Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
748
questions
1
vote
1answer
46 views
Navier Stokes equations for rotating falling object
I am considering the problem of a rigid body moving in a fluid, free to translate and rotate (say, for example, a falling body in a fluid).
Some of the approaches I found in some articles involve a ...
-4
votes
2answers
75 views
Is it possible that this electromagnetic field propulsion system would not violate any conservation laws? [on hold]
I have recently come up with a design of a conceptual electromagntic field propulsion system which should not violate any conservation laws, particularly the Law of Conservation of Momentum and the ...
0
votes
3answers
95 views
What is the angular velocity in the center of a rotating disc? [on hold]
The center of the disc is its center of mass and the motion of the disc is purely rotational (no translation).
0
votes
1answer
34 views
If $v_{contact,road}$ in rolling motion is zero, how the contact point still manages to move forward? [duplicate]
If velocity of contact point of a rigid body performing rolling motion w.r.t road is zero then how the point gets delocalised from its initial position after some time?
My textbook says, At any ...
2
votes
1answer
97 views
Sagnac Effect and clocks synchronization
I read this from "The Sagnac effect and its interpretation by Paul Langevin", in cylindrical coordinates
$$ ds^2=c^2t^2-dr^2-r^2d\theta^2 $$
...This transformation means that the observer O (...
0
votes
1answer
26 views
A thin rod is standing on a smooth surface [closed]
A uniform thin rod of mass m and length l is standing on a horizontal surface. A slight disturbance causes the lower end of the rod to start falling. find the velocity of the centre of mass of the rod ...
2
votes
2answers
49 views
Addition of angular velocities
I'm trying to understand an argument in Taylor's Classical Mechanics section 9.3.
Consider two frames, 1 and 2, and a body, 3. Let $\mathbf v_{21}$ be the relative velocity of frame 2 w.r.t. frame 1, ...
0
votes
3answers
53 views
Is a rotating object moving or stationary?
Because it rotates in situ, its center of mass does not move, so it is static, but it is rotating, so it is not static, then is it static or moving?
0
votes
3answers
71 views
Contradiction in Euler rotation Equation
By Euler rotation Equation, torque
$$\tau (t)=I \omega '(t) + \omega(t) \times I \omega(t)$$
where $I$ is the inertia tensor in rotating frame and is constant;
$\omega(t)$ is the Angular velocity in ...
0
votes
1answer
30 views
What is the advantage of using a polar coordinate system with rotating unit vectors?
What is the advantage of using a polar coordinate system with rotating unit vectors? Kleppner's and Kolenkow's An Introduction to Mechanics states that base vectors $\mathbf{ \hat{r}}$ and $\mathbf{\...
1
vote
2answers
66 views
Moment of inertia for a random polygon
Is there an easy way to calculate the moment of inertia of an arbitrary 2-dimensional polygon, with respect to an axis perpendicular to the plane of the polygon (passing through the center of mass)?
...
1
vote
0answers
14 views
How to find force needed to lift two wheels off ground during cornering?
I'm attempting to calculate the maximum velocity at which I can safely drive around a corner.
One scenario I'm considering is where all four wheels maintain contact with the ground, but slips. The ...
1
vote
2answers
101 views
If vector $a$ rotate about vector $b$, does vector $b$ also rotate about vector $a$?
For $2$ vectors $\, \vec a,\vec b$, both originate at $[0,0,0]$:
If vector $\vec a$ rotates about vector $\vec b$ when observed from a coordinate system fixed to vector $\vec b$,
does vector $\vec b$ ...
1
vote
1answer
144 views
Does an asymmetric top return to its initial position &orientation, while rotating freely in space? (contradiction in Landau&Lifshitz mechanics book)
The Poinsot's ellipsoid tells us that the angular momentum ($M$) (in the rotating frame) should be lying on the intersection curve between the conservation of momentum sphere radius $|M|$: $M_1^2 + ...
2
votes
1answer
74 views
Application of angular velocity to Euler angles
According to a post here Angular Velocity expressed via Euler Angles you can express angular velocity from euler angles. If I choose Y-Z-Y as a rotation sequence the expression becomes.
$\theta_r, \...
