Questions tagged [rotational-kinematics]

A tag for questions about rotational motion, including angular velocity and angular acceleration.

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Correct frame for angular velocity in quaternion's kinematic

I am reading a paper where the quaternion's kinematic is used, unfortunately the description of the angular velocity does not match with how it's computed, so I have a doubt on which frame $\omega$ is ...
Davide Zamblera's user avatar
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1 answer
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Instantaneous axis of rotation and alpha

Today my sir started rotation. He was teaching instantaneous axis of rotation. I understood it well. But later he was telling something about alpha. He was not clear . As far as I understand he said ...
User13446789's user avatar
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Concept of rotational equilibrium [closed]

Consider a rigid square plate of side length 'a' which can rotate freely about the point O in vertical x-y plane as shown in figure. Plate has a groove AB along its diameter. An insect of mass moves ...
Ahmad Raza Beg's user avatar
2 votes
2 answers
56 views

Confusion about torque [duplicate]

Consider a free body, not hinged about any point. If a force is applied to one end of the body, the body has a net nonzero torque about many points in space. About which will it rotate? Am I wrong in ...
Eisenstein's user avatar
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Example of calculation of angular velocity from the rotation matrix [closed]

Let $\begin{pmatrix} cos(2\pi t^2) & -sin(2\pi t^2) & 0\\ sin(2\pi t^2) & cos(2\pi t^2) & 0\\ 0 & 0 & 1 \end{pmatrix}$ be the rotational matrix around the $z-$axis. How can i ...
yo yo's user avatar
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3 answers
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Angular velocity definition

My teacher gave this as a fact $\vec{v}=\vec{\omega} \times \vec{r}$(cross product) where $\vec{\omega}$ and $\vec{r}$ are angular velocity and position vectors respectively. He also said that this ...
Ganesha Dattatraya Gaonkar CFA's user avatar
-2 votes
2 answers
88 views

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 ...
Ulshy's user avatar
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Why does the period of precession of a gyroscope have to be way larger than it's spin period so that it's motion can be modelled?

Mathematically, torque induced gyroscopic precession may be modelled with the following equation: $$ {\displaystyle T_{\mathrm {p} }={\frac {4\pi ^{2}I_{\mathrm {s} }}{\ mgrT_{\mathrm {s} }}}={\frac {...
ThincThru's user avatar
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2 answers
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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 ...
Xiaobao's user avatar
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Why does the centrifugal force act normal to the surface?

This questions comes from understanding the Tennis Raquet's Theorem, also known as Dzhanibekov's effect in this video: Veritasium's video On the second 8:36, we can see that when they try to add some ...
Ulshy's user avatar
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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 ...
Tom2023's user avatar
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1 answer
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Torque & Axis of Rotation

If a rod has a fixed pivot point, we can calculate the torque - then rotation - by taking the cross product of displacement and force. Does this method only work when an object’s rotation is ...
Fascheue's user avatar
8 votes
2 answers
174 views

Does a bottle flip depend on the bottle's water content?

Me and my friend were doing the bottle flip challenge when after a few unsuccessful attempts, my friend told me to add more water to increase the chances of a successful flip. So my question is Does ...
PandaScientist's user avatar
2 votes
1 answer
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Calculating rotation speed of HI gas from a broadened emission line and rest frequency

This is the question I'm trying to answer, and the given solution is below it. The bit I don't understand is why they used the equation in the highlighted section. The only equation I've found that ...
user374355's user avatar
1 vote
2 answers
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Direction of angular parameters and centripetal acceleration

If the axis of rotation is not passing through the centre of mass but some other point of a rigid body then how do we define the direction of angular parameters that is angular velocity, angular ...
Aspirant29's user avatar
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2 answers
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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.
Sanjay's user avatar
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Calculating moment of inertia for a hollow cylindrical shell of varying amounts of water within it for an experiment about rotational motion [closed]

I am doing an experiment with the overall research question of: To what extent does the amount of fluid within a hollow cylindrical can affect its dynamics while rolling down an inclined plane I was ...
Mostafa ElSanousi's user avatar
1 vote
1 answer
54 views

How to compute linear acceleration in 3D from change in roll, pitch and yaw angles?

We know that if a body is rotating only about $z$-axis along a circle of radius $R$ with an angular rate of $\omega$, then the acceleration of the body in 3D is $a = [0.0\ \ \omega^2R \ \ 0.0]$. Now ...
user146290's user avatar
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2 answers
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How do we properly describe angular displacements, angular velocities, and the relationship between them (in the most general case)?

