Answer to Question #102692 in Mechanics | Relativity for sakshi

Question

A horizontal disk of rotational inertia 7.5 kg m2 with respect to its axis of symmetry is spinning counterclockwise in its plane, about its axis of symmetry at 22.5 revolutions per second. A second disk, of rotational inertia 13.0 kg m2 with respect to its axis of symmetry, spinning clockwise about the same axis (which is also its axis of symmetry) at 20.0 revolutions per second, is dropped on top of the first disk. The two disks stick together and rotate as one about their common axis of symmetry. Determine the new angular velocity of the system.

Answer 1

$$I_1\omega_1+I_2\omega_2=I\omega$$

$$(13)(20)-(7.5)(22.5)=(13+7.5)\omega$$

$$\omega=4.45\frac{rev}{s}$$

Direction: clockwise.