All Questions
Tagged with kinematics rotational-kinematics
210 questions
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How to calculate the velocity of a point on a rigid body that is both translating and rotating?
I'm trying to figure out a problem involving the motion of a rigid body in 2D. The body has:
A translational velocity $\mathbf{v} = (v_x, v_y) $ at its center.
An angular velocity $\omega$ around its ...
2
votes
3
answers
126
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Angular velocity basics
Is angular velocity only defined for circular motion or can it be described for lets say projectile motion as well?
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1
answer
53
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How to calculate angular and linear components of a force acting upon a 3d object?
apologies if this isn't worded great: I don't know all the technical terms for what I'm describing.
Given a 3D object in space (no gravity or air resistance or anything), let's say its center of mass ...
2
votes
2
answers
74
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Does angular absement exist?
Probably a dumb question. I'm a highschool student, and I don't even know if it is even possible to integrate an angle (for reference, I haven't even learnt integration yet at school, my calculus ...
- 31
2
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2
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131
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How does a sphere roll on ground, no really?
Everyone knows this right!
Consider the ground to be the $xy$ plane and consider gravity to be acting along the $-z$ direction. If a sphere (mass $M$, radius $R$) is placed on the ground and given ...
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1
answer
75
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Does spinning the umbrella slow down the fall more?
Ignoring its structural weakness, if you jump from some height and use an umbrella to slow down the fall, would making it spin while you're falling affect the speed in any way?
- 379
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0
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47
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The stupidest question ever on relative kinematics and angular velocity [duplicate]
I am scratching my head on a very basic formula whose meaning escapes my intuition.
On basically all texts of mechanics the following result is derived:
Suppose that a rigid body is moving with ...
- 114
1
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3
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58
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How is momentum conserved in this collision with loosely-connected spheres?
There are three identical spheres. B and C are loosely connected with a light inextensible string, and A approaches B directly at some initial velocity $v$. There is no angular momentum.
A and B have ...
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306
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Circular motion at relativistic speed
I am working on a personal hard science-fiction project but when I analysed the following situation, in the context of special relativity my conclusion seems counter intuitive and perhaps I am ...
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1
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1
answer
80
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How does relative motion work for an extended object?
I have this conceptual doubt which might be flawed very badly but I don't understand this particular thing. For example, if one end of a stick is moving with velocity $v_1$ and the other with $v_2$, ...
- 123
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22
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Closed form solution for the linear acceleration of a particle on 3D rotating object given momentum and MoI?
Is there a closed-form solution for the linear acceleration of a particle on a rigid body undergoing some arbitrary rotation in 3D with no external forces, given its angular momentum vector and its ...
- 357
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1
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129
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Absolute Angular Velocity - How to use?
From my dynamics course, we were introduced to the so-called absolute angular velocity of a rigid body. Below is a short diagram:
The following equation for the velocity of point P on a rigid body is ...
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4
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1
answer
144
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Determining a direction/projection/heading for an object in 3D space after it has been rotated
I hope this is a good place to find an answer. Regardless, Worldbuilding looks like a great forum to follow.
I'm not a math wiz and I've tried to tackle this problem many times over the past decade or ...
- 51
0
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0
answers
41
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How to measure Angular Velocity observed from A non-stationary frame?
A stationary observer observes a rotating disc with radius 1 at angular velocy w. Let's say this disc is centered at origin in xy plane (all angular Velocity mentioned in this question is around the ...
- 131
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1
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34
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How to compute the force on a mass traveling along a parametric curve? [duplicate]
Suppose a mass (m) is traveling along a parametric curve {x(t), y(t)} where x(t), y(t) are twice differentiable. What is the centrifugal fore on the mass as a function of time?
I am an engineer, and I ...
- 103
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1
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193
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Zero acceleration in circular motion while the body is accelerating
I was going through László Holics book (300 Creative Problems in Physics) and came across this question:
The radius of the tire of a car is $R$. The valve cap is at a distance $r$ from the axis of ...
0
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1
answer
77
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To find the displacement of a rolling body
When calculating the displacement of a rolling body do we just calculate the displacement due to Vcom in a particular time t or additionally need to consider also the displacement that may be produced ...
0
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1
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93
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Is this motion rotation or curvelinear translation?
Arrow orbit around point C like graph show.
Is motion of arrow, rotation or curvelinear translation according to physics definition?
