Consider the case of a rotating wheel at rest and starting a clockwise rotation, meaning the negative direction of the angular velocity, and increasing (negatively) its value up to -12 rad/sec for 2 seconds. It then maintains a constant velocity for 2 seconds, and then uniformly reduces the magnitude of the velocity for 2 seconds until the wheel is momentarily stopped and restarts its rotation counter-clockwise with positive angular velocity, accelerating up to 20 rad/sec in 2 seconds and remaining at a constant rotation for 2 more seconds. Finally, the wheel stops gradually in 2 seconds. Next, you can see the graph of angular velocity versus time of this rotation

1. Consider the case of a rotating wheel at rest and starting a clockwise rotation, meaning the negative direction of the angular velocity, and increasing (negatively) its value up to -12 rad/sec for 2 seconds. It then maintains a constant velocity for 2 seconds, and then uniformly reduces the magnitude of the velocity for 2 seconds until the wheel is momentarily stopped and restarts its rotation counter-clockwise with positive angular velocity, accelerating up to 20 rad/sec in 2 seconds and remaining at a constant rotation for 2 more seconds. Finally, the wheel stops gradually in 2 seconds. Next, you can see the graph of angular velocity versus time of this rotation:

1. Apply the angular position equation.

with θo=0, wo=0, substituting the value of the angular acceleration in the range from 0 to 2 seconds obtained in question 2, perform the tabulation of values to fill the following table; describe the type of parabola and draw the graph:

Tabulation of values

Graph

1. Continue applying the angular position equation, but now in the following form:

Here you must substitute the values of initial angular velocity (ω1) and angular acceleration (α1), which correspond to the range from 2 to 4 seconds. Applying the value of t=2 seconds and the corresponding value θ from the table of question 17, obtain the value of   θ₁, in order to write the equation of the line, describe its characteristics, tabulate its values and draw the graphs:

Tabulation of values

Graph

1. Continue applying the angular position equation for the following range from 4 to 6 seconds:

Here you must substitute the values of initial angular velocity (ω1) and angular acceleration (α1) which correspond to the range from 4 to 6 seconds. Applying the value of t=4 seconds and the corresponding value θ from the table of question 18, obtain the value of θ₁, in order to write the equation of the line, describe its characteristics, tabulate its values and draw the graphs:

Tabulation of values

Graph

1. Continue applying the angular position equation for the following range from 6 to 8 seconds:

Here you must substitute the values of initial angular velocity (ω1) and angular acceleration (α1), which correspond to the range from 6 to 8 seconds. Applying the value of t=6 seconds and the corresponding value θ from the table of question 18, obtain the value of  θ₁, in order to write the equation of the line, describe its characteristics, tabulate its values and draw the graphs:

Tabulation of values

Graph

1. Continue applying the angular position equation for the following range from 8 to 10 seconds:

In which you must substitute the values of initial angular velocity (ω₁) and angular acceleration (α1), which correspond to the range from 8 to 10 seconds. Applying the value of t=8 seconds and the corresponding value θ  from the table of question 19, obtain the value of  θ₁, in order to write the equation of the line, describe its characteristics, tabulate its values and draw the graphs:

Tabulation of values

Graph

1. Continue applying the angular position equation for the following range from 10 to 12 seconds:

Here you must substitute the values of initial angular velocity (ω₁) and angular acceleration (α1), which correspond to the range from 10 to 12 seconds. Applying the value of t=10 seconds and the corresponding value θ from the table of question 20, obtain the value of  θ₁, in order to write the equation of the line, describe its characteristics, tabulate its values and draw the graphs:

Tabulation of values

1. Finally, draw the full graph (range from 0 to 12 seconds) using the graphs drawn in the previous questions: