so orbits around the Sun. For this problem use the tollowing constan Mass of the

Question

so orbits around the Sun. For this problem use the tollowing constan Mass of the Earth: 5.97 x 1024 kg (assume a uniform mass distribution) Radius of the Earth: 6371 km Distancc of Earth from Sun: 149,600,000 knm Part (a) Calculate the rotational kinctie encrgy of thc Earth due to rotation about its axis, in joulcs Numeric : A numcric value is expected and not an expression K.R Part (b) What is the rotational kinetic energy of the Earth due to its orbit around the Sun, in joules? Numerie : A numeric value is expected and not an expression. Kr,O=

Explanation / Answer

Rotational kinetic energy is

KE = 1/2Iw^2

I = moment of inertia = 2/5MR^2

I = 2/5 x 5.97 x 10^24 x (6371 x 10^3)^2

I = 9.693 x 10^37 kg-m^2

angular velocity (w) = 2pi / (24 x 3600) = 7.27 x 10^-5 rad/s

KE = 1/2 x 9.693 x 10^37 x (7.27 x 10^-5)^2

KE = 2.57 x 10^29 J

b)

I = MR^2

I = 5.97 x 10^24 x (149600000 x 10^3)^2

I = 1.336 x 10^47 kg-m^2

w = 2pi / t

w = 2pi / (365 x 24 x 60 x 60)

w = 1.99 x 10^-7 rad/s

KE = 1/2Iw^2

KE = 1/2 x 1.336 x 10^47 x (1.99 x 10^-7)^2

KE = 2.64553 x 10^33 J

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