Question

Over the last billion years the length of a day has increased from 18 hours to 24 hours. (“Hours” here are the current hours, 3600 s.) Find the average angular acceleration of the Earth during this period.

Answer 1

Initial length of a day = 18 hours = 18*3600 s = 64800s

So, initial angular speed = 2*pi / 64800s = 9.7*10^-5 rad/s

Final length of a day = 24 hours = 24*3600 s = 86400s

So, final angular speed = 2*pi / 86400s = 7.3*10^-5 rad/s

Time taken for this acceleration = 1 billion years = 10^9 years = 10^9*365.25*24*3600s = 3.16*10^16 s

So, the average angular acceleration of the Earth during this period = final angular speed - initial angular speed/ Time taken for this acceleration = 7.3*10^-5 rad/s - 9.7*10^-5 rad/s / 3.16*10^16s = -7.68*10^-22 rad/s^2