All Questions
10 questions
0
votes
5
answers
186
views
Why the normal vector addition does not seem to work in centripetal acceleration? [duplicate]
It is known that centripetal acceleration acts at an angle of 90 degrees to the tangential velocity. This acceleration vector then causes an increment $\mathbf{a} \Delta t$ to be added to the original ...
- 105
0
votes
2
answers
358
views
Circular motion equivalent in three dimensions [closed]
Are there equations or even a concept of circular motion/tangential acceleration/centripetal acceleration in three dimensions? Maybe something called "spherical acceleration"? or am I just ...
- 75
1
vote
3
answers
391
views
Is the acceleration vector half of the gradient of velocity squared?
Consider the differentiation of speed squared with respect to time:
$$\frac{d(v^2)}{dt}=\frac{d(\mathbf v\cdot\mathbf v)}{dt}$$
$$=2\mathbf v\cdot\frac{d\mathbf v}{dt}$$
$$=2\mathbf v\cdot\mathbf a$$
$...
0
votes
1
answer
91
views
2D rotation dynamics/control systems as a complex number
I have a dynamic system (it's a rocket in a 2D plane), that I'd like to model the orientation of using complex numbers to remove the need for trig functions in my ode.
I'm having trouble defining the ...
- 1
15
votes
3
answers
4k
views
Why does solving the differential equation for circular motion lead to an illogical result?
In uniform circular motion, acceleration is expressed by the equation
$$a = \frac{v^2}{r}. $$
But this is a differential equation and solving it gets the result $$v = -\frac{r}{c+t}.$$
This doesn’t ...
- 153
2
votes
4
answers
686
views
Work done by a vector field (Force field) on a particle travelling along a curve
Assume a particle travelling along a curve, the work done by any Force field on the particle while moving along a curve is given by the line integral of $\vec{\bf{F}} \cdot \vec{\bf{dr}}$, but shouldn'...
- 367
0
votes
0
answers
162
views
Integration of equation of motion in polar coordinates
We have the equation of motion in polar coordinates:
$$\frac{d^{2}\vec r}{dt^2} = (\frac{d^2 |\vec r|}{dt^2} - |\vec r|\cdot (\frac{d\theta}{dt})^2)\hat r + (|\vec r|\cdot \frac{d^2\theta}{dt^2}+2\...
- 13
3
votes
2
answers
203
views
When exactly does error tend to zero in calculus?
I've come across many instances where sometimes the error tends to zero but other times it does not. Let me give you a few examples.
1.
When I calculate the area of a sphere summing up discs of ...
- 1,106
1
vote
3
answers
174
views
Integral ambiguity
I'm a bit confused with some notation I encounter in physics calculus. Consider this:
Taken from here.
Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf p}}{dt} ...
1
vote
2
answers
158
views
Showing $ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$
Can someone please explain how this equation is valid, using intermediate steps if available?
$$ m\int \frac{d\textbf{v}}{dt} \dot \normalsize \textbf{v}dt = \frac{m}{2}\int \frac{d(v^2)}{dt}{}dt$$
...
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