Questions tagged [angular-velocity]
The time derivative of angular position used when studying rotating objects or systems.
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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 ...
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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 ...
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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 ...
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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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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?...
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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 ...
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How to calculate total moment around $z$-axis when the armlengths are not the same for all motors on a hexacopter?
I wonder how I can calculate the total moment around $z$-axis at a given rotational velocity for the motors on a hexacopter. My intuition tells me that motors that are more distant to center of mass ...
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Angular velocity in planetary motion
Torque about centre of sun is zero.
$$T=Ia$$
So angular acceleration is zero too, so angular velocity should remain constant.
However it is not the case. Please tell where I went wrong.
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Angular velocity definition
My teacher gave this as a fact $\vec{v}=\vec{\omega} \times \vec{r}$(cross product) where $\vec{\omega}$ and $\vec{r}$ are angular velocity and position vectors respectively. He also said that this ...
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Rotating Reference Frames And Their Phenomenon
In a rotating reference frame, while observing the proper motion of stars due to your spin, would you perceive time dilation when closely observing those stars?
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How is the angular velocity tensor defined?
Assume we have a position vector $\mathbf r$ dictating the position of a particle in a rotating frame. Then, for a time dependent rotation matrix $\mathbf R(t)\in SO(3)$ that describes the motion of ...
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Very basic question about a rotating rod's kinetic energy [closed]
I have been trying to understand how to calculate the kinetic energy of a rotating rod that also has translational movement. I have written my question down on paper because I think it is more clear ...
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Shouldn't acceleration of a car be due to kinetic friction? [closed]
During pure rolling when the car is at a constant velocity the velocity of the bottom part of the tire will be 0. But if we push on the gas we apply an angular acceleration on the tire. So now the ...
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Average angular velocity and speed
Are the magnitude of average angular velocity and the value of the average angular speed always same? If not then can you please give an example.
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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 ...
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How do we properly describe angular displacements, angular velocities, and the relationship between them (in the most general case)?
If we are merely describing rotations through a fixed axis through the origin, then it is enough to characterize angular displacements by an angle $\theta\in(-\pi, \pi]$. Real-life rotations are not ...
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Ambiguity in angular velocity? Two different possible angular velocity vector assignments for the motion of a particle?
To simplify things, consider a particle moving in circular motion counterclockwise (from the $+z$ position looking down at the $xy$-plane), so the position is $\vec{r}(t) = (a\cos ct, a\sin ct, 0)$.
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Why are angles so weird?
I'm potentially asking quite a stupid set of questions here but I'm wondering if there is some overarching theory about why angles, and "rotational" quantities which deal with them, have ...
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Does the formula $ V =\omega r$ holds in angular frequency
$ V =\omega r$ can I use that formula if $\omega$ is angular frequency instead of angular velocity?
V is velocity
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Predicting position given constant angular + linear acceleration with a non-fixed axis
My readings on rotational motion always describes rotation around a fixed axis: that is, an object on a string, basically, and changes to angular velocity will alter speed such that the radius is ...
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Does angular momentum of rotating body depend on its position?
This question might be silly. But angular momentum $\vec{L} = \vec{r} \times \vec{p}$. It always confuses me whether or not angular momentum depends on the origin because the position vector does ...
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Friction on a Spinning Platform
I do not understand at all why, if an object is sitting on a spinning platform, the friction force is towards the center. I understand the need for a centripetal force during circular motion, but ...
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Why dimension units of radius is not $\rm m/rad$ or $\rm cm/rad$? [duplicate]
Radius is not a just simple size or length between the two points. The radius shows the connection of linear and angular values. Something must indicate the information about a perpendicularity of the ...
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Does the angular velocity of the sun around its axis affect gravity?
Lets say I am in a circular orbit around the sun. From the suns perspective, Im 'rolling' circles in its gravitational well.
But from my perspective I'm just being stationary. Spacetime is flat for me ...
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Computing angular velocity on a different point of body
Suppose you have a rigid body and you have two local coordinate systems on the body at $P_1$ and $P_2$ and we can write a vector in the $P_2$ coordinate system using $P_1$ via the transformation $v_{...
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Astronaut with Jet Engines: Applied Forces and Angular Momentum over Time
Let's say that we have an astronaut in space of length $L$ and mass $m$:
Because of some truly irresponsible space agency, they've attached jet engines to this fellow's arms as depicted in the ...
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Cat righting reflex: Is the cat's angular speed zero or non-zero? (Or is it more complicated?)
The cat righting reflex (Wikipedia article) allows a cat to change its orientation in the absence of initial angular momentum or external forces. A theoretical model would work like this: the cat ...
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A diver makes 2.5 revs on the way from a 10-m-high platform to the water. Assuming zero init. vert. vel., find the avg ang. vel. during a dive [closed]
Free-fall kinematics gives 1.43 sec until the diver hits the water. $\omega$ is easily found from 2.5 rev/1.43 sec = 1.75 rev/s = 11 rad/sec. My question results from the following: Kinematics also ...
