Question

A uniform disk turns at 2.4 rev/s around a frictionless axis. A non rotating rod, of the same mass as the disk and length equal to the disk's diameter is dropped onto the freely spinning disk (see the figure). They then both turn around the axis with their centres superposed. What will be the angular frequency in rev/s of the combination when they start rotating together.

• A. 1.2 rev/s
• B. 2.0 rev/s
• C. 1.44 rev/s
• D. 0.96 rev/s

Answer 1

The correct option is C 1.44 rev/s

Apply conservation of angular momentum:
$I_i{\omega }_i=I_f\omega f$
$\Rightarrow \frac{1}{2}m{R}^2\times 2.4=(\frac{1}{2}m{R}^2+\frac{m(2R{)}^2}{12}){\omega }_f$
$\Rightarrow {\omega }_f=1.44rev/s$