Which equation represents centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle around which the object is moving. The equation that captures this concept is given by the formula ( a_c = \frac{v^2}{R} ), where ( a_c ) represents centripetal acceleration, ( v ) represents the tangential velocity of the object, and ( R ) is the radius of the circular path.

This relationship illustrates that as the speed of the object increases or as the radius of the circular path decreases, the centripetal acceleration increases. Thus, it is essential for maintaining the circular motion of the object. This equation is fundamental in mechanics when analyzing situations involving circular motion, such as satellites in orbit, cars going around a curve, or any scenario involving rotation around a center point.

The other equations provided do not relate to centripetal acceleration; instead, they represent different concepts in mechanics. For instance, one relates force and mass, while another involves gravitational force, and yet another provides power in relation to work done over time. Understanding where these equations apply helps clarify why only the equation ( a_c = \frac{v^2}{R} ) is