Question

A thin circlar ring of mass M and radius r is rotating about its axis with a constant angular velocity w. Four objects perpendicular diameters of the ring. The angular velocity of the ring will be:

• A. $\frac{M\omega}{M + 4m}$
• B. $\frac{(M + 4m)\omega}{M}$
• C. $\frac{(M - 4m)\omega}{M + 4m}$
• D. $\frac{M\omega}{4M}$

Answer 1

Answer: (A)

$\frac{M\omega}{M + 4m}$

Answer 2

Initial angular momentum of ring

L=Iw = Mr2w

Final angular momentum of ring and four particles system L=(Mr2 + 4mr2)w

As ther e is no torque on the system therefore angular momentum remains constant

$Mr^{2}\omega = (Mr^{2} + 4mr^{2})\omega'$ ⇒$\omega' = \frac{M\omega}{M + 4m}$