What is definition and types of translation and rotation?
I find ...
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2
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122
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Why does $\vec{a}=\vec{\omega}\times \vec{r}$ as well as the velocity does?
Today I came in class and in one of the problems the teacher used $\vec{a}=\vec{\omega}\times \vec{r}$ which made me very confused because I don't know where it comes from, it seems pulled out of thin ...
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2
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501
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Why do I get $\alpha = \omega ^2$ in angular acceleration?
In a 2D plane, the tangential acceleration of an object moving in uniform circular motion is, using the fact that $ v = \omega r$ :
$$a_t = \frac{v^2}{r} = \omega^2 r$$
and we know the relationship ...
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2
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253
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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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4
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2
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943
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Mass travelling with constant speed in a circle
Imagine a 2D circle has a point mass traveling along its circumference with constant speed. The only force experienced is centripetal. However, if we take the 2D plane the circle sits on and rotate it ...
3
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1
answer
302
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Relation between "method of moving frames", spin connection, Cartan forms, and classic rotational kinematics in $\mathbb{E}^n$
I want to know how the "method of moving frames" involving things like connection 1-forms, torsion 2-forms, spin connections, etc. are applied to basic rotational kinematics in flat 3-space (...
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2
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1
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72
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(Circular motion) Acceleration is given, so why asked for more? [closed]
The full question is below.
A car starts from rest and moves around a circular track of radius $32.0\,\text m$. Its speed increases at the constant rate of $0.500\,\text{m/s}^2$.
(a) What is the ...
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1
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1
answer
58
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Estimating angular velocity of rigid body via position
Suppose you have current state of a rigid body is $S_t = [\theta_t, \phi_t, \psi_t]$ and your past state is $S_{t-1} = [\theta_{t-1}, \phi_{t-1}, \psi_{t-1}]$
How would you estimate angular velocity ...
- 982
1
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1
answer
60
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Conceptual difficulty with with component accelerations in polar coordinates
In kinematics why is the acceleration along the radius not the time derivative of the velocity along that radius?
0
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1
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145
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Linear and angular velocity of a falling rod in the corner of a room [closed]
A uniform rod of length l and mass m is sitting vertically in a frictionless environment in the corner of a room, having a floor beneath it, and a wall to its left. It gets slightly off balance and so ...
- 357
1
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1
answer
36
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Kinematics: Minimum length of horizontal path to fall back onto initial position after traversing half circle [closed]
Our professor asked us today what the minimum length of a horizontal line would have to be such that if an object moved on it with a constant initial velocity, went into a half-circle loop and fell at ...
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0
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1
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110
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Trajectory of particle thrown from the center of rotating frame of reference
So we have a rotating platform with two frames o reference: the one which is static, $O:\{x,y,z\}$, and the one wich is rotating along the platform, $O':\{x',y',z'\}\ (z\equiv z')$. The platform is ...
- 420
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1
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54
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Coordinates-free, geometry-free, algebraic way to derive facts about circular motions
I would like to derive the following facts about non-uniform smooth circular motion in three dimensions.
The sole boundary conditions given are:
Three dimensions of Euclidean space, one dimension of ...
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2
answers
61
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What would be the unit of the vectors spanning the Jacobian matrix?
Let the general forward rate kinematics equation be given as follows:
$$ \begin{bmatrix} \boldsymbol{\omega} \\ \boldsymbol{v} \end{bmatrix} = \begin{bmatrix} \boldsymbol{J}_1 & \boldsymbol{J}...
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1
answer
757
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I am very confused about net acceleration and angular acceleration in circular motion [closed]
I have seen in many places that angular acceleration can be zero but net acceleration can't be zero in circular motion. I want to know whose components are tangential and radial acceleration (net or ...
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5
answers
1k
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Why can I use kinematic equations for circular motion
I am trying to understand why I can use the kinematic equations with circular motion. From my understanding I can only use the kinematic equations if the acceleration is constant but in circular ...
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0
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37
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How to calculate total sum of orientation changes in 6 DOF data from a Motion tracker?
I'm using data from a motion tracker that give provides 6 coordinates for every frame ( with frame rate of 240Hz)
Position: x, y, z
Orientation: azimuth(yaw), elevation(pitch), roll
I can calculate ...
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0
votes
1
answer
359
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Is friction equal to gravitational force during rolling down a ramp?
