Circular Motion Problem -- Ball on a String Spinning in a Vertical Circle

[Al-Layth]

Homework Statement

A ball of 5.0 kg mass is attached to the end of a long wire and whirled around in a perfect
circle of 0.9 m radius in the vertical plane. Calculate the following:

Calculate the Minimum Velocity and Minimum Angular Velocity

Relevant Equations

#F= m\frac{v^2}{r} = mw^{2}r#

#m: Mass#
#v: Speed#
#r: Circle Radius#
#w: Angular Velocity#

#F= m\frac{v^2}{r} = mw^{2}r#

#m=5#
#r=0.9#

#F= 5\frac{v^2}{0.9} = (0.9)5w^{2}#

#5\frac{v^2}{0.9} = (0.9)5w^{2}#

#\frac{v^2}{0.9} = (0.9)w^{2}#

#v=0.9w#

then I get stuck cause I have both unknowns in one equations (i bet it has something to do with the question’s use of “minimum” but I don’t know where to go from here) so help mee thx

 

[mjc123]

The question says the circle is in the vertical plane. What else do you have to take account of in this case?

 

[Orodruin]

Where is the velocity minimal? What is required for the string to be taut there?