If the ball is released from rest at a height of 0.63 m above the bottom of the track on the no-slip side, what is its angular speed when it is on the frictionless side of the track

When the ball is on the frictionless side of the track , the angular speed is 89.7 rad/s.

Explanation:

Consider the ball is a solid sphere of radius 3.8 cm and mass 0.14 kg .

Given ,  mass, m=0.14 kg

Ball is released from rest at a height of, h= 0.83 m

Solid sphere of radius, R = 3.8 cm

                                       =0.038 m

From the conservation of energy

                          ΔK  = ΔU  

Here ,

 v=

=

= 3.408 m/s

Hence, angular speed when it is on the frictionless side of the track,

   = (3.408 m/s)/(0.038 m)

  =  89.7 rad/s

Hence , the angular speed is 89.7 rad/s