Questions tagged [angular-velocity]

The time derivative of angular position used when studying rotating objects or systems.

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Angular and linear velocity of a circle

Let's assume I have a circle of radius $r$ and I apply a constant force at a point on the circumference of the circle that is perpendicular to the distance vector which goes from the centre of the ...
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Strapdown gyroscopes and body frame angular velocities

I am trying to make some sense on strapdown interial navigation systems, which i thought i understood... I thought that a strapdown intertial navigation system produced body frame expressed angular ...
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Conceptual confusion about the relative angular velocity of particles in a rigid body

Let me explain my doubt with help of an example consider a disc of radius $2R$ rotating with contant angular velocity $\omega$ locate two particles $A$ at a distance $R$ from centre and $B$ at a ...
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Is Earth’s rotation slowing down or speeding up?

Section ‘Slowing down of the Earth’ of the Wikipedia article Leap second has the following paragraphs: A mathematical model of the variations in the length of the solar day was developed by F. R. ...
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Total Angular Momentum in an orbit

I have just learned that the total angular momentum of a system is measured by adding the angular momentum of the Center of Mass and also the angular momentum of matter rotating around the Center of ...
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The movement of a bowling ball while throwing it

When a bowler pushes a bowling ball into the lane he rotate his wrist so he apply a force to rotate the ball if I only Know the angle of rotation and the value of the force how can I find the angular ...
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How can I prove the existence of rest points in rigid motion with all speeds orthogonal to $\vec{\omega}$?

If in a rigid motion there is a point at rest, then all speeds are normal to $\vec{\omega}$ (assumed $ \neq \vec{0}$), to prove choose the rest point as origin and explot fundamental equation of rigid ...
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How Can I Understand The Resulting Movement of this Situation Using Cross Product Based on Geometry?

I am at the moment writing a script for a video talking about angular vectors and how to find them in discussion about how a top stays upright. Currently, I am relating equations like $\vec v = \vec \...
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Doubt regarding calculation of angular velocity

The doubt arose because of this question- It is a popular question from JEE $2016$, an exam annually held for engineering aspirants in India. My confusion is regarding point (D), one of the correct ...
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Derivative of Euler angles in terms of angular velocity

What is the relationship between the derivative of an euler angle and the angular velocity vector? Can the euler angle derivatives be represented in terms of angular velocity.
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Derivative of rotation matrix produces angular velocity vector

I am trying to understand how and why the angular velocity vector is related to the derivative of a rotation matrix. I understand that for a rotation matrix $R(t)$ one has $R(t)R(t)^T = I $, so $\dot{...
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Confusion regarding the answer to a question about $(v_T)^2/r$

In this answer to the question "Intuitive explanation for why centripetal acceleration is $\frac{v^2}{r}$": https://physics.stackexchange.com/a/190532/262601 (excerpt from the answer is ...
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Why doesn't $v_T = \omega r$ involve the direction of its variables?

We derived $v_T = \omega r$ by the following procedure, and it's said that $v_T = \omega r$ "is a relation between the magnitudes of the tangential linear velocity and the angular velocity". ...
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Angular and Linear Velocity question on Wiki definitions

I have a question regarding the following forms in the case that both angular velocity and radius change in a time quantum. Wiki defines angular velocity in two dimensions as: $$ \omega = \frac {d \...
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What is the reason for so many of uniform circular motions even after so many irregularities in phenomena like motion of planets?

A body remains in uniform circular motion around another body due to the centripetal force between them, when the first body keeps moving with a specific velocity. This is more possible in an isolated ...
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Analysis of motion of a body following an elliptical trajectory

We are all familiar with a body traversing uniformly ( or non uniformly ) along the circumference of a circle. We get nice relations because of the symmetry of the figure and the distance between ...
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How to relate these two formulas of angular velocity?

Consider the following picture: with $\vec{v}(t)$ the velocity of a particle at time t, $\vec{a}(t)$ its acceleration at time t and $\vec{a_n}(t)$ its normal acceleration at time t. I want to ...
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Do Angular velocity represents the Area of Circular Segment?

Since, $L=mvr \qquad$ [considering magnitude only. So, I am ignoring the vector sign for now] where $L=$ Angular Momentum $v=$ linear velocity $r=$ radius of the circular path $vr=$ Angular ...
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How can astronauts rotate their body in empty space ? How do they undergo “angular displacement” without any external torque? [duplicate]

How does the astronaut in the following video do what he is doing ? https://youtu.be/7ZPVg3qD07g?t=145 This question is kind of a follow up to Why don't we ever see astronauts on space walks ...
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How to calculate the tangential velocity?

I am trying to measure the tangential velocity from an Inertial Measurement Unit (IMU) sensor. I read from an article that they calculate the tangential velocity according to the explanation below: $v ...
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1answer
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Proper fully defined notation for angular velocity

Yeah, so, I know that objects rotate, about a point, in a chosen frame of reference. I was wondering if there is a mathematical notation that tells you the following : Point of rotation of a body ...
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Does centripetal force remain the same if the radius increased and the mass decreased in that way the number of rotation remain as previous?

I copied this question from my textbook. An object is being rotated in the vertical plane with a rope of length 90cm by a circus man. And the object rotates 100 times per minute. Suddenly the object's ...
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A question about angular momentum and angular velocity of a symmetrical body

I know that a symmetrical body rotating round a fixed axis, at a constant angular velocity, has the vector angular momentum and the vector angular velocity parallel, but if the angular velocity isn't ...
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Why is angular momentum $mvr$ and not $mvr^2$ or $mvr^3$?

