Question

A disc of moment of inertia $2{\text{kg-m}}^2$ revolving with $8\text{rad/s}$ is placed gently on another disc of moment of inertia $4{\text{kg-m}}^2$ revolving with $4\text{rad/s}$, in the same direction. What is the angular velocity of the composite disc?

• A. $\frac{5}{16}\text{rad/s}$
• B. $\frac{3}{16}\text{rad/s}$
• C. $\frac{16}{3}\text{rad/s}$
• D. $\frac{16}{5}\text{rad/s}$

Answer 1

The correct option is C $\frac{16}{3}\text{rad/s}$

From conservation of angular momentum principle,

$I_1{\omega }_1+I_2{\omega }_2=(I_1+I_2)\omega$

$\Rightarrow 2\times 8+4\times 4=(2+4)\omega$

$\Rightarrow \omega =\frac{16}{3}\text{rad/s}$

Hence, option $\left(C\right)$ is the correct answer.