Rotation on a Frictionless Table#

Question Text#

Mass $$m_1$$ on the $$horizontal$$ frictionless table of the figure is connected by a string through a hole in the table to a hanging mass $$m_2$$. With what angular speed $$\omega$$ must $$m_1$$ rotate in a circle of radius $$r$$ if $$m_2$$ is to remain hanging at rest? Find an expression for $$\omega$$ in terms of $$m_1$$, $$m_2$$, $$r$$, and $$g$$.

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

For

Use

$$m_1$$

m_1

$$m_2$$

m_2

$$g$$

g

$$r$$

r