# A solid disk, spinning counter-clockwise, has a mass of 12 kg and a radius of 6 m. If a point on the edge of the disk is moving at 15 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Dec 25, 2016

The angular momentum is $= 720 \pi = 2262 k g {m}^{2} {s}^{- 1}$
The angular velocity is $= \frac{10 \pi}{3} = 10.5 r a {\mathrm{ds}}^{- 1}$

#### Explanation:

The angular velocity,

$\omega = \frac{v}{r} = \frac{15}{6} H z = \frac{5}{3} \cdot 2 \pi r a {\mathrm{ds}}^{- 1} = \frac{10 \pi}{3} r a {\mathrm{ds}}^{- 1}$

The angular momentum is

$L = I \omega$

Where $I$ is the moment of inertia

For a solid disc, $I = \frac{1}{2} \cdot m \cdot {r}^{2}$

$I = \frac{1}{2} \cdot 12 \cdot {6}^{2} = 216 k g {m}^{2}$

The angular momentum is

$L = 216 \cdot \frac{10 \pi}{3} = \left(720 \pi\right) k g {m}^{2} {s}^{- 1}$