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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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Integration of Euler rate of change

I am working on a project for designing an autonomous boat and for my kinematic model, I would like to use the body-fixed angular velocity to mathematically estimate the orientation of the boat in ...
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1answer
40 views

Calculate Linear Velocity and Angular Velocity After Collision, in SceneKit

Here is an attached scheme which i want to write my own custom wall reflection method to simulate the ball collision having right (or left, or top/back) spin. As an example, i have created wall node ...
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1answer
49 views

Rotational Kinematics and Angular Velocity Vector Transformation

Say we have a rigid body with a body-fixed coordinate system XYZ and an inertial coordinate system (North - East - Down) XoYoZo. If we use the x-y-z convention and rotate the body fixed frame first ...
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Rotating particle about the cylinder [closed]

There is fixed vertical cylinder of radius 8cm.One end of thread of length of 1.2m is attached to cylinder and other to a particle which starts moving with constant velocity 6m/s perpendicular to ...
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2answers
116 views

Speed of the rotating block [duplicate]

Problem: A block tied to a string is rotating with an angular velocity $\omega$ on a frictionless table. The string passes through a hole in the center of the table. If the string is pulled and the ...
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2answers
2k views

Is the right hand rule a trick to avoid tensors?

I have read in this answer that "to represent angular momentum as a vector you need to use a right hand rule. This is annoying, because physics at ordinary scales is reflection invariant but ...
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1answer
48 views

Proof regarding curl of a vector [closed]

I'm stuck in this problem where we need to prove that the curl of the velocity vector is twice the angular velocity of a rigid body in circular motion. How do I prove it? I am very new to the concepts ...
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1answer
60 views

An interesting problem from circular motion [closed]

Consider this situation: Two individuals are seating side by side on a Merry-go-Round moving with angular velocity $\omega$) seats they are just seating next to one another. Now the person A is ...
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1answer
23 views

calculate the time elapsed for a robot to pass certain distance with a load [closed]

For a robotics project I wanted to find the optimal gear ratio for my robot to travel 10 meters. Unfortunately. the acceleration is nonconstant, and that proved to make my life much harder. I think I ...
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1answer
35 views

Calculating angular velocity of rolling object with just gravity?

From what I have learned, you can calculate what the angular velocity of an object will be based on its potential energy. Say there is a situation where: acceleration due to gravity = 10 m/s² ...
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0answers
18 views

forward and angular velocity addition

I share some data here which is related to my question. ...
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1answer
54 views

How to calculate the radius of a curve based on vehicle wheel speeds of a car

I have data of the 4 differen wheelspeeds of a vehicle during driving time. Based on that I want to calculate the radius of a curve it is taking. The following are my current thoughts that seem to be ...
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2answers
39 views

Speed of two objects orbiting around a central axis

This question has been bugging me for quite some time and i'm not too sure if i'm missing out some important factor in the understanding of this scenario: Given two objects of equal mass and size ...
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3answers
78 views

rotation matrix in quaternion representation

is the the rotation matrix corresponding to the quaternion different from the rotation matrix corresponding to the quaternion error (between desired and actual value) ? Let $\mathrm{Q}$ be the ...
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0answers
31 views

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 ...
1
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1answer
44 views

Time derivative of vector in rotating frame with angular velocity about a rotating axis

In general, I know that if you have a vector $\vec{F}$ in a rotating frame, and the frame has an angular velocity $\vec{\Omega}$ that the time derivative of $\vec{F}$ in a fixed frame would be $$\frac{...
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1answer
53 views

Why is the derivative of the quaternion equal to the Kronecker product of the quaternion itself and the angular velocity?

the dimension of $ \dot{\mathrm{Q}}(t)$ is 4x1 but the following product is 4x4 $$ \dot{\mathrm{Q}}(t)=\frac{1}{2}\mathrm{Q}(t)\otimes\overline{\Omega}(t)\ , (1) $$ equation (1) is part of the ...
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1answer
28 views

Question about angular speed

Lets assume that the motions of the Moon around the Earth and of the Earth around the Sun are uniform circular. If $\omega_L, \omega_T$ are the respective angular speeds find $\omega_L/\omega_t$. ...
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2answers
155 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,...
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1answer
33 views

Why angular velocity is increasing by time and not decreasing due to friction/conservation of energy law? [closed]

This first picture has the question A ring of mass $M_1$, radius $R_1$, and rotational inertia $MR^2$ is initially sliding on a frictionless surface at a constant velocity $v_0$ to the right, as ...
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3answers
447 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
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2answers
49 views

How to nullify effect of Centrifugal force/centripetal force

I have a track over which a rectangular object moves. The object holds sensitive material which should not move too much. Then there is a 90 degree turn of the track with some radius of curvature. ...
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3answers
60 views

Is Moment of Inertia, always, independent of angular velocity? [closed]

I once heard in a ted talk that the elementary particles like electron and proton can exist in two different positions at the same time. Now,I'm trying to understand a rotating rod from this ...
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1answer
99 views

Why angular velocity is a vector quantity? [duplicate]

Angular displacement isn't a vector quantity (according to some websites) then how angular velocity can be a vector? shouldn't it be a scalar?
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1answer
38 views

Calculation of polar velocity components given cartesian counterparts

I would like to calculate the polar velocity components given the position $(x,y)$ and velocity $(u_x,u_y)$ in Cartesian coordinates. First of all, $$ r=\sqrt{x^2+y^2}\text{ and }\theta=\tan^{-1}\left(...
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2answers
95 views

Why does Wikipedia state that angular velocity is equal to angular frequency? [duplicate]

Isn't Wikipedia wrong? At the Wikipedia article Angular frequency it says that angular frequency and angular velocity are equal. But how on earth are they equal? Angular velocity is changing all ...
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3answers
70 views

When the oscillator is a system with an angle can we define the angular frequency to be the radians per unit time covered by the system itself?

