WILL GIVE BRAINLIEST AND 30 POINTS!
What is a criterion for all products made using the process of technological design?

The product must be cheaper than similar products.
The product must be available to any user who wants it.
The product must solve the problem for which it was designed.
The product must be capable of solving a variety of problems.

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.