Hi I've been working through some examples from the course material we use in physics class, but one thing keeps confusing me: What is the difference between centripetal and radial acceleration? For instance, when we have a particle traveling in a circular path, the acceleration towards the center of the circle may be written as Ar (a sub r)=-Ac= - v^2/r, while other times it is written simply as Ac=v^2/r. The text book (JS Physics for Scientists and Engineers) seems to use both. Where is the negative sign coming from? I made a quick sketch. Am I right if i think that the radial acceleration is negative in the first circle (to the left) and it is positive in the circle to the right? Is it just due to how I pick the axis and how I define positive direction? Thanks in advance.
Same thing. v^2/r is the magnitude of the radial acceleration; the direction is toward the center. Whether that's positive or negative just depends on how you define your sign convention. Yes.
Radial acceleration is equal to centripetal acceleration when the radius remains constant (with a +/- sign depending on definition). If radius changes as a function of time, you have to add the explicit second derivative of radius with respect to time. [tex]a_r = a_c + \ddot{r} = -\omega^2 r + \frac{d^2r}{dt^2}[/tex] Similarly, tangential acceleration will pick up a term that depends on the second derivative of angle with respect to time and a Coriolis Effect term.