Question

(3 points) A disk is spinning freely with angular speed 6.0 rad/s when a second identical disk, initially not spinning, is dropped on it so that their axes coincide. In a short time the two disks are co-rotating. a) Sketch the initial situation and the consequential situation. b) What is the angular speed of the new system? c) If a third such disk is dropped on the first two, find the final angular speed of the system.

Answer 1

Answer:

a) The sketch is attached.

b) The angular speed of the new system is 3 rad/s

c) The angular speed of the new system is 2 rad/s

Explanation:

b) The angular speed of the system is:

$I_{i} w_{i} =I_{f} w_{f}$

Where

Ii = I

If = I + I

wi = 6 rad/s

Replacing:

$I*6=(I+I)w_{f} \\w_{f} =\frac{6I}{2I} =3rad/s$

c) If a third disk is dropped, the angular speed is:

$I*6=(I+I+I)w_{f} \\w_{f} =\frac{6I}{3I} =2rad/s$