I read on stackechange that in springs or any one dimensional oscillator the angular frequency is just describing a rate of angle change in the associated circle on which it's projected. Something ...
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2answers
210 views

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 ...
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0answers
31 views

Plane rotation of a bar in a viscous fluid, computation of the torque

Assume a rigid, cylindrical bar which rotates around $\Omega$ (axis of a engine). The bar is immersed in a fluid of kinematic viscosity $\nu$ and has a plane motion. What is the torque applied to ...
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1answer
53 views

What is the relationship between radius and tangential velocity?

So imagine you had a tennis racket. Let's say it is 27 inches. The swinger will swing the racket and at the tip of the racket it's going a certain speed. If we increased the length of the racket to ...
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1answer
23 views

Lunar angular frequency

I have this question from my teacher which quite confuses me. It asks to calculate lunar angular speed, when we know that the Moon circles Earth in 27.3 day. Why is number (27.3) significant here? ...
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0answers
31 views

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 ...
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0answers
23 views

Exit velocity of ball from spinning wheels launcher

I'm having some difficulty figuring this out. I'm trying to figure out the exit velocity of a ball after being squeezed through two spinning wheels. I have wheel weight, radius, angular velocity, ...
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1answer
51 views

Do whirlpools in water have the same rotation speed regardless of size?

I recently read that all flat disk galaxies have the same rotation speed regardless of mass and size, so I was wondering if this same feature was visible in any other similar rotation such as a ...
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1answer
28 views

Angular Kinematics and conservation of Energy: A uniform, thin rod of length L and mass M pivots vertically

In the above image a rod is released at Point A and travels to point B. The question in this case is to find an expression for the velocity at point B. I attempted this in two ways, conservation of ...
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0answers
29 views

How do I find out the net thrust produced by a propeller?

I am trying to find out the thrust that a propeller produces. Since a propeller can have various different types of inclination for it's blades as well as several parameters such as number of blades, ...
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3answers
51 views

How do you calculate the distance from center for centripetal force equation for long objects such as board or a hammer?

I am trying to calculate the centripetal force for an enlongated object like a fan blade. Where do I measure to to get the distance from center. Would I measure from the center to the end of the ...
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2answers
472 views

Non-constant angular velocity in orbit

Consider a pair of objects in elliptical orbits around a common center of mass. For all considerations of angular motion and torque, the pivot point of interest is the center of mass in this ...
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2answers
62 views

Angular acceleration and angular velocity relationship

It is given that angular velocity is the rate of change in the angular position of a body while the angular acceleration is the rate of change in angular velocity. Other relationships include that ...
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2answers
46 views

Do wheels travel slower when rolling compared to sliding?

If we have a wheel rolling down a hill with some amount of friction that causes angular motion and an ice cube that slides down the hill with no friction with the surface, which one accelerates/...
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1answer
69 views

How do you calculate the moment of inertia given the mass and final velocity of a hollow sphere?

The equation for the moment of inertia of a hollow sphere is I = 2/3mr^2. However, the radius is unknown and I am only given the mass and final velocity of a hollow sphere rolling down a ramp. How ...
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1answer
100 views

Euler's equation for a rotating frame when the inertia tensor is non-diagonal

Wikipedia's entry for Euler's equation states: In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a ...
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2answers
185 views

Relative Angular Velocity

Two particles describe the same circle of radius 'a' in the same direction with same speed 'v'. What is their relative angular velocity? Angular velocity of both the particles is v/a. It's direction ...
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1answer
61 views

Nearly circular orbits (and their angular frequency)

In 'nearly' circular motion, the radius is not constant. If the force is central the and the angular momentum is still conserved, we have a central force: where $r_0$ is equilibrium position. For ...
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1answer
113 views

Rotating Cone - Finding Energy and Momentum

I think I've a conceptual lacuna that needs to be filled, when it comes to a rigid body possessing angular velocities along more than one axes. Here's my doubt - Consider the following solid cone (...
2
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1answer
89 views

Angular acceleration in rigid bodies

This is a concept which is bothering me a lot. I'm sure there are other duplicates to this question but on seeing a few such duplicates, I haven't yet obtained an answer. My question is, for a rigid ...
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0answers
24 views

in 2D, does it make sense to decompose the velocity of a robot into its linear and angular parts?

I am reading a document that describes some variables regarding a robot's movement. According to the document, you can decompose the velocity into its linear and angular parts. However, the ...
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3answers
221 views

Why is angular velocity a vector quantity? [duplicate]

Angular velocity is $$\omega= \frac{dƟ}{dt},$$ here $\theta$ and $t$ are scalar quantities. But $\omega$ is a vector quantity. Why is it such? So far I know the direction of $\omega$ is along the ...
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3answers
275 views

What is the physical meaning of the principal axes of inertia?

What is the physical meaning of the principal axes of inertia? I used to think that the axes of inertia are, in some sense, the only axes about which the body can rotate without the angular momentum "...
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0answers
24 views

How to increase power in a geared system using P = (omega)(torque)

Could someone give me a basic, intuitive explanation on how to increase power in a geared system using the P = omega*torque formula? By geared system I mean two connected gears, where the first one ...