Mass inside a Rotating Cone#

Question Text#

An inverted cone whose walls make an angle theta with the vertical axis. The vertical height measured from the pointed end is h.

As shown in the figure, a small block of mass \(m\) is placed inside an inverted cone. The mass is put into rotational motion around the inside of the cone around a vertical axis with period \(T\). The walls of the cone can be assumed to be frictionless, and make an angle \(\theta\) with the vertical. What is the value of \(T\) if the block is to remain at a height \(h\) above the apex of the cone? Give your answer for \(T\) in terms of \(m\), \(h\), \(g\), and \(\theta\).

Note that it may not be necessary to use every variable. Use the following table as a reference for using each variable:











Answer Section#


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