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Angular displacement refers to the change in the angle as an object rotates around a fixed point. Imagine it as an arc length on the edge of a circle made by the rotating object.
To calculate angular displacement, you find the difference between the initial and final angular positions. Mathematically, it's represented as:

• \( \Delta \theta = \theta - \theta_0 \)

Here, \( \theta_0 \) is the initial angle, and \( \theta \) is the final angle. It's important to note that angular displacement can be positive or negative depending on the direction of rotation.
This direction is usually represented using algebraic signs. A positive value indicates a counterclockwise rotation, while a negative value indicates a clockwise rotation.
You use radians to measure angular displacement because they provide a direct relationship to the arc length.

Angular motion describes any object moving along a circular path. It involves not just angular displacement, but also angular velocity and acceleration.
In angular motion, every angle covered means the object has undergone some rotation. This rotation forms the basis of measuring how fast or slow the rotation happens.
Angular velocity further defines how swiftly the angle changes with time. It tells us the rotational speed and direction:

• \( \omega = \frac{\Delta \theta}{\Delta t} \)

Here, \( \omega \) is the angular velocity, \( \Delta \theta \) is the angular displacement, and \( \Delta t \) is the elapsed time. The measure is in radians per second \( \text{rad/s} \).
For a complete description of angular motion, it's useful to understand angular acceleration, which measures how quickly the angular velocity changes. But in many typical angular motion problems, such as calculating average angular velocity, we focus on just angular displacement and elapsed time.

Rotational kinematics is similar to linear kinematics but deals specifically with rotational motion. It helps predict future motion of rotating objects based on known parameters like time, angular displacement, and angular velocity.
Generally, the basic equations of rotational kinematics mirror those of linear motion. This includes relations between angular displacement, velocity, and acceleration.
Even though this exercise focuses on average angular velocity, it's part of a broader study of rotational motion that incorporates:

• Initial and final angular velocities
• Constant angular acceleration
• The relationship of these parameters over time

By understanding these concepts well, you can tackle more complex tasks, such as predicting the point where an object will stop or speed up under constant torque.
Rotational kinematics forms the backbone of many practical applications, from engineering mechanisms to understanding celestial movements.