gyro is weird

alctel

Gyro seems to weird when i think abt it using the transport theorem.
i mean for a spinning dish, symmetric one,
{Total moments acting on it} = Hdot + w x H --- (1)
where H is the angular moment of the dish, w is its angular velocity.

then when i consider that it spins inside a box.
when u lift it and alter the direction, u will FEEL that sth is acting aginst u.
but how it can be quantified by transport theorem?
{Total moments acting on box + dish} = H'dot + w' x H' --- (2)
where H' is the angular momentum of the box + dish,
as well as the w'.
how to put (1) into (2)?... perhaps im not thinking straight

please enlighten me.