Converting yaw between frames

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Hi all, I have a query regarding converting yaw between frames.

The velocity commands (linear and angular) received from the base local planner are in term of robot's frame. Let says that I want to convert the velocity commands into the map's frame in gazebo, do I need to do conversion on the angular velocity?

My intuition is that since the orientation of z-axis in both robot frame and map frame are the same, the yaw in both frame should be the same right?

The reason I asked this question is because after I did an angular velocity conversion between the robot frame and world frame, the values I got are different.

1st update: The way I did the conversion is as such, rot is the double value of the original angular velocity.

(Q_is geometry_msg::quaternion , QS_ and QS_tr is geometry_msgs::QuaternionStamped )

 Q_ = tf::createQuaternionMsgFromYaw(rot_);
 QS_.header.frame_id = "base_link";
 QS_.header.stamp = ros::Time();
 QS_.quaternion = Q_;

 listener.transformQuaternion("/map", QS_, QS_tr);
 yaw = tf::getYaw(QS_tr.quaternion);