# 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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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### 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 ...
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### 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 ...
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^...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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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 ...