Rotatie met constante hoekversnelling - II

The first and second equations of rotational motion with constant angular acceleration both have time as a variable.

However, the third equation is independent of time. To derive the third equation, begin by rearranging the first equation of rotational motion to obtain an expression for time. Then, substitute the value of time in the second equation of rotational motion.  

Now, rearrange the θ₀ term and multiply both sides by 2α_z. Simplifying it further gives an expression for the final angular velocity in terms of initial angular velocity, angular acceleration, and the difference between the final and initial angular displacements. This is the third equation of rotational motion.

On the other hand, the fourth equation can be obtained by substituting the first equation for rotational motion into the second equation. 

This equation gives the relationship between the final angular position of an object with respect to the initial angular position, the rotation with constant angular velocity, and the rotation due to a change in angular velocity.