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Quantifying the eastwards motion of an object in free-fall on the equator
I've been reviewing the correspondence between Hooke and Newton, trying to understand how an object falls eastwards, as predicted by Galileo as well. I've read two things:
As an object falls, it ...
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Angular momentum and velocity about a point about which a rigid body is not rotating
Suppose a rigid body of mass $m$ is rotating about its centre of mass with angular velocity $ω$, and the centre of mass is translating with linear velocity v, consider two cases:
(I) we want to ...
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Resolving varying $ω$ in Kepler's Law's Proof
I'm having trouble understanding where $d^2r/dt^2$ comes from and what it stands for. What force is this? I'm not able to find any FBD's on google that mention any other force besides gravitational ...
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The form used when calculating relative angular velocity
When calculating relative angular velocity, there are two forms.
$\omega_{ab}=\omega_a - \omega_b$
Some textbooks use the relative angular velocity as shown above to guide the synodic period
$\...
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Can particles have same mass and angular velocity but different radius, while being strung together? [closed]
I'm currently trying to solve the following problem:
The following figure consist of 4 particles, each of mass $m$. All embedded in a rod of negligible mass. The distance between any pair of ...
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Pushing the bar from different points, which gives a better spin? [closed]
If we apply force for a short time, which one makes a better turn around the circle?
I know that normally pushing from a far is a better spin because of torque. But i think there may be different ...
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Verification of Accelerometer offset Formula, Offset occurring due to placement of Accelerometer away from centre of rotation in a rigid body [closed]
I have evaluated the Accelerometer offset occurring due to placement of Accelerometer away from the centre of rotation of body. In the below evaluation I am trying to calculate Accelerometer's reading ...
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What is the relation between the relative velocity of a rod on top of two rotating roller?
I'm recreating this setup: https://www.youtube.com/watch?v=q3G-qi_iWXE&t=3s&ab_channel=CanadianYoungPhysicists%E2%80%99Tournament
I found that the rod's oscillation decays under low angular ...
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Unit of $v$ in $v=rω$ [duplicate]
unit of velocity is m/sec but in $v=rω$
unit of $r$ is metre and unit of $ω$ is radian/sec so unit of $v$ should be radian*metre/sec but it is m/sec how
I know this is dimensionally correct but I dont ...
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Does applying a series of torque forces to an object result in a constant angular velocity about a particular axis?
Imagine an object floating in space with no significant gravitational forces. We poke the object a few times from various angles. It will end up spinning in a certain way.
Is it the case that this &...
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Linear velocity is cross product of angular velocity and position
Why is linear velocity is cross product of angular velocity and position?
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Vectors and One-forms in Cylindrical Coordinates and the Angular Momentum
The angular component of the velocity of a particle in cylindrical coordinates has different units if we consider the vector component $v^{\phi}$ or the one-form component $v_{\phi}$:
$$ v^{\phi} = \...
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Can the angular velocity of a prolate spheroid change over time in the absence of external forces?
Given a prolate spheroid (ie a Rugby Ball/American Football), with an initial angular velocity about an axis that coincides with one of the shape's primary axes, it seems obvious that in the absence ...
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Angular velocity of a cylinder rolling inside of another cylinder [closed]
Problem
Find the kinetic energy of a homogeneous cylinder of radius $a$ rolling inside a cylindrical surface of radius $R$.
My attempt
First, I known that the kinetic energy of the rolling cylinder &...
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Is accelerated rolling with slipping possible?
I have a conceptual question regarding the following tasks. Two cylinders with different coefficients of friction are rolling down a inclined plane, thus accelerating. According to the task, due to ...
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Calculating angular velocity with known rotation matrix and translation
I have an available rotation matrix between two points, as well as a translation but how to calculate angular velocity in the body frame?
I know how to calculate angular velocity when there is no ...
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What is the difference between Larmor frequency and cyclotron frequency?
The Larmor frequency and cyclotron frequency differs by a factor of two. The later being twice the former. So when a magnetic field is applied when we can say that electron has Larmor frequency and ...
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Proof of additivity of angular velocity
Let $E$ be the 3-dimensional space with origin $O$ (and without any preferred frame of reference) and assume that we have three orthonormal frames $F_k = \{e_1^k,e_2^k,e_3^k\}$ for $k=1,2,3$.
Suppose ...
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Can we prove that a constant central force pointed towards a point produces circular motion?
I was analysing the motion of a body when a single, radially inward force acts on a body, and I was trying to prove this is indeed circular motion, using geometry and looking at what happens at ...
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Angular velocity without a reference
Have been pondering a scenario for a while.
A disc of mass M rotating in endless vacuum space. By that, I mean that no point of external reference exists long enough for rotation to have any ...
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