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Angular speed is a measure of how quickly an object rotates or revolves around a fixed point or axis. It's analogous to linear speed but instead relates to rotation. In the context of our exercise, the initial angular speed (\( \text{ω}_i \)) of the engine’s rotor is given as 2000 rad/s, indicating a very swift rotational motion.

For an object slowing down, like the airliner engine's rotor, angular speed decreases over time. This deceleration is described mathematically by the equation \( \text{ω} = \text{ω}_i - \text{α}t \) where \( \text{ω} \) represents the final angular speed, \( \text{ω}_i \) is the initial angular speed, \( \text{α} \) is the angular acceleration, and \( t \) is the time. To enhance comprehension of the solution, consider angular speed as the rotational equivalent of the speed you experience when driving; just as you watch the speedometer change as you apply the brakes, so too does the rotor's angular speed decrease when the engine is turned off.

Rotational motion pertains to objects moving in a circular path around a central point, such as the earth orbiting the sun, or in our case, an airliner's engine rotor spinning on its axis. The key aspects of rotational motion are radius, angular speed, and angular acceleration. In our exercise, the focus is purely on the rotor's change of angular speed, representing its rotational motion.

Understanding rotational motion involves grasping that all points on the rotor move through the same angle but cover different linear distances depending on their distance from the axis—similar to runners on different tracks of a racing field. The outermost points move faster to complete a rotation, but the angular speed, measured in radians per second (rad/s), stays the same for all points on the rotor.

Kinematics is the branch of mechanics that deals with the motion of objects, including displacement, velocity, and acceleration, without considering the forces that cause the motion. The kinematic equations used in linear motion have direct analogs in rotational motion, with angular displacement, angular speed, and angular acceleration replacing their linear counterparts.

In our example of the engine rotor, kinematics allows us to predict the future state of motion by using the known values of angular speed and angular acceleration. By applying the kinematic equation \( \text{ω} = \text{ω}_i - \text{α}t \) for deceleration, we predict the rotor’s angular speed at any given time, until it comes to rest. This is powerful as it gives us insights without needing to know the specifics of the forces involved, such as friction in the engine.