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Answer to Question #26257 in Mechanics | Relativity for zameer

Question #26257
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
Expert's answer
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

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