Answer:
The average angular acceleration is 0.05 radians per square second.
Explanation:
Let suppose that Ferris wheel accelerates at constant rate, the angular acceleration as a function of change in angular position and the squared final and initial angular velocities can be clear from the following expression:
Where:
,
- Initial and final angular velocities, measured in radians per second.
- Angular acceleration, measured in radians per square second.
,
- Initial and final angular position, measured in radians.
Then,
Given that ,
and
, the angular acceleration is:
Now, the time needed to accelerate the Ferris wheel uniformly is described by this kinematic equation:
Where is the time measured in seconds.
The time is cleared and obtain after replacing every value:
If ,
and
, the required time is:
Average angular acceleration is obtained by dividing the difference between final and initial angular velocities by the time found in the previous step. That is:
If ,
and
, the average angular acceleration is:
The average angular acceleration is 0.05 radians per square second.