A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig=20 kg*m^2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is Is= 5*10^5 kg*m^2. Neither the spacecraft nor the gyroscope is originally rotating. They gyroscope can be powered up in an negligible period of time to an angular speed of 100 rad/s. If the orientation of the spacecraft is to be changed by 30 degrees, for what time interval should the gyroscope should be operated?.

Question

A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig=20 kg*m^2 about the axis of the gyroscope.  The moment of inertia of the spacecraft around the same axis is Is= 5*10^5 kg*m^2.  Neither the spacecraft nor the gyroscope is originally rotating.  They gyroscope can be powered up in an negligible period of time to an angular speed of 100 rad/s.  If the orientation of the spacecraft is to be changed by 30 degrees, for what time interval should the gyroscope should be operated?.