# Mass inside a Rotating Cone#

## Question Text#

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:

For

Use

$$m$$

m

$$h$$

h

$$g$$

g

$$\theta$$

theta