Final answer:
The question appears to seek the third derivatives w_{xxx}, w_{yyy}, and w_{zzz} of w=(x^2+y^2+z^2)^(1/2). However, the provided information is off-topic or incomplete, discussing rotational kinematics instead. More context is needed for a full solution.
Step-by-step explanation:
To find the third derivatives w_{xxx}, w_{yyy}, and w_{zzz} of the function w=(x^2+y^2+z^2)^(1/2), we would need to perform partial differentiation three times with respect to each variable. However, judging from what is provided in the question, it appears to be either incomplete or off-topic, mentioning equations related to rotational kinematics that don't directly apply to the calculation of the required third derivatives for the function of w given. If the actual question seeks to relate kinematics with the function w, more context would be required for a proper solution.