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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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Understanding terms Twist and Wrench

In kinematics, physics and especially robotics, we often encounter the terms Twist and Wrench. Twist is (LinearVelocity, AngularVelocity) and Wrench is (Force, Torque). The reason I'm confused is I ...
Shital Shah's user avatar
12 votes
2 answers
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Angular Velocity expressed via Euler Angles

On the top of the fourth page from here, the author trivially derives the components of angular velocity, expressed via Euler angles of the system. I fail to understand how the components of angular ...
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Direction of angular velocity

Angular velocity is the rate of angular displacement about an axis. Its direction is determined by right hand rule. According to right hand rule, if you hold the axis with your right hand and rotate ...
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Effect of the tail of the cat in the falling cat problem

To explain why a falling cat can turn by 180 degree without external torque and without violation of the conservation of angular momentum, one usually models the cat as two cylinders as in http://en....
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Angular Velocity via Extrinsic Euler Angles

I am wondering if the angular velocity of a rotating coordinate system, if expressed through extrinsic Euler angles, is $(\dot{\alpha},\dot{\beta}, \dot{\gamma})$ since extrinsic Euler angles are ...
Eric CZH's user avatar
26 votes
7 answers
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How is it that angular velocities are vectors, while rotations aren't?

Does anyone have an intuitive explanation of why this is the case?
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Why is angular velocity of any point about any other point of a rigid body always the same?

I have the following question regarding an ideal rigid body. Firstly, is it always true without any exceptions that the angular velocity of any point about any other point on a rigid body is always ...
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Can the direction of angular momentum and angular velocity differ?

While studying rotational mechanics, I came across a section where it mentioned that angular momentum may not necessarily be parallel to angular velocity. My thoughts were as follows: Angular ...
Physicsapproval's user avatar
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Example where angular momentum and angular velocity are not parallel

I am unable to visualize any case where angular momentum and angular velocity of an object are not parallel.
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Does Earth's Rotation Affect Its Shape?

The question I am working on is, "Consider the following. (a) Find the angular speed of Earth's rotation about its axis. rad/s (b) How does this rotation affect the shape of Earth?" I am ...
Mack's user avatar
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What if the net force provided for a circular motion is larger than the required centripetal force?

Will an object be pulled towards the centre linearly if the net force provided for a circular motion is larger than the required centripetal force? And why? For example, if the object in a circular ...
Diamond Physics's user avatar
48 votes
5 answers
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Intuition as to why the orientation (of a 3D object) is not a conserved quantity?

Say you start off floating in space, in a fixed position and orientation, with zero linear and angular velocity, with no external forces. So you are a closed mechanical system. By twisting your body ...
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Why is body frame angular velocity nonzero?

This question is relevant to Euler's angles and Euler's equations for a rigid body. Why aren't $\omega_1$, $\omega_2$ and $\omega_3 = 0$ in the body frame? How can we measure $\vec\omega$?
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Changing Rotation Direction in Mid Air

Not sure whether this is an appropriate question for this site, but could anyone explain the physics behind how this skier is able to change his direction of rotation mid-air? https://www.youtube.com/...
Trent's user avatar
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Physical meaning of the moment of inertia about an axis

In the context of rigid bodies, the inertia tensor is defined as the linear map that takes angular velocity to angular momentum, that is, the linear map $I : \mathbb{R}^3\to \mathbb{R}^3$ such that $$...
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Is direction of angular velocity just a definition or has a physical significance?

I am a high schooler so I don't know a lot of fancy maths but I do know some of calculus and multiplication of vectors as dot or cross product. I am learning about Angular velocity. And I am confused ...
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What actually is the vector of angular momentum?

