Question

A uniform disk, such as a record turntable, turns at 5.0 rev/s around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk. They then both turn around the spindle with their centers superposed. What is the angular velocity in rev/s of the combination?

Answer 1

Answer:

$w=3rev/s$

Explanation:

The motion has two steps so is going to be before and after analysis

Before:

$L=I*w$

$L=\frac{1}{2}*m*R^2*w$

$L=\frac{1}{2}*m*R^2*\pi *f$

After:

$L'=\frac{1}{2}*m*R^2*w+\frac{1}{12}*m*R^2*w$

$m*R^2w'*(\frac{1}{2}+\frac{1}{3})$

$\frac{5}{6}*m*R^2*\pi*f'$

Angular momentum is conserved

$L=L'$

$L=\frac{1}{2}*m*R^2*\pi *f=\frac{5}{6}*m*R^2*2*\pi *f'$

$f'=\frac{6}{10}*5rev/s$

$w=3rev/s$