If you had to stop the earths spinning ? Do this for your own good. You have bee

Question

If you had to stop the earths spinning ?

Do this for your own good. You have been assigned the task of stopping the Earth's spinning over a period of one week by using solid rocket boosters used to launch the space shuttle. Each booster can exert a thrust force of 15 times 106 N and bums for 2 mnts. Calculate the minimum number of rocket boosters you will need to get the job done. Neglect effects due to Earth's atmosphere. Show your work in detail. You have been assigned the task of stopping the Earth's spinning within a week by using solid rocket boosters used on the space shuttle. Calculate the angular momentum of Earth rotation about the North- South axis. Assume that these boosters will bum at a constant rate for 2 mnts. How many boosters will you need?

Explanation / Answer

Moment of inertia of earth= 2/5 MR2=2/5 *5.97*1024*(6.38*106)2=9.72*1037 kg.m2.

Force due booster, F=15*106 N

Torque due to booster= FxR=15*106*6.38*106=9.57*1013 Nm.

Angular acceleration, ?= torque/Inertia=9.57*1013/9.72*1037=1.0324*10-24 rad s-2.

Change in angular speed due to each launch= ?*t=1.0324*10-24*120sec=1.2388*10-22 rad/sec

Angular speed of earth= 2?/time period =2*3.14/24hrs=7.2722*10-5 rad/sec

Let us launch n boosters, then:

n*1.2388*10-22=7.2722*10-5

n=5.870*1017 boosters.

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