Question

Two discs are mounted on frictionless bearings on a common shaft. The first disc has rotational inertia $I$ and is spinning with angular velocity $\omega$. The second disc has rotational inertia $2I$ and is spinning in opposite direction with angular velocity $3\omega$, as shown in figure. The two discs are slowly forced towards each other along the shaft until they couple and have a final common angular velocity of

• A. $\frac{5\omega }{3}$
• B. $\frac{7\omega }{3}$
• C. $2\omega$
• D. $1.5\omega$

Answer 1

Answer: (A)

Total initial angular momentum
= Total final angular momentum
$2l[+3\omega ]+l[-\omega ]=[2l+l]{\omega }_c$
$\therefore$ Common angular velocity,
${\omega }_c=\frac{5\omega }{3}$