So, the concepts "centripetal" and "radial" is almost the same but have a small difference that former only for 2-D phenomenon while the later may accept 3-D, right?
But, if that true, while they said that, "This proves that centripetal acceleration is indeed radial (i.e acting along radial...
Oh, yes, I see. As the Taylor Series of \frac{1}{x^2} diverges at 0, I cannot simply multiply it with x to evaluate 1/x at 0, right? And it is unreasonable to multiply an expression that diverges (to \infty) with a variable that come to zero and conclude that the multiplied expression come to...
Surely the last limit isn't 0. But my problem is that the strange result I obtain when
I treat \frac{1}{x} as x\times TaylorSeries\_of(\frac{1}{x^2}).
I wonder where is my error when I calculate the limit by this method!
I see that if using the Taylor series above to determine the value of \lim_{\substack{x\rightarrow 0}}\frac{1}{x^2} we will obtain infinity, which is according?
I am doing something that I sure that I'm wrong, but I cannot realize the error. See as below:
\frac{1}{x}=x\times\frac{1}{(x^2)} ________\(1\)
Taylor Series of \frac{1}{x^2}:
\frac{1}{x^2}=\frac{1}{\alpha}+\sum_{k=1}^\infty g(k)(x-\alpha)^k
In which
k is from 1 to infinity...
At http://cnx.org/content/m13871/latest/ I find:
This information seem to be very clear to understand, but, then, they say that:
(It is inside paragraph discuss about Direction of centripetal acceleration)
It starts the confusion...
I don't really know what do they mention?
Can anyone...
Can anybody please explain me the difference between "centripetal" and "radial"? I get stuck in distinguishing them!
centripetal force, centripetal acceleration...
radial force, radial acceleration...
I also don't understand why they say that "In uniform circular motion, the difference...