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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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1 answer
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Angular velocity of a particle moving in 3D

I have a particle trajectory where particle position is available at discrete time steps with respect of (0,0,0) in 3D. Time step is 0.05 sec. For reference, positions are shown in following image. ...
-1 votes
2 answers
637 views

Derivative of transformation matrix for 6-DOF dynamics

I'm implementing a planner for a 6-DOF underwater robot and I'm using the dynamics derived in chapter 7.5 of Fossen's HHandbook of Marine Craft Hydrodynamics and Motion Control. I'm using the ...
2 votes
3 answers
210 views

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
1 answer
443 views

Angular velocity - Gyroscope

I am currently researching the gyroscope on my own and i came across the concept of angular velocity. The torque ($T$) on a gyroscope is caused by $R\cdot F$, where the force i consider it to be ...
3 votes
6 answers
159 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 ...
2 votes
6 answers
318 views

Why is the angular speed at the axis of rotation of a rotating disc equal to the angular speed at any other point on the disc?

I was just reviewing classical mechanics problems on Khan Academy and got the following question: I knew that the angular speeds at points II, III, and IV must be equal, but I'm not sure how you'd ...
-1 votes
0 answers
22 views

How many centimeters will the ball rise due to the motion? [closed]

A small ball with a mass of 50 grams is in a spherical bowl with a radius of 10 cm. The bowl rotates at a frequency of 5 revolutions per second around a vertical axis. How many centimeters will the ...
0 votes
4 answers
402 views

Angular velocity about an arbitrary point

Consider a rigid body rotating with angular velocity $\vec{\omega}$. Now, we know that this $\vec{\omega}$ is an intrinsic property for the rigid body, in the sense that: Each point on the rigid body ...
0 votes
1 answer
32 views

What is the tangential velocity at the end of an arm with three joints? [closed]

I am trying to determine the tangential velocity of a part being held on the end of a SCARA robot and if each of its joints is moving at a different angular velocity. This is analogous to a human arm ...
1 vote
2 answers
460 views

Angular velocity and banking angle

In a swing ride in an amusement park, the angle and speed of a seat in circular motion can be modelled by the banking angle equation: $$\tan \theta=\frac{r\omega^2}{g}$$ Since tan of $90^{\circ}$ or $\...
0 votes
2 answers
474 views

If torque is the driver of rotation, why doesn't more torque (rotational force) mean faster rotation?

I got confused about the car. In most places they said that for acceleration when we start we need more torque (which is consistent with the fact that the highest acceleration is in first gear). But ...
1 vote
1 answer
686 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 ...
1 vote
0 answers
33 views

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, ...
8 votes
4 answers
19k views

Proof of centripetal acceleration formula ($a_c = v^2/r$) for non-uniform circular motion

The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$ However, all the proofs I've seen rely on the fact that it is ...
0 votes
3 answers
80 views

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 ...
1 vote
2 answers
108 views

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
0 answers
66 views

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 ...
4 votes
2 answers
112 views

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
0 answers
43 views

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 ...
3 votes
2 answers
169 views

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 ...
2 votes
1 answer
318 views

Overturning torque on a car navigating a curve

The car shown above with mass M is turning to the left with an uniform angular speed W on a circular path with radius R. When the angular speed is increased to a critical value C, one of the normal ...
1 vote
3 answers
416 views

Does the angular velocity of a spinning disk increase if it has a completely inelastic collision with a object with a greater tangential velocity?

A roller of radius 10cm is spinning with a angular velocity of 15 rad/s. It has a completely inelastic collision with a hunk of clay, with mass m moving at 3m/s at it's very bottom edge. Does the ...
0 votes
4 answers
82 views

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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0 answers
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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?
1 vote
3 answers
98 views

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 ...
0 votes
1 answer
200 views

Is Ang. Momentum Conserved about Front wheel of car?

I know that as a car accelerates on earth, for the car-earth system angular momentum is conserved. Attached is a nice animation for simplistic proposes. https://www.animations.physics.unsw.edu.au/jw/...
1 vote
3 answers
468 views

How to find angular velocity vector of a three dimensional rigid body given velocity of three non-collinear points on the same?

The position of a three-dimensional rigid body is completely defined by specifying position vectors of three non-collinear points on the body. Similarly, one can define the motion of the rigid body by ...
1 vote
1 answer
593 views

Tangential velocity - Spherical coordinates

In a spherical coordinates system ($r$, $\theta$, $\phi$ ), assuming an angular rotation $\omega_z$ around the z-axis, the tangential velocity of a point can be expressed as: $$V_x = -\omega_z R \sin\...
0 votes
1 answer
49 views

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 ...
2 votes
1 answer
53 views

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 ...
1 vote
2 answers
532 views

Calculate a rotational speed for an object spinning in 3 axes

I've got an object spinning in 3 axes and I'm tracking it with a motion capture system. For each timepoint, depending on how I export the data, I either get 4 columns of data for the quaternion ...
0 votes
2 answers
79 views

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 ...
0 votes
1 answer
306 views

Derivative of angular velocity in a rotating frame

Taylor Relies on these relations $v = \omega \times r$ $\frac{d}{dt}Q = \omega \times Q$ To show that $a = a' + 2 \omega \times v' + \omega \times \omega \times r' + \alpha \times r' ...
1 vote
1 answer
444 views

Angular velocity in body-frame vs inertial frame

This question is based on the nomenclature and definitions in Structure and Interpretation of Classical Mechanics. In Section 2.2, we start with a rotation $\mathscr{M}(q(t))$ where $q$ is the path ...
0 votes
4 answers
1k views

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 ...
1 vote
2 answers
37 views

Angular velocity vs Angular frequency

Are these two omega same? (angular frequency of a current oscillating loop and angular velocity of a rotating body)
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 ...
4 votes
3 answers
3k views

Instantaneous axis of rotation [duplicate]

If there is sphere rolling on the horizontal surface without slipping. Then we know the instantaneous axis of rotation is the point which is in contact with surface. Now my doubt is, why the angular ...
0 votes
2 answers
49 views

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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3 answers
117 views

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 ...
0 votes
0 answers
22 views

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 ...
6 votes
2 answers
325 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 ...
1 vote
1 answer
261 views

Rolling motion, sliding, contact point, friction

I have a question about rolling motion. So suppose we throw a bowling ball with no initial angular velocity, only linear velocity $v_0$. At first it will be sliding on the ground. Let the kinetic ...
0 votes
3 answers
292 views

Measure imbalance from within wheel

I want to measure static imbalance in a (car) wheel, using an accelerometer. This imbalance can be caused by tire, rim damage, dirt in the tire etc. The imbalance causes the center of mass to be ...
1 vote
0 answers
48 views

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}{\...
0 votes
2 answers
750 views

Angular velocity of disc from induced motion

I came across a question regarding linear momentum $L$ and it's conservation, however I tried and got confused. It reads: A $40kg$ girl stands on the very edge of a rotating disc of mass $50kg$ and ...
2 votes
1 answer
77 views

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 ...
2 votes
3 answers
2k views

Adding angular velocity vectors

We know we can add two angular velocity vectors to get a total angular velocity. Whereas I more of less understand the basic principle and the mathematical formulation, I have problems in visualizing ...
-1 votes
3 answers
81 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 = \...
3 votes
3 answers
2k views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...

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