To describe circular motion, we will use radians and not degrees. But you will need to convert back and forth between these two measurement systems.

2π=360°

Next examine the distance and radian relationship.

Some terms to be familiar with when solving word porblems:

• 1 Revolution = 2πr
• 1 Rotation = 2πr
• 1 Cycle = 2πr
• 1 Spin = 2πr
• 360° = 2π rad
• 180°= π rad

The measurement of a radian is not a unit. It is a measurement. This is because if I rearrange the formula s=rθ for θ. I get a length measurement divided by another length measurement.

These length units divide out. The term, "rad," is used to represent the radian on an answer. It is used on answers as if it was a unit of measurement.

In linear kinematics, the average velocity is defined as how quickly the postion is changed. In rotational motion, the velocity is called the angular velocity and it is defined as how quickly the angled is changed. The lower case Greek letter omega, "ω," is used to represent the angular velocity.

Δθ = θ_f - θ_o. The units for the angular velocity are radians/second. This is written as "r/s."

Previously acceleration was described as the how quickly the velocity changes. With rotational kinematics the angular acceleration is defined as how quickly the angular velocity, ω, changes. The formula is

α is the angular acceleration. "α" is the lowercase Greek letter alpha. Δω is the ω_final - ω_initial. Δt is the elapsed time.