# A solid disk, spinning counter-clockwise, has a mass of 18 kg and a radius of 4 m. If a point on the edge of the disk is moving at 7/3 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Dec 8, 2016

The angular momentum is $= 527.8 k g {m}^{2} {s}^{- 1}$
The angular velocity is $= 3.7 r a {\mathrm{ds}}^{- 1}$

#### Explanation:

The angular velocity is

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

$v = \frac{7}{3} m {s}^{- 1}$

$r = 4 m$

$\omega = \frac{7}{3} \cdot \frac{1}{4} \cdot 2 \pi = \frac{7 \pi}{6} r a {\mathrm{ds}}^{- 1}$

The angular momentum is $L = I \omega$

Where $I$ is the moment of inertia

For a solid disc $I = m {r}^{2} / 2 = 18 \cdot {4}^{2} / 2 = 144 k g {m}^{2}$

The angular momsntum is
$L = I \omega = 144 \cdot 7 \frac{\pi}{6} = 168 \pi k g {m}^{2} {s}^{- 1}$