If an object spins around a central point, it gets angular momentum which is a vector with an orientation dependent on whether its clockwise rotation or anticlockwise, i get that. But what the vector ...
Daniel .S's user avatar
1 vote
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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
1 vote
3 answers
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Rotation of rigid body with two different angular velocities

Consider a cylinder that rotates about a vertical fixed axis with angular velocity $\vec{\Omega}$ while rotating about a vertical axis passing through its center of mass with angular velocity $\vec{\...
Sørën's user avatar
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4 answers
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Proof of centripetal acceleration formula ($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 ...
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Why is angular velocity the same for all points on a spinning disk, even though they are at different radii from the center?

Why is angular velocity the same for all points on a spinning disk, even though they are at different radii from the center?
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Is there a formula for the rotation vector in terms of the angular velocity vector?

Euler's theorem of rotations states that for any rigid body motion with one point fixed is equivalent to a rotation about some axis passing through that fixed point. So let's consider a rigid body ...
Keshav Srinivasan's user avatar
6 votes
1 answer
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How much effort would be required to fix the Earth's rotation?

Given that the earth's rotation has been slowing down by very slight amounts over time, forcing us to introduce leap seconds and so forth into our clocks and calendars, I would like to ask if this ...
user2813274's user avatar
5 votes
3 answers
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How can I relate linear and angular motion using a single formula? [closed]

I want to relate linear and angular motion using a single formula. Assume I have a 10m rod, and I apply a force of 5N on it, 2.5m away from the axis of rotation for 1s. How can I determine the ...
Vatsal Manot's user avatar
4 votes
1 answer
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Cases in which angular velocity and angular momentum point into same direction

I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, $\vec{L}...
martin's user avatar
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Bead threaded on a smooth rod - why does spinning it at constant $\omega$ cause the bead to slide radially outward?

We over a thought experiment of sorts in class today, and I'm trying to look for some help to better wrap my head around it. For this experiment, I ask you to image a frictionless rod rotating ...
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Is angular frequency the same as angular velocity or are they different?

I know there are duplicates. But the answers seem to disagree and also I have more specific questions related to this title. First of all, most questions on this site which ask this question have ...
bilanush's user avatar
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3 answers
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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 ...
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2 answers
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Rotational physics of a playing card

A playing card leaves a dealers hand with some angular velocity. As the card slides across a table the friction of the table causes the rotation to slow. How is the friction coefficient between the ...
Vindictive's user avatar
0 votes
1 answer
1k views

Proving that the angular velocity of a rigid body is the same about any point

Please consider the below image which is from Rana and Joag, Classical Mechanics. They build on a proof, which I reiterate below and through it they show that angular velocity of any point B in the ...
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Why is the velocity different for different points on a rolling wheel?

Lets take the following example According to above examples it means that velocity at the above portion is max while the velocity at lower portion is min. But I think it should be the same at both ...
Junaid S.'s user avatar
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14 votes
2 answers
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Dynamics of counter-rotating flywheels

I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ...
user1055643's user avatar
11 votes
7 answers
3k views

Does cutting of trees affect spin angular momentum of earth?

Cutting trees reduces earth's moment of inertia. So the spinning velocity of earth should be reduced day by day. Does it really happen?
rock's user avatar
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2 answers
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Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
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10 votes
8 answers
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Proving that the angular velocity vector is equal to a limit involving the rotation vector

The angular velocity vector of a rigid body is defined as $\vec{\omega}=\frac{\vec{r}\times\vec{v}}{|\vec{r}|^2}$. But I'd like to show that that's equivalent to how most people intuitively think of ...
Keshav Srinivasan's user avatar
10 votes
1 answer
3k views

How different can the directions of angular momentum and angular velocity be?

A recent question uncovered a fact that can be very surprising to those not previously aware of it: the angular velocity $\vec\omega$ and the angular momentum $\vec L$ of a rotating body are vectors ...
Emilio Pisanty's user avatar
9 votes
3 answers
1k views

How do we formally define the "angular velocity vector" of a point about an axis?

