Question

A uniform disk of mass 21 kg, thickness 0.5 m, and radius 0.6 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.8 s. What is the rotational angular momentum of the disk

Answer 1

`29.69 kgm^2/s`

Step-by-step explanation:

So suppose the axis of rotation is perpendicular to the surface of the disk, then the moment of inertia can be calculated as the following:

`I = mr^2/2 = 21 * 0.6^2/2 = 3.78 kgm^2`

We can convert the rotation speed in term of 0.8 seconds per revolution to the angular velocity knowing that each revolution is 2π

`\omega = 2\pi / 0.8 = 7.85 rad/s`

Then the rotational angular momentum of the disk is:

`\omega I = 7.85 * 3.78 = 29.69 kgm^2/s`

In case the axis of rotation is parallel with the surface, the moment of inertia would have a formula of:

`I = m(3r^2 + h^2)/12 = 21*(3*0.6^2 + 0.5^2)/12 = 2.3275 kg m^2`