A disc of mass 100g and radius 10cm has a projection on its circumference. The mass of projection is negligible. A 20g bit of putty moving tangential to the disc with a velocity of 5ms^-1 strikes the projection and sticks to it. The angular velocity of disc is

M = 100 gm = 100 x 10^-3 = 10^-1 kg 

m = 20gm = 2 × 10^–2 kg 

R = 10cm = 10^–1m, v = 5m/s 

Angular momentum of putty before collision, 

L₁ = mvR = 2 x 10^-2 x 5 x 10^-1 = 10^-2 kg m²/s

from Law of conservation of angular momentum, 

L₁ = L₂

${10}^{-2}=\left(\frac{{\mathrm{MR}}^2}{2}+{\mathrm{mR}}^2\right)\mathrm{\omega }$

${10}^{-2}=\left(\frac{{10}^{-1} \mathrm{x} {\left({10}^{-1}\right)}^2}{2}+2 \mathrm{x} {10}^{-2} \mathrm{x} {\left({10}^{-1}\right)}^2\right)\mathrm{\omega }$

$\mathrm{\omega }=\frac{100}{7}\approx 14.29 \mathrm{rad}/\mathrm{s}$