Rotation with Constant Angular Acceleration - I

The equations derived for linear motion also hold true for rotational motion if the linear motion variables are replaced by their rotational motion counterparts.

Let ω_0z be the angular velocity of the rotating object at any time t equal to zero and ω_z be its final angular velocity at later time t. If the angular acceleration, α_z, of the object is constant, it can be written as the difference between final and initial angular velocity over time t.

Rearranging this expression, the first kinematic equation for rotational motion is obtained. Thus, the angular velocity at any time equals the sum of initial angular velocity and the change in angular velocity.

To derive the second equation, two equations for average angular velocity are used. One, average angular velocity equals the total change in angular displacement over time t.

Two, for constant acceleration, average angular velocity equals the average of the initial and final velocity. Solving these two equations, the second equation of rotational motion is obtained.

Here, the angular position of an object at any time is represented as the sum of its initial angular position, the displacement moved under constant initial angular velocity, and the angular displacement traveled during the change in angular velocity.