What is the formula for centripetal force?

The correct formula for centripetal force expresses the relationship between mass, velocity, and radius in a circular motion context. Specifically, centripetal force (Fc) is defined as the force required to keep an object moving in a circle and is dependent on the object's mass (m), the square of its velocity (v²), and the radius (r) of the circular path.

When an object moves in a circle, it constantly changes direction, which means it is accelerating towards the center of the circle. The acceleration in this case is known as centripetal acceleration and can be formulated as ( a = \frac{v^2}{r} ). Thus, when you combine this acceleration with the object's mass, you derive the centripetal force as ( Fc = m \times a = m \times \frac{v^2}{r} ). This leads to the formula ( Fc = \frac{m \times v^2}{r} ), which clearly highlights how both velocity and radius influence the required centripetal force.

The choice of a formula that uses the velocity squared in its formulation emphasizes the fact that the force increases significantly with increases in speed, since velocity is squared, highlighting the non-linear relationship between