Question

A uniform circular disc of radius r is placed on a rough horizontal surface and given a linear velocity v₀ and angular velocity ω₀ as shown. The disc comes to rest after moving some distance to the right. It follows that

• A. 3 v₀ = 2ω₀ r
• B. 2 v₀ = ω₀ r
• C. v₀ = ω₀ r
• D. 2 v₀ = 3 ω₀ r

Answer 1

Answer: (B)

2 v₀ = ω₀ r

Answer 2

Since the disc comes to rest, it stops rotating & translating simultaneously.

⇒ v = 0 & 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 ⇒ mv₀ r – I₀ ω₀ = 0

⇒ m v₀ r = I₀ ω₀ ⇒ m v₀ r = $\frac { 1 } { 2 }$ m r² ω₀.

⇒ 2 v₀ = ω₀ r.