We know angular momentum $L = mvr$, where $v$ is the velocity in the direction perpendicular to the distance from the source to the object whose $L$ we are trying to measure. My question is why $L$ ...
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Angular speed of a line segment [closed]

The length of line segment joining P and Q is constant and equal to 10m. The velocities of P and Q are in directions inclined at angles 30 and 60 respectively with PQ . If the speed of P is 90m/s , ...
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Relative angular velocity of rigid bodies [closed]

If all the points in a rigid body have same angular velocity (say, $\vec{\omega}$), then why is angular velocity of point $A$ in the body w.r.t. point $B$ in the body is still $\vec{\omega}$ and not $\...
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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 ...
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1answer
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How to Calculate Linear and Rotational Velocity from Multiple Thrusters in Space

I'm trying to simulate space thrusters in Unity. If I have a spherical ship in space (assume no drag/gravity around) with two thrusters at positions p1 and p2 in relation to the ships center of mass ...
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What is the orbital angular velocity of a satellite?

Angular velocity ω is by definition the runned angle $dθ$ per time $dt$ elapsed: $ω=dθ/dt$. If the time elapsed in a specific point on the earth's surface is $dt$, the dilated time elapsed on ...
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How do we implement the speed differential for the Ackermann steering?

I'm working on a vehicle that uses four independent motors to control both the steering and speed for each wheel. I'm using Ackermann steering, and I've already got the steering angles down for the ...
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1answer
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Difference between pulling from center of mass, and from the top of a wheel

A homogeneous cylinder with radius $R$ and mass $M$ is pulled with constant horizontal force $F$ across a table. There are two cases, one where the cylinder is pulled from its center of mass and one ...
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Confused about linear displacement in circular motion

We know that velocity is the derivative of displacement w.r.t. time. Keeping this mind, suppose that we are traveling across a circle where we go from point A to point B. In textbooks, it is said that ...
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Will the angular momentum change when we put together an object with 0 angular momentum and an object with actual angular momentum?

Consider this problem: A simple coupling for connecting two axes in a motor consists of two cylindrical plates (r = 0.6 m) that can be pressed together if necessary. Plate A with mass mA = 6 kg is ...
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How does a proper motion displacement of $x$ arcseconds/year mean a star is moving at $x$ AU/year?

I trying to understand the author's answer to this question: I don't understand the part underlined red. How does 3.6pc mean 3.6AU? It says a "distance of 3.6AU", but doesn't say what is ...
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Where is the angular velocity when linear velocity takes place and vice versa?

We can see the body is moving in a straight line with a linear velocity 10 m/s. After 4 second it is 50 m away from the observer. And assume it to continue to move straight. Also by the relation v=rω ...
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How to calculate the change in angle due to the righting moment of a ship?

I trying to calculate how the forces on a boat (initially out of equilibrium) work to right it. The cross section of the boat is a convex polygon and constant throughout its length. I can find the ...
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1answer
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Angular momentum about centre of mass is not always equal to $I_\text{com}\omega$, Right?

Angular momentum about a point on the rotational axis is equal to sum of angular momentum perpendicular to rotational axis and angular momentum parallel to rotational axis. The perpendicular component ...
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Angular velocity of Pendulum

I am a high school student and investigating about Wilberforce Pendulum. I do not understand the mathematical theory of Wilberforce Pendulum. I want to know how angular-velocity changes when the ...
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1answer
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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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Precession - why decompose to angular momentum component?

I always see it is conventional (in Landau-Lifshitz for example) to decompose the angular velocity vector to 2 components: axis of symmetry and angular momentum vector, and then define the angular ...
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Time Dependent Spiral motion

I am trying to model a particle traveling through a high efficiency dynamic separator (which allows me to separate solid particles by their size) The problem boils down to spiral motion, in the radial ...
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1answer
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A 1 meter radius ring spins around its axis at 10 revolutions per second. It is now dropped to the ground [closed]

A 1-meter radius ring spins around its axis at 10 revolutions per second. It is now dropped to the ground, where it rolls steadily in a straight line. Assuming it does not lose any energy to friction, ...
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505 views

How to find the max angle the pendulum reaches during oscillation?

I have a pendulum that is swinging with no loss of total energy. Is it possible to find out the maximum angle, $\:\theta_{o}$ to which the pendulum reaches, based on only the following information? ...
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571 views

What is wrong with this reasoning about angular velocity $\omega$?

Satellite $X$ orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass. What is $\frac{\text{centripetal acceleration of ...
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Axial/pseudovectors in three dimension

I have often read about the fact that angular momentum vector is a pseudo vector, that is, an axial vector. According to what I remember pseudo vectors are those vectors that do not change their sign ...
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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 ...
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1answer
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Movement of marbles on a turntable with no friction

Question is as the title: A stable turntable with no friction with marbles on it is made to spin by a torque. How is the movement of the marbles; does it fly off the turntable? I thought that since ...
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69 views

Time derivative of $\rm{atan2}$ when $x=0$

I want to take the time derivative of the $\rm{atan2}$ function to calculate an azimuth rate in spherical coordinates, given position and velocity in Cartesian $xyz$ coordinates. $$\rm{atan2}(y, x) = \...
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Determination of the speed and angular velocity of 4 rolling cylinders between planks

According to the picture, there are four identical cylinders, with radius R, that are rolling without slipping at every contact point. The upper plank is moving with speed 2v (m/s) towards the right, ...
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2answers
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Uniform / rigid rotation in fluids, velocity gradients and resulting friction

In the derivation of the Navier-Stokes equation e.g. in Landau & Lifshtiz Volume 6 on fluid mechanics it is stated that the viscous stress tensor $\sigma_{ij}^{\prime}$ must also vanish when the ...

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