Rotation motion or circular motion refers to a type of motion where an object moves in a circular path around a fixed point. This motion can be observed in various mechanical systems, such as spinning wheels, rotating turbines, or a rotating Earth.

Mathematical Formula: The mathematical formula that describes rotation motion is based on rotational kinematics and dynamics. Here are some fundamental equations:

1. Angular Displacement (θ): It represents the change in an object’s angular position and is measured in radians. The equation is given by: θ = s / r where: θ = angular displacement s = arc length or distance moved r = radius of the circular path

2. Angular Velocity (ω): It measures the rate at which an object rotates or changes its angular position. The equation is given by: ω = Δθ / Δt where: ω = angular velocity Δθ = change in angular displacement Δt = change in time

3. Angular Acceleration (α): It represents the rate at which an object’s angular velocity changes. The equation is given by: α = Δω / Δt where: α = angular acceleration Δω = change in angular velocity Δt = change in time

4. Rotational Kinetic Energy (K): It represents the energy associated with an object’s rotation motion. The equation is given by: K = (1/2) I ω^2 where: K = rotational kinetic energy I = moment of inertia of the rotating object ω = angular velocity

These equations provide a basic understanding of rotation motion and can be further expanded or modified depending on specific circumstances or advanced applications.