle? $w=\frac{\partial u}{\...
Xin's user avatar
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2 votes
1 answer
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Understanding angular velocity $\omega$ as a vector

I would like to validate my understanding of angular velocity as a vector. Suppose we have a particle $P$ moving around in $3D$ space in some arbitrary way. At any given point in time, we would like ...
Aviv Cohn's user avatar
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-1 votes
3 answers
83 views

Can we equate SHM with motion in a circle?

So in SHM, $v = r\omega\cos\omega t$. But we also know that $v = r\omega$ from circular motion. Then, we can write $$r\omega = r\omega\cos \omega t$$ $$1 = \cos\omega t \tag{1} \label{1}$$ $$0 = \...
MegrajChauhan's user avatar
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2 answers
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Angular Velocity and Angular acceleration when the position vector is changing

I was watching a lecture about circular motion and how angular velocity and angular acceleration differ if origin changes.The teacher at 9:10 says that we cannot apply the formula $a=rα$ as position ...
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Why angular momentum keeps the giroscope standing in "impossible" orientations?

I am trying to understand how gyroscopes can maintain rotation in different "impossible" orientations when spinning. I saw that the behaviour in zero-g is slightly different. On Earth, the ...
Yi Qiang Ji's user avatar
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4 answers
166 views

Why isn't the tangential velocity of circular motion zero?

Why is tangential velocity 2πr/T if the body's total displacement in the end of one revolution is zero?
D4NT3 tennyson's user avatar
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1 answer
51 views

Conversion of linear velocity to angular velocity and vice versa

This is very similar to this question, with the main difference being that it doesn't assume that $\vec v=\mathbf0$. Assume that you have a rolling and sliding sphere with radius and mass 1 with a ...
nonhuman's user avatar
2 votes
1 answer
74 views

The Kerr metric applied to a solid rotating body

Can the Kerr metric be used as an exterior solution to analyse the vacuum outside a rotating solid body or does it only apply to a rotating black hole? If it can't, is there an alternative exterior ...
KDP's user avatar
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3 answers
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Is the radius equal to length/radians? [closed]

Is the radius equal to the length/radians. Since the circumference is 2 pi times r and radians of an entire circle is 2 pi r should be equal to lentgh/radians I needed this proof to understand why we ...
Thedambamjam's user avatar
1 vote
5 answers
302 views

The behavior of $\sin {\omega t}$ at relativistic frequencies

The product $\omega t$ is a dimensionless quantity and the same is true for $\sin{\omega t}$. If they are dimensionless, then they are identical between the rest and relativistic frames because there ...
Stevan V. Saban's user avatar
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2 answers
113 views

Why does a mass winding up around a cylinder not lose it's velocity? [closed]

All solutions online I could find to this question takes it as a preconceived fact that as the mass winds, its motion will be perpendicular to the acceleration provided by the thread and hence the ...
Vedansh Tyagi's user avatar
0 votes
2 answers
123 views

Calculating the magnitude of the average acceleration of a clock hand

I've been stuck on the following question from Isaac Physics for quite some time now and I'm not really sure where to even begin: The time shown on a clock changes from 4:00 to 4:30. The minute hand, ...
Developer's user avatar
2 votes
1 answer
43 views

Equivalent Characterizations of Rigid Bodies & Angular Velocity Interpretation

In rotational kinematics, there seem to be two common characterizations of a rigid body: A rigid body is any collection of particles with position vectors $\textbf x_1,\textbf x_2,...$ such that the ...
William Deng's user avatar
27 votes
2 answers
6k views

Is the speed of Earth's spinning constant over a given 24 hours?

