Because of the friction between the water in oceans with the earth’s surface, the rotational kinetic energy of the earth is continuously decreasing. If the earth’s angular speed decreases by 0.0016 rad/day in 100 years, find the average torque of the friction on the earth. Radius of the earth is 6400 km and its mass 6.0 × 1024 kg.
The average frictional torque is 
Given
The time taken for the angular speed of the earth to decrease by 0.0016 rad/day is given as 100 years. Radius of the earth is 6400 km and its mass 6.0 × 1024 kg.
Formula Used
To find the formula of the frictional torque we find the product of the moment of inertia and the angular acceleration of the object as
where
is the average frictional torque, I is the moment of inertia and α is the angular acceleration.
Explanation
To find the angular acceleration for the torque formula we state the basic finding
The initial angular velocity of earth is ω=2ϖ
The final angular velocity of earth is ω=2ϖ-0.0016 rad/day
Hence, to find the angular acceleration we find the value of acceleration by putting the value of initial and final velocity in the formula
The moment of inertia of the spherical earth is given by the formula of sphere as
Therefore, the frictional torque is calculated as
