Answer:
a) τ = 4.47746 * 10^25 N-m
b) E = 2.06301 * 10^13 J
c) P = 3.25511*10^21 W
Explanation:
Given that,
The radius of earth r = 6.3781×10^6 m
The angular speed of earth w = 7.27*10^-5 rad/s
The time taken to reach above speed t = 5 yrs = 1.57784760 * 10^8 s
The mass of earth m = 5.972 × 10^24 kg
The inertia of sphere I = 2/5 * m* r^2
Solution:
angular acceleration of the earth from rest to w is given by α:
α = w / t
α = (7.27*10^-5) / (1.57784760 * 10^8)
α = 4.60754*10^-13 rad/s^2
The required torque τ is given by:
τ = I*α
τ = 2/5 * m* r^2 * α
τ = 2/5 *(5.972 × 10^24) * (6.3781×10^6)^2 * (4.60754*10^-13)
τ = 4.47746 * 10^25 N-m
Power required P to turn the earth to the speed w is:
P = τ*w
P = (4.47746 * 10^25)*(7.27*10^-5)
P = 3.25511*10^21 W
Energy E required is :
E = P / t
E = (3.25511*10^21) / (1.57784760 * 10^8)
E = 2.06301 * 10^13 J
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