Suppose you swing a ball of mass (m) in a vertical circle on a string of length (l). as you probably know from experience, there is a minimum angular velocity you must maintain if you want the ball to complete the full circle without the string going slack at the top.1. find an expression for the minimum angular velocity using only the terms (g) and (l).2. evaluate the angular velocity in rpm for a 65 g ball tied to a 2.0-m-long string.

a)

b)N= 21.29 rpm

Explanation:

   Given that

Mass of the ball =m

Length of string = L

Lets take angular speed = ω

The centripetal force on the ball

F = m ω² L

To complete the circle ,at the top condition the force due to gravity should be equal to the centripetal force

Gravity force = mg

F= mg

m ω² L = m g

ω² L =  g

When L= 2 m  

Lets take g =10 m/s²

ω = 2.23 rad/s

To convert in rpm

N=Speed in rpm

N= 21.29 rpm

the answer for apex is the lowest

see earlier