# A solid disk, spinning counter-clockwise, has a mass of 6 kg and a radius of 8/5 m. If a point on the edge of the disk is moving at 7/4 m/s in the direction perpendicular to the disk's radius, what is the disk's angular momentum and velocity?

Jan 18, 2018

The angular momentum is $= 8.4 k g {m}^{2} {s}^{-} 1$ and the angular velocity is $= 1.094 r a {\mathrm{ds}}^{-} 1$

#### Explanation:

The angular velocity is

$\omega = \frac{\Delta \theta}{\Delta t}$

$v = r \cdot \left(\frac{\Delta \theta}{\Delta t}\right) = r \omega$

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

where,

$v = \frac{7}{4} m {s}^{- 1}$

$r = \frac{8}{5} m$

So,

The angular velocity is

$\omega = \frac{\frac{7}{4}}{\frac{8}{5}} = \frac{35}{32} = 1.094 r a {\mathrm{ds}}^{-} 1$

The angular momentum is $L = I \omega$

where $I$ is the moment of inertia

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

The mass is $m = 6 k g$

So, $I = 6 \cdot {\left(\frac{8}{5}\right)}^{2} / 2 = \frac{192}{25} k g {m}^{2}$

The angular momentum is

$L = \frac{192}{25} \cdot 1.094 = 8.4 k g {m}^{2} {s}^{-} 1$