A spherical asteroid with radius r = 123 m and mass M = 2.50×1010 kg rotates abo

Question

A spherical asteroid with radius r = 123 m and mass M = 2.50×1010 kg rotates about an axis at four revolutions per day. A "tug" spaceship attaches itself to a vehicle which follows the asteroid's south pole (as defined by the axis of rotation) and fires its engine, applying a force tangentially to the asteroid's surface keeping the direction of the force in the same plane. The initial situation is shown in the figure. (Figure 1) . Part A If F = 265 N, how long will it take the tug to rotate the asteroid's axis of rotation through an angle of 11.0 by this method?

Explanation / Answer

MoI J = 2/5 mr^2 =123*2.50*10^10/2.5 =
torque T = F*r = 265*123 = 32,595.00 Nm
/t = = T/J = 265*2.5/(123*2.50*10^10) = 2.15*10^-10 rad/sec^2
=11/360*2PI = 0.1919 rad
2 = *t^2
t = 2/ = 0.1919*2/(2.15*10^-10) = 42.250 sec

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