Gyro question

Read the picture please. My question is: where does the work done by torque T go and is the equation on left all right? No gravity, no friction.
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 Come on man, how come this problem be an Introductory Physics homework?
 Trying showing some work and explaining the situation a little. What you're given and such. All i see is a spinning disc with some 'spin' and torque.

Gyro question

Sorry.

The "spinning disk" is a gyro spinning at angular speed omega and the moment of inertia about this spinning axis is I.

A torque T is applied on the gyro and perpendicular to spin axis, the torque is also called gyroscopic torque.

The rotation caused by torque T is theta. theta dot is derivative of theta, theta dot dot is second order derivative of theta. Moment of inertia about theta axis is Iy (perpendicular to spin axis).

My question: is the equation on the left of the picture all right? The work done by T (gyroscopic torque) contributes to what, where it goes finally?
 The work done by T torque is the... κινητικη ενεργεια... kinimatecal or mobility energy how you call it. If I understood correct the T at first stops the gyro THEN makes it move with a different dirrection. So at first it has negative work (takes from it's energy because of the movement) and after the stop it gives to it.
 Not that case. The spinning gyro is at rest at beginning; then a torque is applied. What happens? If torque is dismissed after a while, then what?
 Solved! I figured it out.

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