Question about a Conical Pendulum

[patiladitya98]

Homework Statement

A conical Pendulum, a uniform, thin rod of mass m and length l, rotates about a vertical axis with angular velocity omega. Find the angle between the vertical and the rod.

Homework Equations

The Attempt at a Solution

I know the usual approach to solve this question, write the pseudo force of an elemental and then integrate, as we sit on a rotating frame of reference. I was wondering if there's anyone who's solved the question in an inertial frame instead? It may get a bit complicated in an inertial frame, but I was curious if we can solve it, because I tried to, and failed.

 

[jbriggs444]

When in doubt, the answer is always the same: Start with a free body diagram. What forces exist and what accelerations exist?

The centripetal force required to keep the entire rod in uniform circular motion is the sum of the centripetal forces required to keep each individual piece in uniform circular motion. Instead of integrating centrifugal forces, integrate centripetal forces and you ought to get a very similar result.