Centripetal acceleration vs Radial Acceleration?

Question

Hi everyone, i was just wondering if anyone knows the difference between the two accelerations? Why does centripetal acceleration has an equation of a=v^2/r while the radial acceleration has a formula very similar but opposite

a=-v^2/r ? I know radial acceleration is when an object travels along a curve and centripetal is when it travels in a uniform circular manner, but why isn't dirrection toward the center for radial like centripetal? isn't the curve kinda attracting the object toward it's center? i really appreciate it if I could get and answer for this! Thanks!

Answer 1

The word 'centripetal' indicates the direction towards the center whereas the word 'radial' indicates the direction along the radius from center outwards. That is the reason for the opposite sign.

It is not true to say that radial acceleration is when an object moves along a curve and centripetal is when it moves along the circular path. Both are for any curvilinear motion. The word 'radial' means from center outwards. Thus it is the question of language and not much of physics.