If we are merely describing rotations through a fixed axis through the origin, then it is enough to characterize angular displacements by an angle $\theta\in(-\pi, \pi]$. Real-life rotations are not ...
Maximal Ideal's user avatar
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3 answers
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Ambiguity in angular velocity? Two different possible angular velocity vector assignments for the motion of a particle?

To simplify things, consider a particle moving in circular motion counterclockwise (from the $+z$ position looking down at the $xy$-plane), so the position is $\vec{r}(t) = (a\cos ct, a\sin ct, 0)$. ...
Maximal Ideal's user avatar
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Calculate small rotations from displacements

I am performing a modal test on a cantilevered beam-like structure, free at one end and fixed at the other end but with flexible constraints, similar to rotational springs in all 3 directions. The ...
Pibroch1913's user avatar
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28 views

Angular acceleration to linear acceleration for a rope and beam

So say that I have a beam that can rotate around a pivot, with a rope attached at some radius. The rope also always passes through another point such that the length of the rope from this point to ...
Slink's user avatar
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4 votes
2 answers
924 views

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 ...
restless_resistor's user avatar
1 vote
3 answers
70 views

Do objects with non-uniform shapes and mass distributions rotate as a result of gravitational attraction?

I was thinking about orbital mechanics this morning and a question arose: do objects with non-uniform shapes and mass distributions rotate as a result of gravitational attraction? Thinking through the ...
Polynomial's user avatar
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3 answers
57 views

Is it possible for a single torque to rotate a sphere of uniform density at rest from one arbitrary orientation to another?

If I had an object at rest in some arbitrary rotational position, is it possible to apply a single force to it in order to rotate it to a second rotational position? This would be assuming the object ...
Patrick McCaffrey's user avatar
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24 views

Predicting position given constant angular + linear acceleration with a non-fixed axis

My readings on rotational motion always describes rotation around a fixed axis: that is, an object on a string, basically, and changes to angular velocity will alter speed such that the radius is ...
bigmoon_smallplanet's user avatar
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1 answer
40 views

Does a rotating body resist acceleration in a direction that is perpendicular to the direction of the rotation of the body?

I would like to know if a rotating body resists acceleration in a direction that is perpendicular to the direction of the rotation of the body. Say for example there is a bicycle wheel with a tire on ...
user57467's user avatar
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3 votes
1 answer
167 views

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 (...
J Peterson's user avatar
2 votes
1 answer
57 views

(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 ...
Stanley's user avatar
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Can an object have more than one axes of rotation? [duplicate]

A few answers I found say "no." Perhaps because the conditions for rotation around multiple axes have not been met. However, I have seen a couple of videos of objects spinning around both ...
RobotMan's user avatar
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0 answers
29 views

Linear and Angular kinematics for vehicle attitude and position estimation

I am building a robotics college level project, an unmanned aerial vehicle or a drone. I am using a mpu 6050 IMU for getting instantaneous acceleration and angular velocity of the system. I will be ...
Akash Sagar's user avatar
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0 answers
61 views

Ehrenfest paradox and the link to general relativity

I've seen several sources stating that Einstein was partially inspired by the Ehrenfest paradox when thinking about general relativity. However in the Ehrenfest paradox the non-Euclidean nature of the ...
Simon Mackenzie's user avatar
1 vote
1 answer
40 views

A rigid body rotation with 3 joints

I was playing around a physics simulation and I saw this. (One of my first questions , forgive if this question is too simple or has grammatical errors) Here it is in action. I wanted to figure out ...
Krave37's user avatar
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1 vote
1 answer
59 views

Torque on a rotating axle [closed]

The problem is from the book Classical Mechanics by David Morin. Here's my attempt One of the principal axes will be along the rod ($\hat x_1$) and other two will be passing through the center ...
Shashank's user avatar
1 vote
1 answer
129 views

Acceleration in rotating frame

I’m confused by the subscript of rot and in, short for rotating frame and inertial frame respectively. When we calculate the acceleration in the inertial frame, on the left side of the equation, we ...
Xiang Li's user avatar
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0 votes
2 answers
27 views

A diver makes 2.5 revs on the way from a 10-m-high platform to the water. Assuming zero init. vert. vel., find the avg ang. vel. during a dive [closed]

