Question

Two wheels $A$ and $B$ are mounted on the same axle. Moment of inertia of $A$ is $6 \, kg \, m^{2}$ and it is rotating at $600 \, rpm$ when $B$ is at rest. What is the moment of inertia of $B$ , if their combined speed is $400 \, rpm$ ?

• A. $8 \, kg \, m^{2}$
• B. $4 \, kg \, m^{2}$
• C. $3 \, kg \, m^{2}$
• D. $5 \, kg \, m^{2}$

Answer 1

Answer: (C)

Applying the principle of conservation of angular momentum,
$\left(I_{1} + I_{2}\right)\omega =I_{1}\left(\omega \right)_{1}+I_{2}\left(\omega \right)_{2}$
$\left(6 + I_{2}\right)\frac{400}{60}\times 2\pi =6\times \frac{600}{60}\times 2\pi +I_{2}\times 0$
Which gives, $I_{2}=3 \, kg \, m^{2}$