When we solve for a free symmetric top we find that in body fixed frame, the angular velocity precesses. My confusion is regarding the calculation of omega in body frame. When i am in the body fixed frame, shouldn't the angular velocities be zero, because everything is fixed in this frame?
The angular velocity of some object with respect to an inertial frame can be expressed in any frame. Oftentimes it is expressed in a body-fixed frame. This practice dates back to Leonhard Euler. It turns out to be quite practical because that is the frame in which angular velocity sensors such as gyroscopes sense angular velocity.