Question

A uniform 2.68-kg circular disk of radius 16.1 cm is rotating counter-clockwise about an axis through its center with an initial angular speed of 42.1 radians per second. A second uniform 6.68-kg circular disk of radius 34.6 cm that is not initially rotating is dropped flat onto the first disk so that the axis of rotation of the first disk passes through the center of the second disk.

Find the angular speed of two disks when they'r e moving together

Answer 1

From the conservation of angular momentum:

$$I_1\omega=(I_1+I_2)\omega'$$

$$0.5m_1r_1^2\omega=(0.5m_1r_1^2+0.5m_2r_2^2)\omega'$$

$$\omega'=\frac{(2.68)(0.161)^2(42.1)}{((2.68)(0.161)^2+(6.68)(0.346)^2)}=3.36\frac{rad}{s}$$