The earth’s rate of rotation is constantly decreasing, causing the day to increase in duration. in the year 2006 the earth took about 0.840 s longer to complete 365 revolu- tions than it did in the year 1906. what was the average angular acceleration, in rad> s2 , of the earth during this time?

Approximately .

Explanation:

Angular acceleration is equal to .

Apparently, for this question, the time taken is . The challenge is to find the change in angular speed over that period of time.

Let the time (in seconds) it took to complete revolutions be in the year 1906. In 2006 that number would be .

Each revolution is radians. revolutions will be an angular displacement of in radians. Angular speed is equal to .

The average angular speed in 1906 could thus be written as .

Similarly, the average angular speed in 2006 could be written as .

The difference between the two will be equal to:

.

Since the value of (about the same as the number of seconds in 365 days) is much bigger than , apply the approximation .

.

And that's approximately the average change in angular velocity over a period of 100 years. Apply the formula for average angular acceleration:

.