Questions tagged [rotational-kinematics]
A tag for questions about rotational motion, including angular velocity and angular acceleration.
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Euler angles and inertia tensor
Please note: What I'm looking for is $\alpha_0$ and $\beta_0$ in a form similar to Eq.(3) that will eventually give Eq.(1). Note that the inertia tensor is not a rotation matrix so I'm not trying to ...
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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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If a body is lying on a frictionless surface, and we give it an impulse, will it start rotating about its center of mass?
If not, about what point will it rotate? If we want to know about what point an object will rotate in questions like these, how do we figure it out?
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Concept of polarization in microwave rotational spectroscopy
I am trying to understand the concept of polarization of molecules after they are excited by a microwave pulse. The context is:
The complexes are produced in a pulsed supersonic jet expansion of a ...
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Rotation of a sphere on two different axes
You have a small globe, which is mounted so that it can spin on the polar axis and can be spun about a horizontal axis (so that the south pole can be on top). Give the globe a quick spin about the ...
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If a weak light source is attached to a string, and someone swing this light source in circle. It seems that this light source is brighter. Yes or no
It may be truly a question of life and death.
You know those glow sticks.
As a sailor it is a good idea to carry one on our lifevest.
Falling into the sea, those glow stick make a light source that ...
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Why is the angular speed at the axis of rotation of a rotating disc equal to the angular speed at any other point on the disc?
I was just reviewing classical mechanics problems on Khan Academy and got the following question:
I knew that the angular speeds at points II, III, and IV must be equal, but I'm not sure how you'd ...
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Non-Euclidean geometry of rotating disc
Landau, in his Classical Theory of Fields Textbook remarks (while explaining GR) that a rotating disc viewed from an inertial frame of reference will no longer remain euclidean since the periphery ...
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Can some one explain to me why, when I include translational kinetic energy ($\frac{1}{2}mv^2$), I run into problems dealing with rotational motion?
Overall, the problems I know when to use it are when there is something like a rotating pulley disk which has a string wrung around it and a block at the end falling down. Another place I know when to ...
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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 ...
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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 ...
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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 ...
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Thermal fluctuations in orientation of point particles
I am modeling group of point particles with 6 degrees of freedom each - 3 positional degrees of freedom and 3 orientational degrees of freedom. So, each particle has 3 position coordinates and a unit ...
user67800
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Model for rolling gears down a slope doesn't fit experiment
I have derived a model for what happens when one rolls a gear down a slope, and I have performed an experiment, however the experiment doesn't fit the model. Where did I go wrong?
The model
When a ...
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Motion of a catapulted point mass moving freely inside a spherical bucket
I am trying to study the motion of a point mass inside the bucket of a catapult.
The catapult is shooting downward (i.e. describing a rotation of 180° from the horizontal axis) and I would like to ...
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Foucault pendulum, where did I go wrong?
I wanted to approximate the number $N$ of periodes needed, such that the foucault pendelum turns one time. Though my result is off by the factor 2 of the results I found.
What I did: I assume the ...
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Translational acceleration due to rotation
Sorry for boring you, my friends. I am haunted by re-deducing an expression of translational acceleration in ANSYS theory reference about acceleration effect. It takes the form of:
$$\lbrace a_t^r \...
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How Burmester's theory converts rotary motion of the crank to linear movement?
I have been studying the mechanism of Klann's Mechanical spider and there it was written that by Burmester's theory it converts rotary motion of the crank to linear movement. I tried searching but how ...
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Why did Feynman tell "we cannot locate earth's angular position, but we can tell that it is changing"?
I was reading "Symmetry in physics" by Feynman, where he wrote:
If we perform sufficiently delicate experiments, we can tell that the earth is rotating, but not that it had rotated. In other words, ...
user36790
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Would a large, small mass object in orbit experience induced rotation
Imagine a large (multiple earth radii), very small-mass ring orbiting The Sun. Half of the ring would be closer to The Sun than the outer half. Since orbital velocity decreases with distance, two free ...
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Rotating Tank of Charged Liquid
Consider a long rectangular tank of dimensions a×b, where a≫b, that is rotating at a constant angular velocity and filled with an incompressible charged fluid. How would one find an equation ...
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Angular velocity versor
I am going back through the definitions of good old Euclidean vectors and trajectories to see whether when i was younger i missed important concepts.
In my notes, and reference book, i found that for ...
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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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Should the rotary vane damper torque be less than the load torque?
The rated torque of a rotary vane damper should be less than or more than the load torque?
In my opinion, if the rated torque is greater than the load torque of the damper, then I believe my ...
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Assistance in writing the rotational constraints of a spool, in rotational dynamics
I came across a very interesting problem involving rotational dynamics, from the series of Cengage Physics books, which was asked in an Indian competitive exam called KVPY.
Write the constraint ...
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Calculating $C$ in $I_{CM} = CMR^2$
I am a bit new here, so please excuse any errors I might make.
I am a student in an AP Physics C: Mechanics course and I am conducting an experiment where I am experimentally calculating the C values ...
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Textbook problem - Struggling with polar coordinates
Recently I am self-learning "Introduction to classical mechanics" by David Morin. There is a problem in chapter as stated below:
Walking east on a turntable
A person walks at constant speed ...
