Answer to Question #26257 in Mechanics | Relativity for zameer

Question

Express the rotational kinetic energy of the earth in terms of its period of rotation. The moment
of inertia of the earth about its spin axis is 8.04 × 1037 kg m2. Calculate its rotational kinetic
energy

Answer 1

The rotational kinetic energy equals:
Ec = I*w^2/2
I -moment of inertia
w - angular speed
In another side:
w = 2*pi/T
pi = 3.14
T - period
Finally:
Ec = I*(2*pi/T)^2/2 = 2*I(pi/T)^2
For the Earth -& T = 24 hours = 24*60 minutes = 24*60*60 seconds
Ec = 2* 8.04 × 10^37 kg m2 * (3.14/(24*3600))^2 =& 2.13*10^29 J
Answer: Ec = 2.13*10^29 J