All Questions
Tagged with definition rotational-dynamics
35
questions
6
votes
2
answers
609
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Why is angular momentum defined so?
We know angular momentum is defined as $mvr$. In the context of Lagrangians and Noether's theorem, this definition pops up as the conserved quantity due to rotational symmetry of the system. Is there ...
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vote
0
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51
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Definition of angular velocity in rotational motion of a non-rigid body? [closed]
Consider a particle in rotational motion with radius r and angular velocity w both varying with time, what is the relationship between the displacement u and w of the particle? $w=\frac{\partial u}{\...
- 11
0
votes
3
answers
88
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Equation of Torque
The magnitude of torque is defined as the product of the perpendicular (to the object) component of the force I apply and the distance between the axis of rotation and the point of application of the ...
0
votes
0
answers
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Motivation behind Definition of Moment of Inertia [duplicate]
I was studying rotational mechanics a while ago, and came across the idea of moment of inertia. The moment of inertia of an object describes its resistance to angular acceleration. The definition of ...
0
votes
1
answer
118
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Problem with Center of mass equation definition
I was trying to motivate the definition for the center of mass formula and I am getting a weird result. For simplicity let's assume two-point masses of mass $m$ and $2m$ connected by a rigid massless ...
- 122
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votes
1
answer
59
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Is Torque always defined about the axis of rotation?
My professor told me torque can be calculated about any point in space, but would such a torque ever make sense even if the particle is rotating about some other axis, on which the point does not lie?
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1
answer
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What is $R$ in torque? [closed]
I am confused of what is $R$ in torque is it the distance to the axis of rotation or to a specific point or origin of axis of rotation (pivot)? the forces should treated as lines?
- 111
1
vote
0
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Why are there two definitions for the angular momentum of a particle with respect to a moving point?
There seem to be two definitions for the angular momentum of a particle with respect to a moving point.
See the figure below. Let $O$ be the origin of a coordinate system in an inertial frame. Let $Q$...
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8
votes
5
answers
607
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Why is torque defined as $\vec{r} \times F$?
Here I cannot convince myself myself that it is units because the torque is defined to be in units of Newton meter is a reiteration of the law stated above. Why was it not $r^2 \times F$ or $r^3 \...
- 460
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votes
1
answer
204
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What's exactly is moment of inertia?
I know that angular momentum can be expressed in terms of moment of inertia tensor as follows,
$$\vec{L}= I_{\text{tensor}}\vec{w}$$
Where $I_{\text{tensor}}$ is tensor for moment of inertia. It can ...
- 658
19
votes
5
answers
2k
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Without saying "cross product" explain why there is a skew-symmetric angular momentum tensor
In Space-Time-Matter Hermann Weyl claims that had we lived in a world of more than three spacial dimensions, we would have known all along that quantities such as angular momentum are skew-symmetric ...
- 2,015
2
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Is the Moment of Inertia tensor symmetric due to rotational invariance of space?
In standard classical mechanics' textbooks (for instance Morin) one finds that while calculating the angular momentum vector of a rigid body for a 3-D general case from the definition:
$$L=r \times p$$...
- 1,441
4
votes
2
answers
280
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What is the physical phenomenon the vector cross product describes?
I have been searching about the cross product and still can't grasp the physical intuition of it. As far as I know, mathematically the cross product is a tool that creates a new vector perpendicular ...
0
votes
3
answers
161
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The unit of Torque [duplicate]
Whenever we define a physical quantity, we know what 1 unit of that quantity tells us. For example, when we say 5 Pa, we're saying 5 N force acts perpendicularly on every unit area of the material but ...
- 87
0
votes
1
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Is the definition of Work done by Torque a general result?
I was going through this post.
In the post the person who asked the question mentioned a statement:
"Lastly, I am emphasizing that I'm am NOT saying that torque is incorrect, only that the work ...
- 1,568