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

Answer 1

The final angular velocity of the disks is 25 rpm.

Step-by-step explanation:

Given that,

Angular velocity
`\omega_(1)= 30\ rpm`

Angular velocity
`\omega_(2)=20\ rpm`

We need to calculate the angular velocity

Using formula of angular momentum

`L=I\omega`

Before the drop, the angular momentum of the system

`L_(s)=I\omega_(1)+I\omega_(2)`

`L_(s)=I(\omega_(1)+\omega_(2))`

`L_(s)=I(30+20)`

`L_(s)=I(50\ rpm)`....(I)

When both disk rotates together then the total moment of inertia is twice the inertia of one disk

`L_(s)=2I\omega`

From equation (I)

`2I\omega=I*50`

`\omega=25\ rpm`

Hence, The final angular velocity of the disks is 25 rpm.