An end of a light wire rod is bent into a hoop of radius r. the straight part of the rod has length l; a ball of mass m is attached to the other end of the rod. the pendulum thus formed is hung by the hoop onto a revolving shaft. the coefficient of friction between the shaft and the hoop is µ. find the equilibrium angle between the rod and the vertical.

Explanation:

By the Law of Sines,

From Newton's Law,

And the last equation again from Newton's Law,

Then if we collect all equations together,

Thus,

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.