a smooth sphere A is moving on a frictionless horizontal plane with angular speed w and centre of mass velocity v. it collides elastically with another identical sphere b at rest. after collision their ang. sped are w1 and w2. thenA- w1

if there is friction bw surfaces of two sphere then due to some frictional torque both sphere will loose some of its rotational KE in the form of heat .... it is given that collision is elastic so there is no change in rotational KE of both particles ...

angular velocity of each body is conserved ....

but for center of mass of both spheres velocity will become diffenrnt ...

from conservation of momentam

mv = mv₁ + mv₂

v₁ + v₂ = v           ...................1

from conservation of KE

mv² = mv₁² + mv₂²              .................2

on solving these two eqns

v₁ = 0 , v₂ = v

these parameters are just after collision....

body dosent move continiously with angular velocity , its linear velocity starts increasing

& angular velocity decreases upto the instant when body starts pure rolling(v = wr) ....