A uniform circular disc of radius r is placed on a rough horizontal surface and given a linear velocity v 0 and angular velocity ω ω 0 as shown. The disc comes to rest after moving some distance to the right. It follows that
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Since the disc comes to rest, it stops rotating & translating simultaneously.
⇒ ⇒ v = 0 & ω ω = 0. That means, the angular momentum about the instantaneous point of contact just after time of stopping is zero we know that, the angular momentum of the disc about P remains constant because frictional force f. N & mg pass through the point P, thus produce no torque about this point
⇒ ⇒ L initial = L final ⇒ ⇒ mv 0 r – I 0 ω ω 0 = 0
⇒ ⇒ m v 0 r = I 0 ω ω 0 ⇒ ⇒ m v 0 r = 
m r 2 ω ω 0 .
⇒ ⇒ 2 v 0 = ω ω 0 r.
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