All Questions
7 questions
-2
votes
1
answer
91
views
From where does the expression of the tangential accerelation come from?
I've seen so many times that the expression of the tangential acceleration is known to be: $$a_t=\ddot{s}$$ but from the expression of the acceleration in spherical coordinates, in the tangential ...
- 69
0
votes
0
answers
85
views
Cartesian coordinate velocity and generalized coordinate velocity
use $x_k$ to denote the kth component of cartesian coordinate, and $q_k$ to denote the generalized coordinate.
Taking the derivate of $x_k(q_1,q_2,q_3,t)$ w.r.t. time, we have
$$\frac{d x_k(q_1,q_2,...
- 105
0
votes
1
answer
468
views
Partial derivative of a 4-velocity
Trying to do some basic manipulations with 4-vectors and I have a question about the proper (no pun intended) approach. It's probably easiest if we look at a simple example. So let's define a 4-...
- 292
1
vote
2
answers
109
views
Derivatives of polar coordiantes?
I'm a undergraduate and I was reading about the polar coordinate system specifically this paper. I don't understand the term: $$\frac{de_r}{d\theta} = e_\theta \text{, and } \frac{de_\theta}{d\theta}...
- 13
0
votes
3
answers
1k
views
How to determine the direction of instantaneous acceleration in a 2D motion? [duplicate]
How do we determine the direction of instantaneous acceleration when the body is moving in a plane (or a 3D space)? This question has been truly bothering me for nearly two weeks. I looked it up, ...
- 876
-1
votes
1
answer
51
views
Assistance interpreting equation
Given a position function of a particle:
$$
\mathbf r=r\,\hat{\mathbf r}\left(\theta\right),
$$
where $\hat{\mathbf r}(θ)$ is the polar unit vector, to find the velocity, we take the derivative which ...
- 13
0
votes
4
answers
5k
views
Sign of acceleration from position-time graph
These three graphs are from my textbook. It states that the acceleration in 1) is positive, 2) is negative and 3) is zero and can be told by looking at the slope.
What I understand from the graph is ...
- 493