# 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 ...
1 vote
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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, ...
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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 ...
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1 vote
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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 ...
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 ...
1 vote
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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 ...
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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 ...
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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 $\omega = 0$?
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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 ...
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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 ...
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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 ...
1 vote
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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 ...
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1 vote
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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)
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### 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 ...
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### 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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### 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 ...
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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 ...
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### 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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1 vote
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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 + ...
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### 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 ...
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### 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 ...
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