All Questions
8 questions
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6
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If a body moves along a path (any path, not just circular) with constant speed, is it's tangential acceleration necessarily zero?
If a body moves along a path (any path, not just circular) with constant speed, is it's tangential acceleration necessarily zero?
I could only find general proofs for the case of circular motion and ...
-1
votes
3
answers
180
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Avoiding a confusion with dot product
Some days ago I have asked a question about a formula for power, many generous people have answered my question and clarify for me that the correct formula of work is
$$\mathrm{d}W= \mathbf{F}\cdot \...
2
votes
1
answer
105
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Work-Kinetic energy theorem derivation
So I came across this derivation in the book Classical Mechanics by Herbert Goldstein. I don't follow from the second step onwards. I understand that there's a dot product, but how do you compute it? ...
- 87
0
votes
3
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84
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How is velocity defined in circular motion in central force field?
In my view the velocity is change of displacement in the increasing direction of displacement. Now in circular motion in central force field the particle is changing its direction then how is the ...
- 1,159
1
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1
answer
2k
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Time derivative of vector in rotating frame with angular velocity about a rotating axis
In general, I know that if you have a vector $\vec{F}$ in a rotating frame, and the frame has an angular velocity $\vec{\Omega}$ that the time derivative of $\vec{F}$ in a fixed frame would be $$\frac{...
- 223
1
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1
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130
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On the derivative of a vector function
In "An Introduction to Mechanics" by Kleppner and Kolenkow, in the section on the time derivative of a vector:
Given $A(t)$ is a vector valued function, then,
$$\Delta A = A(t + \Delta t) - A(t)$$
...
- 179
0
votes
1
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274
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Kinetic energy derivation: Why is $\frac{d \mathbf v}{dt} \cdot \mathbf v= \frac 12 \frac{d}{dt}(v^2)~?$
In Goldstein's Classical Mechanics 3rd edition, page 3, the Kinetic energy is derived by considering the work done on a particle by an external force $\mathbf F$ from point $1$ to point $2$ $$W_{12}=\...
user138458
3
votes
2
answers
134
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Generalization of $F=mv\frac{dv}{dx}=\frac{m}{2}\frac{d}{dx}(v^2)$ to 3-dimensions in a compact notation
Starting from $F=ma=m\frac{dv}{dt}$, in 1-dimension, it is easy to show that $$F=mv\frac{dv}{dx}=\frac{m}{2}\frac{d}{dx}(v^2).\tag{1}$$ Can we generalize this formula in 3-dimensions? In 3D, $$\textbf{...
- 12.3k