Question

A disk rotates freely on a vertical axis with an angular velocity of 30 rpm. An identical disk rotates above it in the same direction about the same axis, but without touching the lower disk, at 20 rpm. The upper disk then drops onto the lower disk. After a short time, because of friction, they rotate together. The final angular velocity of the disks is
A. 50 rpm
B. 40 rpm
C. 25 rpm
D. 20 rpm
E. 10 rpm

Answer 1

Answer:

c. 25 rpm

Explanation:

The inertia of both disk is the same so

$I_1=I_2$

$I_1*w_{1i}+I_2*w_{2i}=I_1*w_{1f}+I_2*w_{2f}$

$I*(w_{1i}+w_{2i})=I*(w_{1f}+w_{2f})$

$w_{1f}=w_{2f}=w_f$

$w_{1f}+w_{2f}=2w_f$

$w_f=\frac{w_{1i}+w_{i2}}{2}$

$w_f=\frac{30rpm+20rpm}{2}$

$w_f=\frac{50rpm}{2}$

$w_f=25rpm$