Can someone explain how to derive ac = v^2/r ? (1 Viewer)

[amdspotter]

^^^

 

[Akshara Patil]

Fc = f = ma (just equate newton's second law with the centripetal force equation)

 

[tyrone97]

The equation for centripetal accelaration is a kinematic one. It is a bit algebraically involved, so I'll point you to two sources
1. http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html

2. https://physics.info/centripetal/

Note that since accelaration is a vector, there are two things that need to be explained:
1. why the magnitude of a_c = v^2/r
2. why the direction of a_c is towards the centre of the circle.

I also note that the response above

Fc = f = ma (just equate newton's second law with the centripetal force equation)

is not a satisfactory one because that just begs the question as to why F_c = mv^2/r is true.