A ball is rotating?

Question

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.

Answer 1

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