What is the Maximum Angular Velocity of a Ball in Horizontal Circular Motion?

[Quantum Mind]

Homework Statement

A ball of mass 0.5 kg is attached to the end of a string of length 0.5 m. The ball rotates in a horizontal circular path about a vertical axis. The maximum tension on the string cannot exceed 324 N. What is the maximum possible angular velocity of the ball in rad/s ?

Homework Equations

mω²/r = tension on the string.

The Attempt at a Solution

I don't think the equation is correct. It should be v and not ω. However, what I wanted to do was to equate the centripetal force with the maximum force on the string. I got the answer as 18, which is not correct. I tried to use mg instead of m but that was wrong too.

The correct equation is T = mg + mLω², but why?

Why can I not use the centripetal force equation here?

 

[technician]

The centripetal force is given by mrω^2 or mv^2/r.
If this ball is on a table in a horizontal circle the r = 0.5m.
If the string is being held in the hand then there will be an angle ∅ to the horizontal.
You will then need to resolve the tension in the string into a vertical component to balance the weight of the ball and a horizontal component to provide the resultant centripetal force.
Hope this helps

 

[technician]

Are sure it is in a HORIZONTAL circle !
The equation you have given as correct is for a VERTICAL circle !