The basic rotational measure of position is angle in radians. Angle is defined by its relationship to a circle. If you construct an arc of a circle containing angle θ then the distance measured along the arc, s, and the radius of the circle, r, are related to θ by s=rθ. A complete circle spans 2π radians.
If a body rotates about an axis fixed in space then the rate of change of the angle between a point on the body and fixed line is the angular velocity, ω (pronounced omega), with units of radians/second. The linear velocity of a point on the body a distance r from the axis is v=rω.
If the angular velociy is not constant then we have an angular acceleration, α, with units of radians/second2. The tangential acceleration of a point on the body a distance r from the axis is at=rα.
This tangential acceleration is separate from and perpendicular to the regular centripetal acceleration needed to make a point on the body travel in a circle. That still has value ac=v2/r=rω2.
If a body starts from angle θ0 with initial angular speed ω0 and constant angular acceleration α then the position and velocity at any future time t are given by
ω = ω0 + αt
θ = θ0 + ω0t + ½αt2
ω2 = ω02 + 2α( θ - θ0)
The rotational equivalent of force is Torque, τ, also called the moment of force. The torque produced by a force F acting a perpendicular distance r from and axis is τ=rF. In the more general case of a vector force F acting at a vector displacement r from an axis the torque is τ = |r||F|sin(angle between).
A torque τ acting on a point mass m held at fixed radius r from an axis will produce an angular acceleration α about that axis and τ = mr2α = Iα where I is the moment of inertia, a rotational quantity that plays the role equivalent to mass in linear motion. For a single point mass m at radius r we have I = mr2. Rigid bodies rotation about a fixed axis also have moments of inertia but they are hard to compute and we are best to look them up in a table.
A body with moment of inertia I rotating at angular velocity has a rotational kinetic energy = ½Iω2.
A body moving generally through space moves with its centre of mass following the trajectory for a point of the same total mass while the body in general rotates about the centre of mass. In that case the total energy is given by ½mv2 + ½Iω2 where I is moment of inertia about an axis through the center of mass.
We can also define the angular momentum L of a body rotating about a fixed axis with angular velocity ω to be L = Iω where I is the moment of inertia about the axis. If a system of bodies moves together in a way that is free from external torques then the angular momentum of the system is conserved.
One of the best examples of conservation of angular momentum is a satellite orbiting a planet under the influence of gravity. Since the gravity force asts along the line joining the bodies it cannot apply a torque. In that case as the distance between the satellite and the planet increases the orbital velocity must decrease to keep Iω constant.