# Can someone help me with an analytical dynamics exercise?

1. Feb 17, 2016

### Doney Felipe MEjia

• Thread moved from the technical forums -- poster is reminded to post in HH and show their work
At a certain instant, the velocity and acceleration of a particle ar defined by v= 3i + 4j - 6k m/s and a=-2i + 3k m/s2. Find the radius of curvature and change of speed of the particle at the instant.

2. Feb 17, 2016

### Henryk

you mean, the rate of change of speed, that is acceleration parallel to the trajectory, right?
I also assume, that i, j, k refer to unit vectors along x, y, z coordinates, respectively.
This is not a hard thing to do. First, you have to construct a unit vector parallel to the velocity vector $\hat v =\frac{ \vec v }{]v]}$.
The parallel acceleration is just a projection of the acceleration onto direction of $\hat v$ , that is $a_{\parallel} = \hat v * (\hat v \cdot \vec a)$
That will give you the answer to the second of your question.
The curvature can be found from the formula $\frac {v^2} r = a_{\perp}$ where $a_{\perp} = \vec a - a_{\parallel}$

I hope that I gave you enough hints. If you have any more questions, let me know.
H

3. Feb 17, 2016

### Doney Felipe MEjia

oh man, thank you so much!! It's really easy to do now, but I was confused about it! I have another question from the other exercise but I want to keep trying solve this exercise. if I don't get to solve it, I'll request your help again. Thanks H.

4. Feb 17, 2016

### Staff: Mentor

Please check your Personal Messages. Schoolwork questions must be posted in the Homework Help forums (where I moved this thread of yours), and you must use the Homework Help Template and show your work when posting schoolwork questions on the PF.