A disc of radius  r is rotating about its center with an angular speed  ω0. It is gently placed on a rough horizontal surface. After what time it will start pure rolling?

Given radius of disc= rAngular speed= ω0Applying law of conservation of angular momentum about a point on the horizontal surface,Iω0=mvr+Iω​⇒mr22ω0=mvr+mr22vr​⇒v=ω0r3Velocity of center of disc when it starts pure rolling isω0r3 From  v=u+at⇒v=at⇒t=va(∵a=μg)⇒t=ω0r3μg