A space station consists of a uniform circular disc. Initially it rotates with angular velocity about the -axis, perpendicular to the plane of the disc and passing through its centre. At booster rockets fire, applying a constant torque about the -axis (in the plane of the disc).
Show that, in the body-fixed system, the angular velocity of the station varies
as
[21 marks]
Calculate the angular momentum of the station at .
[4 marks]
[You may use the fact that Euler's equations for a rotating body have the
forms
[Hints can be found here, but do not follow this link until you have attempted the question on your own.]