The axis of Earth makes a 23.5* angle with a direction perpendicular to the plan

Question

The axis of Earth makes a 23.5* angle with a direction perpendicular to the plane of earth's orbit. As shown in the figure below, this axis processes, making one complete rotation in 25, 780 y. (Assume L = 7.07 times 10^33 kg - m^2/s.) (a) Calculate the change in angular momentum in half this time. kg middot m^2/s (b) What is the average torque procuring this change in angular momentum? N middot m (c) If this torque were created by a single force (pi is not) acting at the most effective point on the equator, what would its magnitude be N

Explanation / Answer

here change of angular momentum

dL = 2*L*sin 23.5 deg

dL = 0.7974*L

angular momentum of earth L = I W

I is Moment of inertia = 2/5 MR^2

and W is angular velocity

L = 2/5 *M*R^2*w

L = 0.4*5.98*10^24*(6.38*10^6)^2*2*3.14/86400

L = 7.07*10^33 kg-m^2/sec

change in angular momentum will be

dL = 0.7974*7.07*10^33

dL = 5.64*10^33 kg-m^2/sec

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B.torque = dL/dt

dt = 25780*365*24*3600/2

torque = 5.64*10^33*2/(25780*365*24*3600)

torque = 1.38*10^22 N-m

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C. torque = R*F

R is radius

F = torque/R

F = 1.38*10^22/(6.38*10^6)

force F = 2.16*10^15 N

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