Question

A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its center and perpendicular to its plane with an angular velocity $\omega$. Another disc of same thickness and radius but of mass $\frac{1}{8}M$ is placed gently on the first disc co-axially. The angular velocity of the system is now

• A. $\frac{8}{9}\omega$
• B. $\frac{5}{9}\omega$
• C. $\frac{1}{3}\omega$
• D. $\frac{2}{9}\omega$

Answer 1

The correct option is A $\frac{8}{9}\omega$

Moment of inertia of the first disc $I_1=\frac{1}{2}M{R}^2$
Moment of inertia of the second disc $I_2=\frac{1}{2}\times \frac{M}{8}{R}^2=\frac{1}{16}M{R}^2$
Angular velocity of first disc $w_1=w$
Angular velocity of second disc $w_2=0$
Using conservation of angular momentum : $L_f=L_i$
$(\frac{1}{2}M{R}^2+\frac{1}{16}M{R}^2)w_f=\frac{1}{2}M{R}^{2}w+0$
$⟹w_f=\frac{8}{9}w$