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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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Physical interpretation of the definition of angular momentum in classical mechanics

To what I understand, the following is a valid way to introduce the angular momentum $\mathbf L$ in the Lagrangian system of a rigid body. We can consider the extended configuration space to be $M\...
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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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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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The relativistic effects of angular velocity

Imagine I have a circular disk in a vacuum. I apply a constant force, so a constant torque on the disk. My first question is: does this disk have a angular velocity speed limit? I believe it does, ...
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What is the relationship between the angular speed and the diameter of the eye of a water vortex?

In a water vortex formed in a plastic bottle, what is the relationship between the angular speed of the water and the diameter of the hole in the cap? I would have expected that according to the ...
Giuseppe's user avatar
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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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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 ...
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Is angular velocity invariant under SR?

Is angular velocity invariant under special relativity, i.e. do all observers in any relative inertial frames measure same value for angular velocity of a system? If not, what is its expression?
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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 ...
tangolin's user avatar
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Are the ideas of angular velocity, angular acceleration, angular momentum, torque, etc only helpful for rigid bodies?

For rigid bodies, all the particles can have different linear velocities but the same angular velocity, so it makes it convenient to talk about the angular velocity instead. From there, we get to ...
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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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Total angular velocity (Kerr metric)

I have a problem with the kerr metric and the "rotating spacetime" in the ergosphere. How can i calculate the angular velocity $\omega$ of an object in the ergosphere (which flys from infinity into ...
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How to get from angular velocity to acquired phase for neutrino oscillations in matter?

I am reading Akhmedovs 2000 paper on parametric resonance, and I cannot figure out the math of this particular passage: The difference of the neutrino eigenenergies in a matter of density $N_i$ is $...
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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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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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Is it possible to determine a final orientation from an initial angular velocity and constant angular acceleration analytically?

I am looking to model the rotation of a ball over time. I have the following information: an initial orientation, as a quaternion an initial angular velocity, as X/Y/Z components, fixed to the global ...
John Doe's user avatar
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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 ...
Thomas Antony's user avatar
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Angular velocity of a coordinate system in General Relativity

In the textbook, The Classical Theory of Fields (Landau & Lifshitz), the authors express the line interval of the 3-dimensional absolute-space in the form $$dl^2=\gamma_{\alpha\beta}dx^\alpha dx^\...
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What should be the correct way to write kinetic energy of this body?

This is not a homework problem. I only want to check my concept. The solution of the question given in my book goes like this: The angular velocity $\omega$ of body about its axis as shown in figure ...
Prateek Mourya's user avatar
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On the Critical Angular Velocity of Stars

I read on Wikipedia that if the Angular Velocity of a star is above its Critical Angular Velocity, it reaches hydrostatic equilibrium in the shape of a Jacobi Ellipsoid. But how exactly would I find ...
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How to obtain the torque from a magnetic moment Lagrangian?

Consider a body with magnetic dipole moment $\vec m$ subject to a magnetic field $\vec B$. We know that the torque on the body will be given by: \begin{equation} \vec \tau = \vec m \wedge \vec B \end{...
Christopher's user avatar
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Does always angular momentum and angular velocity have the same direction?

I was studying how angular momentum is cancelled when it is transferred directly into the origin of the axis of rotation and during the lecture the professor did something and I was pretty confused. ...
nicolas osorio bustos's user avatar
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 ...
navix1337's user avatar
1 vote
2 answers
463 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 $\...
Sankalp Kapur's user avatar
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1 answer
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Does the height a person jumps from onto a rod, affect the rotational height of a rod?

I was explained in a lecture that if lets say, I jumped from height h and grabbed onto a vine, I would reach y height at the tip of the swing. But if I were to jump from 2h, I would still reach the ...
tryingmybest64's user avatar
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Net angular motion of a body in two cases

So here I have two questions and both have nearly the same structure but the method used for both of them is different, not method exactly but formula. So here is the first question, So here is the ...
Saksham Salaria's user avatar
1 vote
3 answers
471 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 ...
Vyankatesh Ashtekar's user avatar
1 vote
1 answer
50 views

What is wrong with this derivation of the relationship between the radius and angular speed of a gear?

