Question

A wheel is rotating at an angular speed $\omega$ about its axis which is kept vertical. An identical wheel initially at rest is gently dropped into the same axle and the two wheels start rotating with common angular speed. Find this common angular speed.

• A. $\frac{\omega }{4}$
• B. $\frac{\omega }{5}$
• C. $\frac{\omega }{2}$
• D. $\frac{\omega }{7}$

Answer 1

The correct option is C $\frac{\omega }{2}$

$initialangularmomentum=I\omega onaddingwheel,MOIbecome2Ibyconservingangularmomentm2I{\omega }^{\prime }=I\omega \Rightarrow {\omega }^{\prime }=\frac{\omega }{2}\therefore newangularspeedis\frac{\omega }{2}$