0
votes
2answers
89 views
Ackermann Steering Angle
Given the position of the vehicle ($x,y$) at different time points, the speed of the vehicle (m/s), the direction the vehicle is facing (heading — in degrees), the track width of the vehicle, and the ...
0
votes
1answer
38 views
What will be trajectory of a free falling rotating fan?
Consider a situation, where a fan is rotating in full swing. Suddenly, the contact between ceiling and fan bearing is broken. What will be trajectory of fan if it falls under the infulence of ...
0
votes
0answers
16 views
Simulation of IMU gyroscope angular velocities
When you simulate the frame of a vehicle, you could have your velocity as $4\times4$ rotation/translation matrix and do Euler integration every frame. Now if you want to simulate IMU as well, it ...
0
votes
2answers
78 views
Why is $\theta=\beta/2?$ - Kinematics [closed]
An aircraft is flying horizontally in a circle of radius $b$ with
constant speed $u$ at an altitude $h$. A radar tracking unit is
located at $C$. Write expressions for the components of the ...
3
votes
3answers
137 views
Is flipping a coin is a stable rotation?
If I rotate a coin with dimensions: 10X10X1
about 1 of the big axes(10) in space, where there is no torque, will the rotation will be stable just like a frisbee or a football regular rotations are? ...
1
vote
0answers
31 views
How many illusionary axes of rotation can coexist?
Consider the answer to this question:
How many different axes of rotation can coexist?
Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation.
Now, that ...
1
vote
0answers
40 views
Rotation of a disk - should there be a centripetal force?
See the diagram. The tension in the inextensible string should exert a torque causing a tangential acceleration on the rim of the disk. But should there always be a force towards the centre of the ...
0
votes
1answer
37 views
Work done by static friction in Rolling
In rolling without slipping, I understand that the velocity of the point where static friction with the ground is 0, and therefore static friction cannot do work. However, from newtons laws, an object ...
1
vote
1answer
42 views
Rotation of Rigid body
How to prove the equation (4.14)
$$ a_{ij} a_{ik} = \delta_{jk} $$
from the equation (4.13)
$$ x_i' x_i' = x_i x_i $$
With summation convention I found it very easy.
But, using summation I am not ...
0
votes
1answer
39 views
Why is this derivation of rotational kinetic energy wrong?
I was trying to derive the rotational kinetic energy of a solid sphere with radius $R$ using the following idea.
Each infinitesimally small shell volume $4\pi r^2 \cdot dr$ at radius $r$ within the ...
0
votes
0answers
15 views
Moment of inertia- a tensor quantity [duplicate]
The moment of inertia is a tensor and the matrix contains nine elements. The off-diagonal elements are like Ixy, Ixz, Iyx and so on. Ixy = mxy.
But M.I. = mass × (perpendicular distance of the ...
1
vote
2answers
53 views
What are the necessary conditions for relative angular velocity to be defined? [closed]
I have certain doubts related to the definition of relative angular velocity .My textbook defines it in the manner given below:-
$$\omega_{AB}=\frac{v_{AB}}{r_{AB}}$$
$\omega_{AB}$ is the relative ...
0
votes
0answers
23 views
Vorticity - Rankine vortex: how can we say that $\frac{\partial u_\phi}{\partial z} = 0$
\subsection{a}
A Vortex formed in a bathtub, tornado or in other real world scenarios, exhibit nearly a solid body rotation in the core while far away from the center the flow is irrotational. This ...
0
votes
1answer
55 views
Relative angular velocity
Two bodies are in circular motion with A at one diameter and having velocity tangentially downwards and B at other end of diameter tangentially upwards. Find angular velocity of particle A wrt B if ...
0
votes
2answers
90 views
Relative velocities in Circular Motion
Recently I saw the following interesting problem
Ann is sitting on the edge of a carousel that has a radius of 6 m and is rotating steadily. Bob is standing still on the ground at a point that is ...
-4
votes
1answer
57 views
Railroad train on tracks [closed]
What keeps the railroad trains on the tracks?
P.S: It is not the flanges, as already remarked by Dr. Richard Feynman.
I want a detailed explanation of this question, if possible.
Thanks.