Context: For instance, the quantity Torque, $\vec{\tau}$ is defined about a point: by the formula $$\vec{\tau}=\vec{r}\times\vec{F}$$ We can use this defintion to define torque about an axis. Let the ...
satan 29's user avatar
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8 votes
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How long was a day at the creation of Earth?

Since the earth is slowing its rotation, and as far as I know, each day is 1 second longer every about 1.5 years, how long was an earth day near the formation of earth (4.5 billion years ago)? I ...
Cameron Aziz's user avatar
8 votes
2 answers
4k views

Intuitive explanation for why centripetal acceleration is $\frac{v^2}{r}$ [duplicate]

There are several ways to write centripetal acceleration $$\frac{v^2}{r} = \omega^2 r = v \omega$$ Are there intuitive explanations for any of these three forms? For instance, I can sort of explain ...
1110101001's user avatar
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7 votes
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Representation Of Linear Velocity as Cross Product

Why is linear velocity represented as cross product of angular velocity of the particle and its position vector? Why not vice versa? (Consider rigid body rotation)
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7 votes
2 answers
2k views

The angular velocity

Is the angular velocity of a rigid body about any point the same as that about the axis of rotation. Also, can we even define angular terms (Angular Velocity, Angular Acceleration, etc) about any axis,...
Kruthik's user avatar
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7 votes
3 answers
1k views

Higher dimensional relation between angular momentum, moment of intertia and angular velocity

In 3 dimensions we have the well known relation (summation convention is being used) $$ L_i = I_{ij} \omega_j $$ However, as is well known the angular momentum and angular velocity are not vectors ...
Borun Chowdhury's user avatar
7 votes
1 answer
1k views

How do we prove the existence of the instantaneous axis of rotation?

Euler's theorem of rotation states that any rigid body motion with one point fixed is equivalent to a rotation about some axis passing through that fixed point. Now it is often said that Euler's ...
Keshav Srinivasan's user avatar
6 votes
3 answers
5k views

Is angular velocity parallel to axis of rotation?

I'm reading the Wikipedia page on angular velocity. It says here of the angular velocity vector in three dimensions that “[t]he magnitude is the angular speed, and the direction describes the axis of ...
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6 votes
2 answers
19k views

Relative angular velocity and acceleration

Background: (Irodov 1.55) Two bodies rotate around intersecting perpendicular axes with angular velocities $\hat\omega_1,\hat\omega_2$. Relative to one body, what is the angular-velocity and -...
Meow's user avatar
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5 votes
3 answers
959 views

Ratio of masses of double star problem

I am currently studying Classical Mechanics, fifth edition, by Kibble and Berkshire. Problem 2 of chapter 1 is as follows: The two components of a double star are observed to move in circles of radii ...
The Pointer's user avatar
3 votes
2 answers
2k views

How rotating body have same angular velocity and acceleration

Does a body rotating about a fixed axis have to be perfectly rigid for all points on the body to have the same angular velocity and the same angular acceleration
Mint Fany's user avatar
3 votes
1 answer
610 views

Doubt regarding calculation of angular velocity

The doubt arose because of this question- Two thin circular discs of mass $m$ and $4 m$, having radii of $a$ and $2 a$, respectively, are rigidly fixed by a massless, rigid rod of length $l=\sqrt{24} ...
Aspirant's user avatar
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3 votes
1 answer
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Tennis serving machine--- How does a spinning ball bounce?

I have an idea of making a tennis serving machine. I will briefly describe what it is: The machine is configured to serve the ball at a fixed speed to the center of the left (or right) service court ...
fx01's user avatar
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3 votes
2 answers
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Angular velocity vector from linear velocity vector

Linear velocity vector is $\vec{v}$ and the distance vector is $\vec{r} $. How is it that angular velocity vector is $\vec{ω}$ = $\frac {\vec{r} × \vec{v}}{|\vec{r}|^2}$ The equation I am aware of is ...
Shaurya Goyal's user avatar