Is the speed that the Earth spins on its axis constant over the course of 24 hours? As opposed to does it turn faster and slower during different hours over any given day even by a very small ...
JohnTrainor's user avatar
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0 answers
106 views

Angular momentum in different frames of reference

I have a question regarding what I think should be a simple dynamics problem, but somehow I’m struggling with it. Imagine an object with mass $m$ coming from the left with velocity $v$. An identical ...
basketas's user avatar
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0 answers
22 views

A ball dropped onto a rotating wheel of various frequencies experiment issues

I'm doing a experiment to find the relationship between the frequency of the rotating wheel and the horizontal distance travelled by the ball dropped onto it. I am manipulating the frequency of the ...
dark sorceror's user avatar
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0 answers
45 views

Is angular velocity and angular acceleration independent of translating frame

[CONSIDERING ALL BODY RIGID] So think of a body which is rotating if I see it from a rotating frame,let's say with same angular velocity then the body will appear rest to the frame , so will have zero ...
Guess's user avatar
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3 answers
95 views

Convention or reality?

In case of a disc rotating about an axis perpendicular to its plane passing through its centre of mass, the torque vector points up or down depending upon direction of rotation. Is it just convention, ...
Dumb person 's user avatar
2 votes
2 answers
116 views

Angular velocity calculation

The statement of the exercise is as follows: The system in the figure consists of a disk of radius R and a bar AB of length 4R, with no slipping between them. The disk rolls and slides on the floor, ...
Lacent Jr S.'s user avatar
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0 answers
82 views

Angular speed around a star for different observers

If we consider an observer orbiting an object with the standard Schwarzschild metric (at a fixed radius and in the equatorial plane), is the angular velocity $\frac{d\phi}{dt}$ observed by an observer ...
XBlake97's user avatar
3 votes
2 answers
132 views

Does dimensional consistency imply the same units?

Can two units having the same dimensions always be used interchangeably? For example $s^{-1}$ and $\frac{rad}{s}$ have the same physical dimension, does that mean we can measure frequency $\nu$ with ...
Jack's user avatar
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1 answer
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Would a stick be perpendicular to an attached wire in centripetal motion without gravity? [closed]

I'm visualizing a system where we have a stick with some non-negligible length attached to a string. The string is attached to a fixed point on the other end, and the stick begins rotating around the ...
abokifas's user avatar
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0 answers
84 views

The frequency is off by a factor of $2 \pi$?

I was reading Morin's Introduction to Mechanics, and the following material came up: At equilibrium point $x_0$ expanding the Taylor series, we see $V(x)=\frac12 V''(x_0)(x-x_0)^2$ so comparing this ...
Aditya_math's user avatar
1 vote
1 answer
60 views

Calculating linear velocity based on the (Euler) rotation matrix having 2 time indices

Normally, we denote a rotation matrix with respect to time as $R(t)$. As I understand, we can only denote like that because the initial observation is assumed to be zero ($t_0 = 0$) and $t$ is ...
Kyle's user avatar
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0 answers
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Angular Velocity measured by a UGV on a curved path is equivalent to Angular velocity of UGV on a straight path

Pre-Condition An FOG IMU is mounted on a high speed Autonomous Vehicle to track linear acceleration and angular velocity of the vehicle under dynamic conditions, Here FOG Z axis (accelerometer + ...
Akash Sagar's user avatar
0 votes
0 answers
28 views

Proof angular velocity is invariant to translation on rigid body [duplicate]

My understanding is for a rigid body the angular velocity between two points fixed on the body is the same for all points. In other words the angular velocity vector would be the same. I can't find a ...
FourierFlux's user avatar
0 votes
2 answers
237 views

Collision Calculation in 2D

For a 2D physics simulation, I need to resolve collisions between two objects in 2D. I have available each object's initial angular velocity, linear velocity, mass, moment of inertia, and center of ...
Jcsq6's user avatar
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0 votes
1 answer
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Conservation of Angular Momentum, why does person rotate only one way?

As seen from the video that i linked, when the wheel is spinning then he doesnt rotate, but as soon as he flips the wheel he will start to rotate. Why he doesn't rotate both counter and anticlock wise?...
wtknow's user avatar
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0 answers
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Procedure to accurately extract the instantaneous velocity and spin information from experimental position data?

I have the time information of 3D position data (discrete) of a sports ball in flight, and I'm attempting to extract the velocity and spin information just using that data as I believe every ...
PASUNURU SAI VINEETH's user avatar

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