0
votes
0answers
43 views
Force on object at South pole
If we have an object of mass $m$, moving on a path of constant longitude travelling at speed v, what will the force on the object be just as it passes the South Pole? We are to assume the Earth is ...
1
vote
2answers
69 views
How to find angular velocity of a spherical object in spherical coordinates
How angular velocity vector is calculated here?
1
vote
1answer
34 views
Calculating acceleration of an object using $x$, $y$ and $z$ coordinates
I have x, y and z coordinates for a test I had carried out for a tool. I had an accelerometer installed on the tool and I used two types of motion to move the tool, rotation and translation. Right now ...
3
votes
1answer
119 views
Does rotation happen throughout the whole x axis of an object simultaneously?
For example, if I draw a line on the side of a pencil top to bottom, then snap one end of it as in launching it due to the pressure of my fingers. Anyways, if I record the pencil launch in slow motion ...
0
votes
2answers
37 views
Why is instantaneous velocity of particle on circular disc perpendicular to position vector taking point of contact as origin during rolling motion
Why is P0P2 perpendicular to velocity vector $\vec{v}_2$ in the diagram?
0
votes
3answers
48 views
Rotational velocity necessary to make apparent weight equal to “real” weight?
I have been trying to find a solution to this, but I never reach same one that my professor provides. The problem is the following:
For an object of mass m standing still on the surface of the ...
0
votes
0answers
23 views
Is it possible to find the linear and angular forces?
Suppose an object has both linear an angular motion. Let's consider the object a sphere.
What we know:
- The angular velocity and acceleration
- The linear acceleration of the center of mass.
- The ...
0
votes
4answers
75 views
A rod rotating about a pivot
A long, uniform rod of length L and mass M is pivoted about a frictionless, horizontal pin through one end. The rod is nudged from rest in a vertical position as shown in figure. At the instant the ...
-1
votes
4answers
139 views
Is the angular momentum in uniform circular motion zero?
In uniform circular motion the direction of linear velocity changes (although magnitude is constant), so linear velocity is not constant and we know that the formula of angular momentum contains ...
1
vote
0answers
66 views
Problem with Impure Rolling [closed]
Can someone explain what happens in the below situation
Looking at it from the planks frame of reference:
The cylinder Velocity= 20(-i)
Net friction force on cylinder f=2umg(i)
(here u=1/2)
...
0
votes
0answers
27 views
Does acceleration of the rim mean just tangential or both tangential and centripetal acceleration?
On my physics homework, the problem specifies that the acceleration of the rim of a flywheel can't exceed 100g. Does this mean that the tangential acceleration only, or the sum of the tangential and ...
0
votes
1answer
334 views
Rotational motion and Circular motion
What is the difference between rotational motion and circular motion? Are they same or they different?
0
votes
2answers
33 views
Point of application of tangential velocity in rotational motion
The tangential velocity of a particle in a rigid body is given by: $\vec{v}=\vec{\omega}\times \vec{r}$. Since the cross product is perpendicular to both $\vec{\omega}$ and $\vec{r}$, the velocity $\...
0
votes
0answers
30 views
Single number to quantify difference between two local reference frames?
I'm working with some satellite data that defines the spacecraft reference frame from two star cameras and two different measurements of orientation configuration of the cameras, and I'm trying to ...
0
votes
8answers
483 views
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 ...
2
votes
3answers
93 views
What is wrong with this reasoning?
Suppose a particle is rotating about a point at a distance $r$, then since $r$ is constant $\frac{\text dr}{\text dt}=0$ so the component of velocity along the position vector should be zero. ...
1
vote
1answer
24 views
Is there a reference frame in which the static friction from rolling does positive work?
I am worried this will be deleted as a duplicate question, so I will try to be extra clear what I am asking:
In some reference frames, static friction can do positive work. If you have a crate in the ...
1
vote
0answers
53 views
Could the source of dark energy be the universe rotating in a higher dimension?
As I understand it, the centrifugal force in a merry-go-round increases as we move further away from the center. Could the universe be spinning in a higher dimension (or even just spinning in a ...
2
votes
3answers
88 views
Can a tilted wheel roll straight?
The common explanation of why a wheel that is falling to one side will turn towards that side to balance itself is gyroscopic precession, i.e. the torque produced by the falling of the wheel plus the ...
