For uniform circular motion,write the equations for centripetal force and centripetal acceleration. Also,provide examples.

(N/A) When a body of mass $m$ moves on a circular path of radius $R$ with a constant speed $v$,it experiences a centripetal or radial acceleration given by $a = \frac{v^2}{R}$. The direction of this acceleration is always toward the center of the circle.
By Newton's second law of motion,the necessary force to provide this acceleration is $F_c = \frac{mv^2}{R}$. The direction of this force is also toward the center of the circle; hence,it is called centripetal force.
In different situations,centripetal force is provided as follows:
$(1)$ For a planet revolving around the Sun,the necessary centripetal force is provided by the gravitational force.
$(2)$ For an electron revolving around the nucleus in an atom,the necessary centripetal force is provided by the Coulombian force (electric force).
$(3)$ For vehicles moving on a level circular track,the necessary centripetal force is provided by the friction force between the tyres and the road.