Find the rotational kinetic energy and angular momentum about its axis of the earth due to its daily rotation. Let ME = 6 x 1024 kg, RE = 6.4 x 106 m and We = 1.157 x 10-5 rev/sec.
To find the rotational kinetic energy of the Earth, we can use the formula:
Rotational Kinetic Energy = (1/2) * Moment of Inertia * Angular Velocity^2
To calculate the moment of inertia of the Earth, we need to know its mass (ME) and radius (RE).
Moment of Inertia of a solid sphere about its axis is given by the formula:
I = (2/5) * m * r^2
Substituting the values, we have:
I = (2/5) * ME * RE^2
Next, we need to find the angular velocity (We) in radians per second. We are given the angular velocity in revolutions per second, so we need to convert it.
1 revolution = 2π radians
Angular velocity in radians per second = We * 2π
Now, we have all the information needed to calculate the rotational kinetic energy:
Rotational Kinetic Energy = (1/2) * I * (We * 2π)^2
To find the angular momentum, we use the equation:
Angular Momentum = Moment of Inertia * Angular Velocity
Angular Momentum = I * We
Substituting the values, we can now calculate both the rotational kinetic energy and angular momentum of the Earth.