Question

A solid disk, spinning counter-clockwise, has a mass of `5 kg` and a radius of `8 m`. If a point on the edge of the disk is moving at `6 m/s` in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Answer 1

`120\ \text{kgm}^2\text{/s}` & `0.75\ \text{rad /s}`

Explanation:

Mas of solid disk `m=5\ kg`

Radius of solid disk `r=8\ m`

Peripheral speed of disk `v=r\omega=6\ m/s`

The angular velocity `\omega` of the disk

`\omega=v/r=6/8=0.75\ \text{rad/s}`

Mass moment of inertia (`I`) of solid disk

`I=1/2mr^2=1/2(5)(8)^2=160\ kgm^2`

Now, the angular momentum `J` of the solid disk is given as

`J=I\omega`

`=160\cdot 0.75`

`=120\ \text{kgm}^2\text{/s}`