ΣF=ma_c (sum of forces equals mass times centripetal acceleration)

Definition

This equation represents Newton's second law applied to circular motion. It states that the sum of all forces acting on an object moving in a circle is equal to the mass of the object multiplied by its centripetal acceleration.

Analogy

Imagine you are swinging a ball attached to a string around your head. The force you exert on the ball through the string is like ΣF, and the ball's mass times its centripetal acceleration represents ma_c. The equation tells us that these two quantities must be equal for circular motion to occur.

Related terms

Centripetal Force: Centripetal force is the net force directed towards the center of a curved path that keeps an object moving in a circle.

Centripetal Acceleration: Centripetal acceleration refers to the acceleration experienced by an object moving in a circular path. It always points towards the center of the circle.

Tangential Velocity: Tangential velocity is the linear speed at which an object moves along its circular path tangent to that point. It is perpendicular to both centripetal force and centripetal acceleration.