text: a ball is rotating? in a horizontal circle at the end of a string (length = 3.2 m) at an angular velocity of 11.5 rad/s.  the string is gradually shortened to 2.7 m without any force being exerted in the direction of the ball's motion.  find the new angular velocity of the ball in rad/s.  and find it's new linear speed in units of m/s. angular velocity varies inversely as the radius. shorten the radius and the angular velocity increases. express this by using a constant k.  11.5=k/3.2              x=k/2.7  divide the 2 equations:  11.5/x=(1/3.2)/(1/2.7) 11.5/x=2.7/3.2 x=11.5*3.2/2.7   =13.63rad/s   linear speed=angular velocity*radius      v=13.63*2.7   =36.8m/s