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Results tagged with reference-frames
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user 282830
A reference frame is a particular coordinate system chosen to represent physical entities. The notion is most often used in special and general relativity to denote particular coordinates chosen on the spacetime manifold.
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Physical significance of the angular velocity vector and its projections along different axes
The magnitude andis not direction of the angular velocity $\vec\omega$ remains the same in the both cases you proposed. The projection of this vector into any axis is, of course, depending on the coor …
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Why do outermost particles on a rotating rigid body gain more kinetic energy?
The energy transferring mechanism is the internal structure cohesive force of the rigid body. The structural binding force between mass 2 and 3 transfer the force applied on mass 2 to mass 3.
Imagine …
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Confused by parallel axis theorem
These two cases are essentially of the same spirit. Your right hand side is a particular case of the right hane side. In the left hand side, the inertial moment at the cernter of mass $I_{CM}=0$, thus …
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Why do pseudoforces always act in opposite direction to acceleration?
Lets set up the notations:
$\vec{r}$ is position vector of point P referred to an rest inertial frame O.
$\vec{r'}$ P referred to the frame A (non-inertial).
$\vec{\xi}$ the origin of frame A measure …
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1
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Accepted
Applying gradient in spherical coordinates to vector in cartesian coordinates
For clarification, write $\vec{u} = u_x \hat{x} + u_y \hat{y} + u_z\hat{z}$ in components, and $d\vec{S} = \hat{r} R^2 \sin\theta d\theta d\phi$
$$
\vec{I} \equiv \oint \oint \vec{\nabla} \vec{u} \ …
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Why is angular momentum conserved in a central field?
Your reasoning about the angular momentums is corrrect. What is needed is an interpretation: note that $\frac{d\vec{L}}{dt} = \vec{\tau}$, and both $\vec{L}$ and $\vec{\tau}$ are dependent on the cho …
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Can the reference point in an inertial frame be accelerated when applying torque equation?
This is not an answer. I post to clarify the mistakes in the answer from John.
Now, lets forcus on your above answer. I show your clearly the errors.
Eq. (3) in this post:
Eq.(3) in John's post.
W …
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1
vote
Accepted
What's the definition of angular momentum on a two-body system?
The angular momentum $\vec{L}$ and torque $\vec{\tau}$ are both dependent on the choice of the origin. But the relation between them is not dependent on the choice of coordinate. Angular momentum is n …
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Applying torque to rigid body on a fixed axel?
Saying that the torque $\vec\tau$ and the rotation axis $\vec\alpha$ forms an angle $\theta$ in between. The projection of $\vec\tau$ on $\vec\alpha$ is
$$
\tau_\parallel=\tau \cos\theta
$$
Hence, the …
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3
votes
Centrifugal Force Dilemma
It is also called fiticious force, or d'Alembert force, or inertial force. I prefer the term inertial force, because we do feel it, not an imagination.
We apply centrifugal force only when we are in a …
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Accepted
Tangential friction acting on a bug as it moves from center to periphery of a rotating disk
In the rotation frame of the disc, the bug (mass $m$) position $\vec{r}'(t)$ relative to the disc. Note that $|\vec{r}'| = | \vec{r} | = r$, the disc frame differs from the prime system only in the a …
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