# A solid disk, spinning counter-clockwise, has a mass of 5 kg and a radius of 16 m. If a point on the edge of the disk is moving at 8 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Mar 16, 2017

The angular momentum is $= 2010.6 k g {m}^{2} {s}^{-} 1$
The angular velocity is $= 3.14 r a {\mathrm{ds}}^{-} 1$

#### Explanation:

The angular velocity is

$\omega = \frac{v}{r}$

where,

$v = 8 m {s}^{- 1}$

$r = 16 m$

So,

$\omega = \frac{8}{16} \cdot 2 \pi = 3.1416 r a {\mathrm{ds}}^{-} 1$

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

For a solid disc, $I = \frac{m {r}^{2}}{2}$

So, $I = 5 \cdot {\left(16\right)}^{2} / 2 = 640 k g {m}^{2}$

$L = 640 \cdot 3.1416 = 2010.6 k g {m}^{2} {s}^{-} 1$