There isn't a single equation that directly gives you the radius of a circular motion. Instead, the radius is usually calculated from other known quantities, such as:

1. Using velocity and angular velocity:

* r = v / ω

* where:

* r is the radius of the circular path

* v is the linear velocity of the object

* ω is the angular velocity (in radians per second)

2. Using centripetal acceleration and velocity:

* r = v² / a_c

* where:

* r is the radius of the circular path

* v is the linear velocity of the object

* a_c is the centripetal acceleration

3. Using centripetal force, mass, and velocity:

* r = mv² / F_c

* where:

* r is the radius of the circular path

* m is the mass of the object

* v is the linear velocity of the object

* F_c is the centripetal force

Important Note:

* The choice of equation depends on what information you have available about the circular motion.

* Remember that the radius is a scalar quantity, meaning it only has magnitude (size).

* It's also important to use consistent units for all quantities in the equations.

Let me know if you have specific information about a circular motion, and I can help you calculate the radius!