A spherical satellite with a radius of 75m is spinning over its own axis with an

Question

A spherical satellite with a radius of 75m is spinning over its own axis with an angular speed of 232rad/s. The satellite has equipment inside distributed such that the satellite can be considered a uniform solid sphere. At some point, due to a failure in the anchor system, all equipment get loose and moves towards the walls of the satellite to form a thin layer such that now the satellite can be considered a uniform thin spherical shell. a) Calculate the angular momentum of the satellite before the failure. b) What is the angular momentum after the failure? c) What is the angular speed after the failure? d) Calculate the rotational kinetic energy before and after the failure.

Explanation / Answer

suppose mass of satellite is m.

a) Angular Momentum = I = (2mr2 /5) x 232 = 92.8m x 752 = 522000m

b) whaterver is changing is inside, no force is acting .

so angular momentum will not change, it will be same.

so after angular mometum = 522000m

c) after failure I = 2mr2 /3

so 522000m = (2m752 /3) x f

f = 139.2 rad/s

d) before,

rot. K.E. = I2 /2 = (2m752 /5) x 2322 /2 = 60552000m J

after,

rot. K.E.f = (2m752 /3) x 139.22 /3 = 36331200m J

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