I'm getting tripped up on something which probably has a simple answer but is presently escaping me at the moment. Let's say that a smaller gear is geared up with a larger gear. If I apply a force ...
Israel's user avatar
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2 answers
536 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 ...
Andycb's user avatar
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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. ...
Junaid Mehmood's user avatar
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0 answers
348 views

What makes an object absorbing angular momentum while colliding with another object?

There is a line of spinning top toys in Japan called Beyblades. So, there is a 'stadium' (surface) along which the Beyblades spin around after being set to spin at high RPMs by the players, and the ...
Babu's user avatar
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Why is precession angular velocity constant?

I am currently studying precession, and have a question regarding the angular velocity of precession. Let's simply use a spinning top in this case. I understand that it is given by the formula $$ \...
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Does the angular velocity of a wheel affect its height in this situation?

If there were no friction at all, and the wheel was spinning with some angular velocity in the initial picture shown below. Would the wheel stay perpendicular to the ground regardless of the angular ...
tranzfat's user avatar
1 vote
1 answer
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Angular Velocity of a point on a deflated tire (gyroscope measurement)

Before I do the experiment, I am a bit confused about the expected signals provided by a 3-axis gyroscope (angular velocities vs. time) mounted on the edge of a (slightly) deflated car tire when the ...
afous afous's user avatar
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 ...
Nobodyspecial's user avatar
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439 views

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{...
woeterb's user avatar
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1 answer
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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 ...
user224768's user avatar
1 vote
0 answers
113 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 ...
rr1303's user avatar
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Transverse speed of hamster in wheel as function of theta

i need help with conceptual understanding of how this system works. A small animal is running in a wheel with radius R, (and 0 mass). When the animal is at an angle $\theta = \alpha $ measured from ...
Arne Morten's user avatar
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1 answer
444 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 ...
Adonis4000's user avatar
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0 answers
94 views

Why is angular motion special?

I'm a biochemist, and not a physicist so bear with me if I say something stupid. I do like to read about physics, though and this is one thing I can't wrap my head around. I was recently reading ...
stords's user avatar
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What are the 3 Euler angles?

I am currently reading up on inertial measurement in aircraft systems. Euler angles are one of the concepts I am a bit confused with. In an Euler angle-rate matrix there seem to be 3 parameters: p, q, ...
Snoop's user avatar
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Angular velocities in moving reference frames

Please refer the image below for a clear idea of my question. So, the instructor has written the angular velocity of the wheel, w.r.t. ground and the unit vectors he used are the ones for the frame B....
Sakazuki Akainu's user avatar
1 vote
1 answer
66 views

Confusion about average force

I'm having a bit of confusion about why I can use the average force to compute the angular frequency in the given example: We have a billiard ball, and hit it with a cue 2/3 under the middle of the ...
Yalom's user avatar
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0 answers
266 views

Angular velocity in body frame to displacement in lab frame?

For the case of a freely spinning symmetric top (no gravity), I derived the following equations, where $\omega_i$ is the angular velocity about a body-fixed axis: $$ \omega_1 = w_1 \cos (w_3 t) $$ $$ ...
Servius's user avatar
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integrating small angular velocities

I know that for a constant angular velocity the following is true: $R=e^{W t} R_0$ where $W$ is an angular velocity tensor, $t$ is a time, and $R$ is a rotation matrix I believe the following is ...
staple's user avatar
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Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
Keir Simmons's user avatar
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0 answers
336 views

Rolling in 3D using Torque, Angular Momentum/Velocity

I'm stuggling to get a simulation working correctly. Below you can see what I am attempting to do. You can also view it here. Can you spot where I'm going wrong? (Calculated at start) 1) Inertia ...
Carl Reid's user avatar
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Why does angular velocity lies in the axis passing through the center of the circumference?

I understand that it can't be placed anywhere on the radius because it doesn't vary with it ( and so of course it doens't make sense to place it anywhere else on the plane), but why do we place it ...
doplumi's user avatar
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184 views

Closed-form equation for orientation and angular velocity over time

If a rigid body, rotating freely in 3d, experiences no friction or other external forces and has an initially diagonal inertia matrix $\mathbf{I}_0$ (with $I_{11}>I_{22}>I_{33}>0$) and ...
JCooper's user avatar
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