For this problem, assuming the Earth is a solid sphere of uniform density; with

Question

For this problem, assuming the Earth is a solid sphere of uniform density; with a mass M_Earth = 5.9722 x 10^24 kg and radius = 6,371.0 km. In addition, assuming that you could walk around the equator on land, you would exert a torque on the earth slowing down its rotation if you walked in the right direction. Assuming you exert an external force on the ground of 51.0 N to keep yourself walking at a constant pace, how long would you have to walk to bring the earth to zero angular speed?

(Also assume the earth’s initial angular speed is exactly 1 rev / 24 hrs).

Explanation / Answer

Here ,

initial angular speed , w = 1 rev/day

w = 1 *2pi/(24 * 3600) rad/s

w = 7.271 *10^-5 rad/s

Now , let the time taken is t

Using second law of motion

torque * time = moment of inertia * angular speed

51 * 6371 *10^3 * t = 0.4 * 5.9722 *10^24 * (6371*1000)^2 * 7.271 *10^-5

solving for t

t = 2.17 *10^25 s

the time taken is 2.17 *10^25 s

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.