I'm studying the motion and forces involved in a ball (bidimensional) rolling down a ramp inclined by an angle $\theta$ from the x-axis.
This is the body diagram (I didn't draw forces but there is ...
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0
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2
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115
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What radius should you take while converting rpm to m/s? [closed]
When converting rpm of, say a helicopter blade, to m/s, the equation used is:$$v_{m/s} = \frac{2\pi{r}}{60}\times N_{rpm} $$ In the equation, we have radius as a variable, as the speed changes with ...
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2
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434
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Integrating Angular Velocity Vector using Rodrigues' Rotation Formula
My understanding is that Rodrigues Rotation Formula can be used to explicitly compute an exact rotation associated with a constant angular velocity vector over a given time step.
How do you derive the ...
- 982
0
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1
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522
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Angular velocity of a particle in uniform circular motion about a general point
This problem was given by our professor.
Consider a particle P executing uniform circular motion wrt the point O with uniform angular velocity $\omega$ anticlockwise whose cordinate is $(2R,0)$ in a ...
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1
vote
1
answer
54
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Vehicular Dynamics [closed]
Consider an open differential connected to two wheels on each side. The wheels are flat discs and are 1400 mm apart. This car is making a turn of radius 7 m at a constant angular velocity of 30 ...
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0
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61
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How is the angle of the front wheel found in Bicycle Kinematics Model for a Car
My question is, in a 4 wheel model, the front wheels have different angles. To simplify things bicycle model is used. In the bicycle model, there is an imaginary wheel in the middle of the front ...
3
votes
1
answer
242
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Kinematics of a rolling disk on a static disk (variation of the Euler disk)
I'm puzzled by the following problem. Consider a simple tilted disk $\mathcal{D}$ of radius 1 (in any unit) rolling without sliding on top of a static horizontal disk $\mathcal{S}$. The normal $\...
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1
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114
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How do I determine at what angle to move to intercept another object moving along a circular path?
I came across this issue on my own. This is not a homework problem.
Two people (you and someone else) are running along a circular track, with known positions in relation to each other, and known ...
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1
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25
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Meaning of this equation of rotational motion
Tinkering around with rotational movement I ended up with this equation:
$$\omega=\frac{v_t}{r}=\frac{v}{r}\sin\theta = \frac{\sin \theta}{r} \frac{dr}{dt} = \frac{\sin \theta}{r} \frac{dr}{d\phi}\...
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1
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156
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Frictional wheels without slipping (gear system)
In the figure below it is stated that the friction force should always be greater than the tangential force in order to prevent slipping between two frictional wheels. My question is that if we apply ...
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2
votes
1
answer
792
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Angular acceleration related to a time dependent rotation matrix $R(t)$
Let the orientation of a coordinate frame $\{b\}$ w.r.t. a static coordinate frame $\{a\}$ be expressed by a rotation matrix $R_{ab}\in SO(3)$ whose columns represent the coordinates of the unitary ...
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4
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1
answer
2k
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Kinematics of a 3-wheeled omnidirectional robot
Consider a 3-wheeled, omnidirectional robot (also called a kiwi drive). To see what this looks like see this YouTube video. We can control the motor speeds using a microcontroller.
Task: We have to ...
- 1,325
1
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3
answers
595
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Is the derivative of the magnitude of a position vector the speed? Is the integral of the speed the magnitude of a position vector?
I'm reading a book titled "Introduction to Mechanics" by Kleppner, and I came across an example: A bead moves along the spoke of a wheel at constant speed $u$ meters per second. The wheel ...
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1
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658
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Tangential velocity - Spherical coordinates
In a spherical coordinates system ($r$, $\theta$, $\phi$ ), assuming an angular rotation $\omega_z$ around the z-axis, the tangential velocity of a point can be expressed as:
$$V_x = -\omega_z R \sin\...
0
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1
answer
83
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Elliptic motion [closed]
I'm given the following motion:
$$x(t)=A\cos(\omega t)\\y(t)=B\sin(\omega t)$$
I'm asked to describe what kind of motion it is and other things. The thing that puzzles me is that my first approach was ...
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1
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1
answer
277
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Resultant velocity in rolling motion
Why is the resultant velocity of a
particle inside a body undergoing rolling without slipping always perpendicular to the line segment connecting it and the instantaneous axis of rotation?
$P_2V_2$ ...
- 13