A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 4.9 rad. What is its average angular acceleration

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.

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