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 2.5 rad.What is its average angular acceleration? A) 0.098 rad/s² B) 0.05 rad/s² C) 1.8 rad/s² D) 0.60 rad/s²

Question

Quizplus · Accepted Answer

We can use the formula for average angular acceleration:

average angular acceleration = change in angular speed / change in time

The final angular speed is given as 0.70 rad/s and the initial angular speed is 0 (since the Ferris wheel starts at rest). The time it takes to rotate through an angular displacement of 2.5 rad can be found using the formula:

angular displacement = (average angular speed)(time)

rearranging this formula gives:

time = angular displacement / average angular speed

Plugging in the values we get:

time = 2.5 rad / 0.70 rad/s = 3.57 s

Therefore, the change in angular speed is:

change in angular speed = final angular speed - initial angular speed = 0.70 rad/s - 0 rad/s = 0.70 rad/s

So, the average angular acceleration is:

average angular acceleration = change in angular speed / change in time = 0.70 rad/s / 3.57 s = 0.098 rad/s^2

The closest answer choice to this value is A: 0.098 rad/s^2, so that is the correct answer.

A Ferris Wheel Starts at Rest and Builds Up to a Final