Free-fall kinematics gives 1.43 sec until the diver hits the water. $\omega$ is easily found from 2.5 rev/1.43 sec = 1.75 rev/s = 11 rad/sec. My question results from the following: Kinematics also ...
Joe's user avatar
  • 9
2 votes
1 answer
131 views

Having trouble deriving the exact form of the Kinematic Transport Theorem

The Kinematic transport theorem is a very basic theorem relating time derivatives of vectors between a non rotating frame and another one that's rotating with respect to it with a uniform angular ...
Amit's user avatar
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1 vote
2 answers
161 views

Upgrading to geometric algebra my proof of energy conservation for a rotating rigid body in $D$ dimensions, and solving the Sylvester equation

I wrote a proof from first principles that energy is conserved in a $D$-dimensional rotating rigid body without external forces, and I'd like to ask for some feedback on improving my math with more ...
Gabi's user avatar
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1 answer
99 views

Why is $\sum_{i}m_iv_i$ equal to zero for a rolling ball?

I was watching a video about rotational kinetic energy in which they derived the formula $$K=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2$$ each point on the circle has a translational velocity equal to the ...
Jaden's user avatar
  • 3
0 votes
0 answers
66 views

Angular Velocity in the Plane of a Lamina

A rigid body (i.e., a 2-dimensional object) has principal moments of inertia about the centre of mass of $I_1 = (\mu^2 -1), I_2 = \mu^2 + 1, I_3 = 2\mu^2.$ I wish to show, using the Euler equations, ...
Vera Leighton 's user avatar
1 vote
3 answers
50 views

In case of an axis where moment of inertia changes with time which of the following equations is valid? [closed]

$$ T = I \alpha $$ $$ L = I \omega $$ $$ T d(\theta) = d(\tfrac12 I \omega^2) $$ If I differentiate the second and third one with respect to time… all three equations give a different expression for ...
Aryamman Bhatia's user avatar
2 votes
4 answers
435 views

Line of action of resultant force of two parallel forces

We take a rigid body as shown in the figure and apply two parallel forces (which do not have the same lines of action) at the ends of the body. Let us assume that $P>Q$. Now as we all know There ...
madness's user avatar
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1 answer
76 views

Angular velocity of a rod and what formula to use while solving

The question is: A uniform rod of length L stands vertically upright on a smooth floor in a position of unstable equilibrium. The rod is then given a small displacement at the top and tips over. What ...
Aditya Bansal's user avatar
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2 answers
111 views

Does a simple pendulum have some radial acceleration at its extreme positions where its speed becomes zero?

Suppose we have a simple pendulum swinging between two extreme positions. At the extreme position its speed becomes zero. As per this reason can I say that at extreme positions radial acceleration (v^...
Shinnaaan's user avatar
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0 votes
2 answers
53 views

Decomposition of 3D rotation (in analogy to translation)

Any displacement along a line can be written as the sum of two perpendicular displacements, which then form a closed triangle with the total displacement vector. My question is: Can something similar ...
David's user avatar
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0 votes
2 answers
64 views

How to model the motion of a cone quantitatively in terms of torques?

Imagine that you apply a force to a cone that is laying on a horizontal plane. The cone moves in a circle upon application of the force but the question I have is how to quantitatively model the ...
Abdul4237's user avatar
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0 answers
33 views

Moment of inertia of a rectangular plate

I am currently trying to solve some moment of inertia questions with the help of "simple" volume integrals. We haven't really been taught at all the derivation of the moment of inertia and ...
Mepep's user avatar
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1 answer
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How to transform Arbitrary Rotation Matrix $A$ to a coordinate system where the $z$ axis lies along the axis of rotation by Similarity Transformation?

In Chapter 4 of the book Classical Mechanics by Goldstein, it was written that "By means of some similarity transformation, it is always possible to transform the matrix A to a system of ...
Lusypher's user avatar
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1 vote
2 answers
245 views

Back and forth oscillation of a screw

When you tend to give a screw a small push when it is resting on a relatively smooth surface, it tends to oscillate/move back and forth in a circular path before stopping. There is no apparent torque ...
Abdul4237's user avatar
1 vote
0 answers
33 views

A rod inclined at angle 60° with the horizontal is dropped on the floor with initial velocity u. How to find axis of pure rotation after collision? [closed]

Coefficient of restitution is $e$. Length of rod is $l$ and its mass is $m$. Before collision, rod performs pure translation, in vertically downward direction with velocity $u$ I know that after ...
KrishPandey's user avatar

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