Unraveling the Mystery of Gyro and the Transport Theorem

[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 I am not thinking straight

please enlighten me.

 

[Valerie Park]

thank you.The transport theorem states that angular momentum is conserved; thus, the total angular momentum at the beginning and end of the process must be equal. In this case, the total angular momentum of the dish and box before the alteration in direction is equal to the total angular momentum after the alteration. Therefore, the total angular momentum of the dish and box is constant throughout the process. This means that when you lift the dish and alter its direction, the total angular momentum of the dish and box will remain unchanged. However, since the direction of the dish has changed, its angular momentum vector (H) will have changed. This change in the angular momentum vector of the dish can be calculated using equation (1). The change in the angular momentum vector of the box can also be calculated using equation (2). The change in the angular momentum vector of the box is equal to the change in the angular momentum vector of the dish, but with the opposite sign. This is because the angular momentum of the system is conserved and the total angular momentum of the dish and box must remain the same. Therefore, the force you feel when you lift the dish and alter its direction is due to the change in the angular momentum vector of the dish and box. This force can be quantified using equations (1) and (2).