Partly due to global warming, the Earth\'s rate of rotation about its axis is co

Question

Partly due to global warming, the Earth's rate of rotation about its axis is constantly decreasing, causing the day to increase in duration. In the year 2006, the Earth took about 0.840s longer to complete 365 revolutions than it did in the year 1906. In other words, the duration of 2006 is about.810 s longer than that of 190G. What was the average angular acceleration (in rad/s^2) of the Earth during this time? Assume that in 1906 the Earth took exactly 24 hours to complete one rotation about its axis.

Explanation / Answer

angular velocity in 1906 is 1 rotation per day = 2 *pi / 24 *3600 rad /s

angular velocity in 2006 is 2* pi / (24*3600 + 0.84/ 365)

So average angular acceleration = (2 *pi / 24 *3600) - (  2* pi / (24*3600 + (0.84/ 365))) / (100 * 365 * 24 * 3600)

= 6.14 8 10^-22 rad/s^2

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