How Does the Sum of Angular Velocities Affect System Motion in Physics?

[yetar]

Homework Statement

Suppose we have a horizental massless tube.
One end of the tube is welded to seomthing that rotates on an angular velocity of w1=(0, 1, 0), on the other end of the tube there is a disk, which rotates with an angular velocity of w2=(0, 0, 2)
The system's angular velocity is w1+w2, and the kinetic energy of the system may be calculated, but I don't understand what is the meaning of the angular velocity w1+w2 in respect to the problem.
Thank you.

Homework Equations

The Attempt at a Solution

 

[arunbg]

If you are asking for the resultant of the two angular velocities, then you have to add them vectorially, component-wise that is.

 

[m2003]

The angular velocity w1+w2 represents the combined rotational motion of the two components in the system - the rotating tube and the rotating disk. It is the sum of the individual angular velocities, and it describes the overall rotational speed and direction of the system. In this case, the system is rotating in the x-z plane with a rotational speed of 2 rad/s in the z-direction and 1 rad/s in the x-direction. This information is useful in calculating the kinetic energy of the system, which is equal to 1/2 * I * w^2, where I is the moment of inertia and w is the angular velocity. The meaning of the angular velocity w1+w2 is important in understanding the overall motion and energy of the system.