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Acceleration in rotating frame
$\renewcommand{\vec}{\boldsymbol}$
$\newcommand{\highlight}{\boxed}$
9.5.3 Velocity and Acceleration in a Rotating Coordinate System
Applying Eq. (9.8) to the position vector $\vec{r}$, we have
$$\...
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How translation, rotation and translation plus rotation of a body can be define particle by particle?
Let use simple example, a uniform rod with center of mass (COM) at the center of rod. The rod is in free space there are no other forces acting on it.
If we apply single force acting on a particle at ...
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What does tangetial velocity change during Conservation of Angular Momentum
Lets say that a particle connected to a string is rotating about an axis O with a uniform tangential velocity of u. Then, the string is pulled towards the axis to decrease its radius (say from r1 to ...
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Velocity of an stationary object when viewed from rotating disk
Suppose I am sitting at the centre of a rotating disk, having an angular speed of 3 radian per second and I observe a tree 4 meters away from me. The tree will have a velocity of 12 meters per second ...
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How do I approximate an angular acceleration vector from a history of orientations?
A rigid body is simulated to move in six degrees of freedom. At every past timestep, I know its displacement vectors $x^{GLOB}$ in the global coordinate frame, as well as 3x3 matrices $R$ that ...
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Does always angular momentum and angular velocity have the same direction?
I was studying how angular momentum is cancelled when it is transferred directly into the origin of the axis of rotation and during the lecture the professor did something and I was pretty confused.
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Relationship between angular and translational velocity on inclined surface
I have been researching about rolling motion and I was calculating a way to predict the translational velocity of the object at the bottom of the incline. I know that the kinetic energy of a cylinder ...
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Will a cylinder/sphere roll on a rope if half of it is surrounded by rope and one end of the rope being pulled?
Rolling a cylinder using a rope having one end fixed and another end mobile
Will the cylinder/sphere roll as per the conditions mentioned in the above question(link)? Are there any additional ...
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Help with derivation of Kinetic Energy of N point masses
There are $N$ point masses as shown in image each with mass $m_i$ and velocity $v_i$.
We need to find the Kinetic Energy of the system. Here is the proof attached I have some doubt in it.
The doubt ...
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How to find angular velocity vector of a three dimensional rigid body given velocity of three non-collinear points on the same?
The position of a three-dimensional rigid body is completely defined by specifying position vectors of three non-collinear points on the body.
Similarly, one can define the motion of the rigid body by ...
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Is there a source that gives a comprehensive framework for tranformations between relatively rotating reference frames?
This is an example of the kind of discussion I am interested in.
Imagine we have a large rotating turntable, kind of like a merry-go-round, but made of some transparent material. On its surface, as ...
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How can I calculate the inertia tensor of a hollow object defined by a triangle mesh?
I want to calculate the mass, center of mass, and inertia tensor of player created objects. Some of the objects will be hollow instead of solid. I am creating a closed triangle mesh for their object. ...
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Strange pattern on fast spinning CD
In the following youtube video and timestamp:
http://www.youtube.com/watch?v=zs7x1Hu29Wc&t=6m51s
one can see a cd spinning very quickly, in slow motion, just before it breaks. I'm not sure I ...
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Particle in Cyclone - height of pipe that will keep the particle pressed against the inside wall
I'm trying to determine the required radius, $R$, and length of a hollow cylinder, $L$, to keep a particle that enters tangentially with an initial velocity $V_{t,i}$ at the top of the cylinder "...
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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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Difference between nutation and polar motion
If you add a mass to your spinning globe or just change the mass distribution does it increase nutation or polar motion? And How do I calculate nutation? For this I take earth as an example. from what ...
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Why is a mechanical advantage less than 1 required for class 3 levers?
From what I understand, mechanical advantage is equal to the ratio of force produced to force applied, which is equal to the ratio of effort to load and effort arm length to load arm length
Therefore,...
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Angular velocity of a particle moving in 3D
I have a particle trajectory where particle position is available at discrete time steps with respect of (0,0,0) in 3D. Time step is 0.05 sec. For reference, positions are shown in following image.
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How does physics deal with perpetual motion in spins?
This is a bit a bit of a weird question. Simply put, if a body such as a planet spins, there is no internal issue (that I know of) that would cause it to eventually stop (by internal I mean that an ...
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Why starts the rotation vector of a body in the intermediate axis theorem to rotate in the same direction as the body?
In this video, explaining the intermediate axis theorem (Dzhanibekov-effect) in a very nice way (around 7:52, from the perspective of the co-rotating frame where centrifugal are present) one can see (...
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Finding The Trajectory of particle Kept on a rotating surface
Suppose we "Keep" a particle on a circular, rotating turn-table, rotating with constant angular velocity $\dot{\theta}$, (i.e, the at $t=0$,when the particle makes contact with the table, the ...
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Can someone help me understand this equation that finds derivative of quaternion when angular velocity is known?
I found the following equation in an IEEE paper:
$\frac{dq}{dt} = \frac{1}{2}\text{Q}\omega$
where $q$ is the quaternion that rotates a vector from the body frame to the world, $q=\left[q(1), q(2), ...
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Stable Rotation Setup for Experiments (table version)
I am looking for a rotation devise like that one in this video below (from 00:40 seconds). Does anyone know where to get one, or have any idea about how to create a nice and stable rotation setup for ...
